Demographic modeling of Hawaiian silverswords, and its implications for conservation

Item Type text; Dissertation-Reproduction (electronic)

Authors Forsyth, Stacey Ann

Publisher The University of Arizona.

Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.

Download date 26/09/2021 03:56:21

Link to Item http://hdl.handle.net/10150/280173 INFORMATION TO USERS

This manuscript has t)een reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.

The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overiaps.

ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600

DEMOGRAPHIC MODELING OF HAWAIL\N SILVERSWORDS,

AND ITS IMPLICATIONS FOR CONSERVATION

by

Stacey Ann Forsyth

Copyright £ Stacey Ann Forsyth 2002

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF ECOLOGY AND EVOLUTIONARY BIOLOGY

In Partial Fulfillment of the Requirements For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2002 UMI Number; 3073218

Copyright 2002 by Forsyth, Stacey Ann

All rights reserved.

UMI

UMI Microform 3073218 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

ProQuest Information and Leaming Company 300 North Zeeb Road P.O. Box 1346 Ann Artwr, Ml 48106-1346 THE raiVERSITY OF ARIZONA iS- GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have Stacey Ann Forsyth read the dissertation prepared by entitled DEMOGRAPHIC MODELING OF HAWAIIAN SILVERSWORDS, AND ITS IMPLICATIONS FOR CONSERVATION.

and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of PhilosODhy

If- ^-OTs Kobert KODTcnaux Date

/Judith Bronstein Date

' iT-/^ ,Lucinda McDade Date

Martha hunter Date

Date

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

ij' Dissertation Director Robert ROblchaux Datle ' STATEMENT BY AUTHOR

This dissertation has been submitted in partial tlilfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission. pro\ ided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder.

SIGNED: 4

ACKNOWLEDGEMENTS

This dissertation would not have been possible without the ad\ ice. help, and support ot'manv indi\ iduals. 1 am especially appreciative of my committee members, all of whom provided valuable suggestions. ad\ ice. and encouragement. Special thanks to my ad\ isor. Dr. Robert Robichaux. whose passion for Hawaiian sih erswords is contagious! Rob's suggestions and attention to detail greatly improved this dissertation, and his incredible turnaround time as editor ensured that it was completed on time. Dr. Judie Bronstein, my unofficial co-advisor, provided valuable advice from the ver\' start of this project and in addition, generously provided a temporary home for me in her lab. I thank Drs. Lucinda .McDade and Molly Hunter for their comments on earlier drafts of these manuscripts, which greatl\- improv ed the quality of this dissertation. In addition to m> committee. Dr. Regis Ferriere provided much needed assistance in the de\ elopment and preliminar\ analysis of the siK ersword matrix model described in this stud> . I am also extremely grateful to many different people living and working in Hawaii, without whom this project would not have been possible. Much thanks to Dr. Lloyd Loope. of the L'SGS-BRD at Haleakala National Park, for his continual interest and support in this project. I am ver\- much indebted to him for his assistance with logistics and tlinding. as well as for his contribution of a long-term demographic data set that became a primarv' focus of this dissertation. Thanks also to Ron N'agata. for assistance with permits: Ellen Vangelder. fellow dog- and book-lover, for help with housing matters, as well as many excellent book recommendations; Forest and Kim Starr, for their boundless enthusiasm about all things botanical, and their endless dedication to the sih ersword monitoring project: and .A.rt Medeiros. natural historian extraordinaire, for his obser\ ations and insights. Thanks to m\- fellow graduate students - past and present - in the L'A Dept. of Ecology and E\ olutionar>' Biology, who ensured that my time at the Univ ersity of •Arizona was a stimulating and enjoyable experience. Special thanks to Jen Weeks. Cath\ Collins. Betsy .Arnold. Eileen Hebets. Margaret Evans. Asher Cutter. Dan Hahn. and Jessie Cable. 1 would also like to thank Clare Ellsworth and Jesus Garcia, two amazing undergraduates, who w ere a tremendous help in the field and lab. 1 am \ er>- gratefial for the endless support of family and friends: Fred and Geri ForsMh. Rachel Fors\th-Tuerck. Beck Freed. Michele Grzenda. Brandon Protas. Ste\ e •Anderson. Debbie Pearson. Jill .A\ er\-. .^nne Leyden. Janet ^'ang. Jeff Steinmetz and Kate Howe. Special thanks to my running gang - Kelly Goldsmith. Sue Clark. Doreen Castillo, and Debbie Nolen - for many tun fimes on the trail... This dissertation was primarily funded by a Graduate Research Fellowship from the National Science Foundation, and by Clairol. Inc.. through a grant from the National Parks Conserv ation .Association. .•Additional funding was provided by the .Arizona Flinn Foundation: the Department of Ecology and Ev olutionary Biology at The University of •Arizona: and the Research Training Grant in the .Analysis of Biological Diversification at The Univ ersity of •Arizona. I also received a year of financial support from the National Science Foundation through the GK-12 (CATTS) program at The University of •Arizona. DEDICATION

Dedicated with Aloha to all those tirelessK' working to preser\ e Hawaii's beautiful places.

^'our passion and dedication are inspiring. 6

TABLE OF CONTENTS

ABSTRACT 7

CHAPTER 1: INTRODUCTION 9

Population viahilin- analysis (Pl'A)

C 'onscrvalion applications 11

This study 12

Explanation o f dissertation format 13

CHAPTER 2: PRESENT STUDY 15

REFERENCES 19

APPENDIX A: DENSITY-DEPENDENT SEED SET IN THE HALEAK.-\LA SILX ERSWORD (ARGYROXIFHIUMSASDWICESSE SSP. SL-iCROCEPHALUM): DEMONSTRATION OF AN ALLEE EFFECT 22

APPENDIX B: MEASURING PLANT REPRODUCTION FOR MATRIX MODEL ANALYSES 60

APPENDIX C: TEMPORAL AND SPATIAL VARIATION IN THE DEMOGRAPHY OF A THREATENED HAWAIIAN PLANT 1U3

APPENDIX D: DEMOGRAPHIC MODELING OF HAWAIIAN SILVERSWORDS (ASTER.ACEAE): IMPLICATIONS FOR CONSERVATION AND MANAGEMENT 215 ABSTR.\CT

Population \ iability analyses based on matrix population models pro\ ide

important information for species management. These analyses enable biologists to

predict future population size and structure, assess extinction risk, and identify- the stages

and transitions in a species" life history that ha\ e the largest etfects on population growth

rate (/.). It is also possible, using these analyses, to weigh the relati\ e effectiveness of

different management strategies.

In this study. 1 constructed a matrix population model for a threatened Hawaiian

plant species, the Haleakala sihersword (Argy roxiphiiim sandwicense ssp.

macrocephalum). in order to assess the viability of this population under different

disturbance and management regimes. 0\ er th e years. I assessed annual variation in

seed set and quantified reproducti\ e \ ital rates for use in a matrix model. These data

v\ ere combined with long-term demographic data in order to construct a stage-based

matrix model for the Haleakala sih ersword. Using this model. 1 examined temporal and spatial \ ariation in silversword demography. 1 also used the model to exaluate management strategies for the Haleakala sih ersword and the related subspecies, the endangered .Mauna Kea sih ersword (Argyroxiphiiim sandwicense ssp. sandw icense).

L sing deterministic and stochastic models. I compared the relativ e impacts of different threats on sih ersword persistence, and weighed the relativ e effectiv eness of different management options. s

The Haleakala silversword was self-incompatible, and percent seed set was positi\ ely correlated with annual flowering plant abundance. Individuals were pollen- limited only in low tlowering years, suggesting a pollinator-mediated .-Mlee effect in this species. Seeds remained \ iable in the field for multiple years, suggesting that a seed stage should be incorporated into the matrix model. Reproducti\e output (e.g.. number of capitula and capitulum size) was strongly correlated with rosette diameter, allowing for size-based estimates of reproduction.

Vital rates and population growih rates \ aried o\ er time and space. In all \ears and plots, adult sur\ i\ al had the greatest impact on /.. Thus, factors influencing adult sur\ i\ al. such as browsing and outplanting. had larger effects on /. than did factors influencing seed set. Management strategies aimed at increasing germination rates or adult sur\ i\ al rates will be most effectix e in ensuring the persistence of silversword populations. 9

CHAPTER 1

INTRODLCTION

The successful management of rare and endangered species requires know ledge of species' population dynamics and the factors influencing their persistence.

Conser\ ation biologists also require tools and techniques to anaK'ze this basic ecological information, in order to predict the fixture of populations and species, and to inform and guide management actions (Menges 1986). In the conserv ation of rare and endangered species, population \ iability analyses (PVAs) based on matri.x population models are important tools that provide useful and relev ant information for species management

(Schemske et al. 1994. Caswell 2001).

Population viability analysis (PVA)

Population \ iability analysis integrates field-collected demographic data with modeling techniques, in order to describe population dynamics quantitati\ ely. One common approach to PV.A. in\ ol\ es the use of matrix population models, which di\ ide a population into age- or stage-based classes and describe how the number and distribution of indiv iduals change over time. Typically, the goals of PVA are to predict future population size and structure, assess extinction risk, and identify the life history stages and transitions that have the greatest effects on population growth rate (Boyce 1992.

Schemske et al. 1994. Caswell 2001. Beissinger 2002). .A.lthough these techniques have the potential to accurately assess population viability (Brook et al. 2000). the precision of 10 such analyses depends on high quality data collected o\ er multiple years (Beissinger

:U02).

Despite the importance of long-term demographic data sets, empirical demographic studies are frequently limited by the number of years and. or populations they include. The average duration of a demographic study is four years. approximateK' the length of a grant or dissertation project (Menges 2000). Such short-term datasets. how e\ er. may fail to \ield accurate results, if they do not encompass the full range of en\ ironmental \ ariation e.vperienced by a population. This issue is particularly true for long-li\ ed species (Brault and Caswell 1993). for which short-term datasets may not be long enough to include a fijll generation. Similarly, studies that do not include multiple sites ma\ fail to encompass the existing spatial variation in demographic processes.

There is some e\ idence that demographic parameters vary across both time and space

(Kalisz and McPeek 1992. Horx itz and Schemske 1995). and this variation may ha\ e important implications for population stability and persistence (Vavrek et al. 1997).

Gi\ en the potential effects of temporal and spatial \ ariation in demographic \ ital rates, incorporating \ ariation in demographic models may be critical (Schemske et al. 1994).

Population \lability analyses may also be limited by the amount of information on a species' natural histor\'. Detailed aspects of a species" biology, including density- dependence. interspecific interactions, and dispersal patterns, are often excluded from

P\'.-\s due to limited information. Frequently, data for at least some part of a species' life cycle are limited. For example, in plants, reproduction is often difficult to quantify and plant P\'.-\s frequently exclude life history stages, such as seeds, that are difficult to monitor o\ er time. In this study. I integrate detailed information on plant reproducti\ e

biology with a long-term demographic data set. in order to conduct a P\'A for a

threatened, long-lived, monocarpic plant species.

Conservation applications

One important application of PVA is the identification of the stages in a species"

life history- that ha\ e the largest relative effects on the population growth rate (/.). This

information, obtained through sensitivity, elasticity, and perturbation analyses, is

essential for determining which life historv' stages will be most effecti\e to target for

management. Using these analyses, it is also possible to predict the impacts on /. of

different disturbance or management regimes; such analyses enable conser\ation

biologists to assess the impacts of different threats, as well as weigh the relati\ e

effectiv eness of different management strategies.

P\'.-\.s based on matri.x population models have been used to inform management

decisions for a variety of taxa. including loggerhead sea turtles (Grouse et al. 1987.

Crowderetal. 1994). desert tortoises (Doak et al. 1994), cheetahs (Crooks et al. 1998).

and \ arious plant species (Oostermeijer et al. 1996. Ratsirarson et al. 1996, Gross et al.

1998). In several of these studies, demographic analyses showed that current

management practices were targeting stages in the species" life history that had verv' little

impact on population growth rate, suggesting that management efforts would be much

more effectiv e if targeted elsewhere in the species" life cycle (e.g., Crouse et al. 1987,

Crowderet al. 1994. Doak et al. 1994. Crooks et al. 1998). Other studies have used i: matrix modeling of demographic data to determine viable levels of har\ esting

(Ratsirarson el al. 1996). compare reserve design strategies (.Andersen and Mahato 1995). e\aluate the effectiveness of predator control techniques (Harding et al. 2001). and determine the most effective frequencies of controlled bums (Burgman and Lamont 1992.

Gross et al. 199S. Caswell and Kaye 2001). Thus, in addition to predicting future population size and assessing extinction risk. PV.As can make valuable contributions to species conser\ ation. by informing and guiding management decisions.

This study

In my dissertation research. I integrate field observations and experiments with modeling techniques in order to better understand the factors influencing the persistence of a threatened Hawaiian plant species. Specifically. I examine the reproducti\ e biology and demography of the Haleakala silversword (Argyroxiphium sandwicense ssp. macrocephalum: .Asteraceae). Endemic to Haleakala volcano on the Island of Maui, the

Haleakala silversword suffered severe declines in the late 19''' and early 20"^ centuries. primariK' due to browsing by alien ungulates, as well as human collection and \ andalism.

Although the sih ersword population increased in size in the late 1900s. following protection from ungulates and humans, this species may currently be threatened by alien social insects that prey on nati\ e pollinators. In this study. I construct a matrix population model based on silversword reproductive biology and demography, and analv'ze the model in order to provide guidelines for the future conser%-ation and 13 management of this species. In the process. I address specific issues related to the construction and analysis of matrix population models.

Explanation of dissertation format

The chapters in this dissertation are included as four appendices. .A.ppendi.\ describes the reproducti\ e biolog\' of the Haleakala silversword. with an emphasis on breeding system, pollen limitation, and temporal variation in reproductiv e success.

Through a combination of observ ations and pollination e.xperiments. this paper demonstrates the presence of a pollinator-mediated Allee effect in the Haleakala sih ersv\ ord. This paper is single-authored and will be submitted to Oecologia for publication.

In .Appendix B. 1 continue my research on silversword reproductiv e biology, with the goal of quantifving reproduction for use in a matrix population model. I examine seed dispersal and longevity, to determine if a separate seed stage should be incorporated into a silversword matrix model. I also quantify relationships between rosette size and different components of reproductive output (e.g.. capitulescence length, number of capitula. capitulum size), in order to estimate the reproductive output of two size-based reproductiv e stage classes. This paper is single-authored and will be submitted to

Journal of Ecology for publication.

Appendix C describes the construction and analysis of a matrix population model for the Haleakala sih ersvvord. 1 use the results from Appendices .A and B. in conjunction with long-term demographic data collected by researchers at Haleakala National Park. 14

Maui. Hawaii, to perform a demographic analysis of the Haleakala silversword. The

primar\- goal of this study was to examine temporal and spatial variation in demographic

\ ital rates, population growth rates, and sensiti\it\' and elasticity parameters. This paper

was co-written bv Dr. Lloyd L. Loope. Research Scientist with the U.S. Geological

Sur\ e\'. Biological Resources Dix ision. and will be submitted to Ecological Monographs

for publication. Dr. Loope provided the demographic data set used in this study and

made editorial comments: 1 consolidated the data, constructed the matrix model,

performed ail demographic analyses, made the corresponding tables and figures, and

wrote the paper.

In .Appendix D. 1 use the matrix model de\ eloped in Appendices B and C to

address conservation and management questions for the threatened Haleakala sil\ ersword

and the critically endangered .Mauna Kea sihersword (Argyroxiphium sandwicense ssp.

SLindwicensc). Specifically. I use deterministic and stochastic models to compare the

relative impacts of different threats on sihersword persistence, as well as to weigh the

relati\ e effectiv eness of different management options. This paper was co-written by Dr.

Robert H. Robichaux. .A.ssociate Professor in the Department of Ecology and

E\ olutionar\ Biolog\' at The L'ni\ ersity of .Arizona, and will be submitted to

Consen ation Biology for publication. Dr. Robichaux contributed data from the Mauna

Kea sih ersword reintroduction program and provided valuable comments on earlier drafts of this paper. 1 constructed the matrix models for the two silversword subspecies, performed all demographic analyses, made the corresponding tables and figures, and wrote the paper. 15

CHAPTER 2

PRESENT STUDY

The methods, results, and conclusions of this study are presented in the papers appended to this dissertation. The following is a summarv" of the major findings in these papers.

In Appendi.x A. I e.xamined the reproductiv e biology of the Haleakala siK ersword

(Argy roxiphium sandwicense ssp. macrocephalum: Asteraceae). a threatened Hawaiian plant species. Specifically. I examined temporal variation in plant reproductive success, in order to determine if plants flowering in low flowering years exhibited lower percent seed set than plants flowering in high flowering years. I collected mature achenes (fruits) from flowering silverswords over a five-year period (1997 - 2001) to quantify seed set. and conducted tw o pollination experiments over multiple years in order to measure pollen limitation and self-incompatibility. The number of flowering plants varied greatly among

\ears. with two high flowering years (1997 and 2001) and three low flowering years

(1998. 1999. and 2000) in the five-year study period. Percent seed set was significantly correlated with the abundance of flowering plants, with silverswords that flowered in high flowering years exhibiting higher percent seed set. Plants flowering as\Tichronousl\- relativ e to other plants in the population (in 1998 and 1999) were pollen-limited, whereas plants flowering synchronously (in 1997) were not. The Haleakala silversword was highly self-incompatible, with bagged capitula exhibiting significanfly lower percent seed set than open-pollinated capitula. Combined, the results of this study suggested a 16 pollinator-mediated Allee effect in the Haleakala sih ersword. with plants that tlowered in lou flowering years exhibiting greatly reduced reproductive success.

My studies on the reproductive biology of the Haleakala silversword continue in

Appendix B. In this paper, my specific goal was to quantify reproductive vital rates for use in a matrix population model. The relevance of matrix model analyses depends on accurate estimates of demographic vital rates, but in plants, reproduction is frequently difficult to quantify due to certain aspects of plant life histories, such as seed dispersal and seed dormancy. In Appendix B. I measured seed dispersal and germination rates, to determine if a seed stage should be incorporated into a silversword matrix model, and used allometric relationships to estimate plant reproduction as a function of plant size.

Silversword seeds as old as four years germinated, suggesting that silversword seeds can remain viable in the field for multiple years, and consequently, that a seed stage should be incorporated into a demographic model. Capitulescence length, number of capitula. and capitulum size were all strongly positively correlated with silversword rosette diameter, allowing for size-based estimates of reproduction. Based on these results. I modified the silversword matrix model in order to incorporate a seed stage, and I used demonstrated allometric relationships to quantify' reproductive output of two size-based reproductive stage classes.

In .Appendix C. I used a long-term demographic dataset. in conjunction with results from .Appendices A and B. to develop a stage-based matrix population model for the Haleakala silversword. Using 20 years (1982 - 2001) of data from eleven permanent plots located on five cinder cones. I examined temporal and spatial variation in 17 demographic vital rates, population grouth rates, and sensitivit\' and elasticity parameters. The sih ersword matrix model included seven life histor>- stage classes - seed, seedling. ju\ enile. small adult, large adult, small reproductive plant, and large reproducti\ e plant - and 16 possible transitions among these different stage classes. In the 20-year period, the population in the plots declined by nearly 50° o. Transitions of grov\ th. regression, and flowering were highly \ ariable o\ er time and space, whereas transitions of stasis were not. Population growth rates (/.) varied o\ er time and space, ranging trom 0.88 (1998 - 1999) to 1.07 (1996 - 1997). and from 0.93 in Plot 3 to 1.04 in

Plot 5. The obser\ ed and predicted stable stage distributions were similar, suggesting that the asvTnptotic analyses conducted in this study were rele\ ant to the current dynamics of this species.

Sensiti\ it\' analyses demonstrated that population grouth rate v\ as most sensitix e to seed germination and to growth of small adults and juveniles, as well as to large adult sur\ i\ al and reproduction. The highest elasticities were associated with stasis of small adults, large adults, and juveniles. The qualitati\ e pattern in sensitivities and elasticities was fairly consistent o\er time and space: adult plant growth and sunival had the greatest relati\ e impacts on population grovuh rate in all years and plots. Parameter sensitivity- and elasticity v\ere both negatively correlated with \'ital rate \ ariability. such that the most \ ariable transitions had the smallest impact on population growth rate. Twelve pairs of transitions were significantly correlated, suggesting that different stage classes of the sih ersword life cycle respond similarly to environmental \ ariation. IS

In Appendix D. I used the matrix population model developed in Appendices B and C to address questions related to the conserv ation and management of the threatened

Haleakala sil\ ersv\ ord. 1 also extrapolated from the model to address management questions pertaining to the critically endangered Mauna Kea silversword (Arg\To.\iphiiim sandwicense ssp. sandwicense). a related subspecies whose life history is nearly identical to that of the Haleakala silversword. I conducted population viability analyses (P\'As) in order to assess the relati\ e impacts of different threats, including alien ungulates (that brov\ se on the plants) and alien social insects (that prey on nati\e pollinators and ma\ therefore reduce seed set levels), on the growth rate of both sil\ersv\ord populations. 1 also compared the relati\ e effecti\ eness of different management strategies on Mauna

Kea. including managed breeding (in which seed set levels are increased through pollen augmentation), greenhouse rearing (in which seed germination and early seedling sur\ i\ al rates are increased), and outplanting (in which juvenile and adult surv i\ al and growth rates are increased). Elasticity and perturbation analyses demonstrated that population growth rate was most sensiti\'e to changes in adult survival rates. Using a series of deterministic and stochastic models. 1 found that factors influencing surv ival rates, such as browsing or outplanting. had much larger effects on /. than did factors influencing seed set. such as social insects or managed breeding. Greenhouse rearing. v\ hich raises germination and seedling sur\ival rates, had \ery large impacts on /.. Our results suggested that management strategies aimed at increasing either germination rates or adult sur\ i\ al rates will be most effective in ensuring the persistence and growth of both silversword populations. 19

REFERENCES

Andersen. M.C. and D. Mahato. 1995. Demographic models and reserv e designs for the California spotted owl. Ecological Applications 5:639-647.

Beissinger. S.R. 2002. Population viability analysis: past, present, future. Pages 5-17 in S.R. Beissinger and D.R. .McCullough. eds. Population viability analysis. The University of Chicago Press. Chicago.

Boyce. .VI.S. 1992. Population viability analysis. .Annual Review of Ecology and Systematics 23:481 -506.

Brault. S. and H. Caswell. 1993. Pod-specific demography of killer whales {Orciniis orca). Ecology 74:1444-1454.

Brook. B.W.. J.J. O'Grady. .A.P. Chapman. M..A.. Burgman. H.R. .A.kcakaya. and R. Frankham. 2000. Predicti\ e accuracy of population \'iability analysis in conserv ation biology. Nature 404:385-387.

Burgman. VI..A. and B.B. Lamont. 1992. stochastic model for the viability of Banksia cuneata populations: environmental, demographic and genetic effects. Journal of .Applied Ecology 29:719-727.

Caswell. H. 2001. .Matri.x population models, second edition. Sinauer Associates. Sunderland. .Massachusetts. US.A.

Casw ell. H. and T.N. K.aye. 2001. Stochastic demography and conserv ation of an endangered perennial plant {Lomatiiim bradshawii) in a dynamic fire regime. .A.dvances in Ecological Research 32:1-51. :o

Crooks. K.R.. M.A. Sanjayan. and D.F. Doak. 1998. New insights on cheetah conser\ation through demographic modeling. Consenation Biology 12:889-895.

Crouse. D.T.. L.B. Crowder. and H. Caswell. 1987. stage based population model for loggerhead sea turtles and implications for conserv ation. Ecology 68:1412-1423.

Crowder. L.B.. D.T. Crouse. S.S. Heppell. and T.H. Martin. 1994. Predicting the impact of turtle e.\cluder de\ ices on loggerhead sea turtle populations. Ecological .Applications 4:437-445.

Doak. D.. P. K.arei\ a. and B. Klepetka. 1994. .Modeling population viability for the desert tortoise in the western Moja\ e desert. Ecological .Applications 4:446-460.

Gross. K... J.R. Lockwood III. C.C. Frost, and W.F. Morris. 1998. .Modeling controlled burning and trampling reduction for conser\ ation of Hiidsonia moniana. Conser\ ation Biology 12:1291 -1301.

Harding. E.K... D.F. Doak. and J.D. .Albertson. 2001. E\'aluating the effectiveness of predator control; the non-native red fo.\ as a case study. Conservation Biology 15:1114-1122.

Hor\ itz. C.C. and D.W. Schemske. 1995. Spatiotemporal variation in demographic transitions of a tropical understory herb: projection of a matrix analysis. Ecological .VIonographs 65:155-192.

Kalisz. S. and M..A. McPeek. 1992. Demography of an age-structured annual: resampled projections matrices, elasticity analyses and seed bank effects. Ecology 73:1082- 1093. 21

Menges. E.S. 1986. Predicting the ftiture of rare plant populations: demographic monitoring and modeling. Natural .\reas Journal 6:13-25.

Menges. E.S. 2000. Population viability analyses in plants: challenges and opportunities. Trends in Ecology and Evolution 15:51-56.

Oostermeijer. J.G.B.. .VI.L. Brugman. E.R. de Boer, and H.C..VI. den Nijs. 1996. Temporal and spatial v ariation in the demography ot'Gentiana pneumonanthe. a rare perennial herb. Journal of Ecology 84:153-166.

Ratsirarson. J. J..\. Silander. Jr.. and .A..F. Richard. 1996. Conservation and management of a threatened Madagascar palm species. S'eociypsis decatyi. Jumelle. Conserv ation Biology 10:40-52.

Schemske. D.W.. B.C. Husband. M.H. Ruckelshaus. C. Goodvvillie. 1..M. Parker, and J.G. Bishop. 1994. Evaluating approaches to the conservation of rare and endangered plants. Ecology 75:584-606.

\'a\rek. M.C.. J.B. McGraw. and H.S. Yang. 1997. Within-population variation in demography of Taraxacum officinale', season- and size-dependent survival, growth, and reproduction. Journal of Ecology 85:277-287. APPENDIX A:

DENSITY-DEPENDENT SEED SET IN THE HALEAIv.\LA SIL\ ERSWORD

(ARGYROXIPHIL MSASDWICESSE SSP. MACROCEPHALL Xf):

DEMONSTR.\TION OF AN ALLEE EFFECT DENSm'-DEPENDENT SEED SET [N THE HALEAK.^LA SILN'ERSWORD

(ARGYRO.UPHIUM SANDIVICEXSE SSP. MACROCEPHALL'Xf):

DEMONSTR.\TION OF AN ALLEE EFFECT

StaccN" A. Forsyth

Department of Ecology and Evolutionary' Biology

University of Arizona. Tucson. AZ 85721

email; forsyth(au.arizona.edu

Key words; Allee effect, monocarpy. pollen limitation, self-incompatibility, synchronous flowering 24

Abstract. Plant species ma\- be subject to .Mlee effects if individuals e.xperience a reduction in pollination services when populations are small or sparse. 1 examined temporal \ ariation in the reproductive success of the Haleakala silversword

(Argy roxiphiiim sandwicense ssp. macroccphaliim). a monocarpic species. o\er ti\e years, to determine if plants flowering out of svnchrony with most of the population (i.e.. in lov\ tlov\ ering years) e.xhibited lower percent seed set than sxnchronously-tlovvering plants (i.e.. those tlowering in high flowering years). Through two pollination experiments conducted over multiple years. 1 also measured pollen limitation (1997-

1999) and self-incompatibility (199S and 1999) in this species. The number of tlowering plants \ aried greatly among years, as did reproducti\ e success. Percent seed set was significantK correlated with the number of plants tlowering in a given year, such that plants flowering in high tlowering years (1997 and 2001) exhibited significantly higher percent seed set than did plants flowering in low tlowering years (1998-2000). In the three-year pollen limitation study, plants tlowering asynchronously (in 1998 and 1999) v\ere pollen-limited, whereas plants flowering s\Tichronously (in 1997) were not. This species is stronglv self-incompatible. Results of this study demonstrate that the Haleakala sih ersword experiences reduced reproductive success in low tlowering years, and suggest that this .A.llee effect is pollinator-mediated. Allee effects in plants are an understudied yet potentially important force with implications for the long-term population dynamics and conserv ation of rare species. 25

introduction

Theoretical and empirical work in conserv ation biology suggests that small

populations are more likely to go extinct than are larger populations, in part due to chance fluctuations in population size (Shaffer 1981. Gilpin and Soule 1986). Small populations ma\- also suffer additional disadvantages due to .A.llee effects, in which indiv iduals experience reduced survival and or fertility at low population sizes (.A.llee 1931. 1938).

In species exhibiting Allee effects, individual fimess is reduced as the population size decreases, with extinction becoming much more likely as the population declines. In some species. .Allee effects are defined by a critical threshold population size, such that if the population falls below this point, extinction is almost certain (Groom 1998). .-Mlee effects mav' be due to a variety of genetic, demographic, and or ecological factors, including increased levels of inbreeding depression or genetic drift, skewed sex ratios, reduced availability of mates, and decreased hunting success with smaller pack size

(.Allee 1938, Courchamp et al. 1999. Stephens et al. 1999. Courchamp and .MacDonald

2001). .Although the role of .Allee effects in the ecology and conservation of animals has received much consideration (Kuussaari et al. 1998. Courchamp et al. 1999. Courchamp and MacDonald 2001). their importance in plants is poorly documented and requires further study (Lamont et al. 1993. Hackney and McGraw 2001). Such studies are particularly important for rare plants, for which the evaluation of .Allee effects and the determination of critical thresholds should be an essential component of conservation efforts (Groom 1998). 26

In animal species, reproductive success may decline in small populations because individuals in these populations are mate-limited (Allee 1931. 1938. Kuussaari et al.

1998. Courchamp et al. 1999). Similar effects can occur in small or isolated plant populations, particularly in species that depend on animal vectors for pollination (Groom

1998). Plant abundance and. or density can potentially impact plant-pollinator interactions, and therefore plant reproducti\ e success, by affecting both the quantity and quality of pollination services received (Kunin 1993. Lamont et al. 1993. Groom 1998.

Hackney and McGravv 2001). Small and; or isolated plant populations may be less apparent or attractive to pollinators, resulting in a lower number of pollinator visits to plants in these populations (Schemske 1980. Jennersten 1988). Lower visitation rates ma\ lead to insufficient pollen transfer, and therefore to decreased seed set for plants located in these areas. In cases where pollinator \ isitation is not affected by population size or density, plants in small populations may still suffer reduced seed set if the effecti\ eness of pollination, due to pollen quality, declines (Kunin 1993. Lamont et al.

1993. Wolf and Harrison 2001). This may occur through the deposition of foreign rather than conspecific pollen, or through the transfer of incompatible pollen, if a self- incompatibilit\- mechanism is present and self or genetically related pollen is deposited

(Kunin 1993. Feinsinger et al. 1991. .Aizen and Feinsinger 1994. Groom 1998. Ramsey and V'aughton 2000). Kunin (1997) found that pollinators visiting dense plant populations were significantly more tlower-constant. and therefore more likely to be canning conspecific pollen, than were pollinators visiting less dense plant populations.

Essentially, the efficiency of pollination, in terms of both the quantity and quality of 27 pollen received, declines as patches become too small or the distance between plants becomes loo great (Courchamp et al. 1999). Obligate outcrossers that rely on animal vectors for pollination are most likely to be affected by .A^llee effects (Huenneke 1991).

Pre\ ious studies that have examined Allee effects in plants have focused on reproductive success in different-sized populations or in patches of varying density

(Lamont et al. 1993. Groom 1998. Hackney and McGraw 2001). Some of these studies ha\ e manipulated plant population size or density and examined subsequent effects on pollinator behavior and;or efficiency (Feinsinger et al. 1991.K.unin 1993. Kunin 1997.

Bosch and Waser 2001. Hackney and McGraw 2001, Mustajiirvi et al. 2001). whereas others have taken advantage of existing variation in plant population size or density

(Lamont et al. 1993. .\gren 1996. Roll et al. 1997. Groom 1998. Bosch and Waser 1999.

VIa\ raganis and Eckert 2001). However, in many species, the abundance of tlowering plants varies greatly among years, even if the overall population size remains fairly constant. This is particularly true for long-lived species exhibiting synchronized tlovvering. in which years of abundant tlowering are separated by one to a few years of little or no tlowering (Janzen 1976, Taylor and Inouye 1985. Kelly 1994). In these species, temporal \ ariation in flowering plant abundance and density may affect reproducti\ e success via the mechanisms described above.

The Haleakala silversword {Argyroxiphiiim sandwicense ssp. macrocephalunv.

Asteraceae; Madiinae) is a long-lived, monocarpic rosette plant endemic to Haleakala

\ olcano on the Island of Maui, Hawaii. As is the case with many other monocarpic plant species. A. sandwicense ssp. macrocephaliim (subsequently, silversword) flowering 28 exhibits a boom and bust pattern, with years of abundant tlowering separated by one to a few years of ver> little tlowering (Loope and Crivellone 1986). In this study. I use the

natural annual \ ariation in abundance of tlowering plants, combined with observ ations and pollination experiments, to test for an Allee effect in the Haleakala silversword. I quantity- sil\ ersword seed set over a five-year period and examine the relationship between annual reproductive success and flowering plant abundance. Specificalh. I address the following questions: (1) To what degree does seed set \ ary among years?

(2) Does among-year \ ariation in seed set correlate with the annual variation in flowering plant abundance? (3) Is the silversword pollen-limited? (4) To what degree is the siKersword self-incompatible? Questions (1) and (2) test for the presence of an .Allee effect: questions (3) and (4) examine a potential mechanism underlying this effect.

Follow ing these analyses. I discuss the conserv ation implications of an .\llee effect in this species.

.Materials and methods

Study sire

I conducted this research at Haleakala National Park (HALE). .Maui. Hawaii (20^

44" N. 156" 13' W). This area is comprised of alpine desert (> 3000 m) and subalpine shrubland (2000 - 3000 m) habitats, which are characterized by low annual precipitation, large diurnal variation in temperature, frequent frost, and relatively bare cinder and ash soils (Juvik and Juvik 1998). Vegetation in this area is sparse and. in addition to the sih ersword. is primarily comprised of a few dominant species, including Diibautia mcnziesii (.Asteraceae). Styphelia tameiameiae (Epacridaceae). Vaccmiiim reticiilatiim 29

(Ericaceae), and Sophora chrysophylla (Fabaceae). Annual precipitation at Haleakala

summit (3341 m) averages 500-800 mm. with the majority of rainfall occurring between

November and April (Kobayashi 1973. Juvik and Juvik 1998). Precipitation is slightly

greater in the silversword habitats (2000-3100 m; 500-1500 mm rain per year; Juvik and

Ju\ ik 1998). primarily due to the cloud layer and moist air associated with a tradewind

in\ ersion present at about 2000 m (Loope and .Medeiros 1994). In these areas, abundant

fog drip is likely an important source of precipitation for the silversword and other

resident species (Kobayashi 1973). Similar to other tropical alpine environments, the

mean daily temperature at HALE only varies about 4°C between the warmest and coldest

months, whereas diurnal temperature changes of up to 20°C are common (Rundel and

Witter 1994).

Siudy Specie's

The Haleakala silversword. a member of the Hawaiian silversword alliance, is one

of tive species in the genus, and one of two subspecies. The other, the Mauna Kea

sihersword (Argy roxiphium sandwicense ssp. sandwicense). is endemic to the Island of

Hawaii. The Haleakala silversword occurs on the cinder cones and la\ a tlows within

Haleakala crater (2000 - 3000 m). as well as on the outer slope near the volcano's

summit (3000 - 3341 m). .After growing for many years as a single basal rosette.

indi\ iduals produce a tall flowering stalk (capitulescence) with hundreds of large radiate

capitula. and die soon after setting seed. Capitulescence height and the number of

capitula are both strongly correlated with rosette diameter (Appendi.x B). Flowering occurs throughout the summer months, typically peaking in July; during this time. 30 tlowering indiv iduals are frequently v isited by native and alien bees, wasps, tlies. and moths (Forsvth. unpub. data). Other observ ations and experiments suggest that nearly all pollination is effected bv- diurnal v isitors, primarily native yellow-faced bees (Hylaeus spp.; Forsvth. in prep.). Due to its extensive interactions with pollinators, herbivores and seed predators, the silversword is likely a key component of H.A.LE"s high-elevation ecosystem (Loope and Medeiros 1994).

Once common throughout Haleakala crater, the silversword suffered sev ere population declines in the late 1800s and early 1900s. primarily due to browsing by introduced goats and cattle, as well as human vandalism (Loope and Crivellone 1986).

The population reached a low in the 1920s but began to recov er in the second half of the

20''' centurv . following federal protection from these past threats. By 1982. the population had rebounded to an estimated population size of 47.640 individuals (Loope and Crivellone 19S6). .\lthough a 1991 census estimated more than 60.000 plants in the population, the most recent census, conducted in 2001. estimated slightlv- less than 50.000 individuals (F. Starr, pers. comm.). current threat to the silversword is the invasion of the .Argentine ant (Linepithcma humile). a predator of native insect species, including pollinators such as Hylaeiis spp. (Cole et al. 1992. Loope and Medeiros 1994). The

Haleakala silversword was federally listed as threatened in 1992 (USFWS 1992).

Silversword flowering

1 obtained long-term silversword flowering records from the U.S. Geological

Surv ev. Biological Resources Division. Haleakala National Park. With the exceptions of

19''^ and 1981. researchers have conducted flowering surveys of H.-\LE everv' year since 31

1969. These annual flowering sun eys are conducted in the fall, immediately following

the tlowering season, in order to quantify the total number of silverswords flowering each

>ear.

Temporal variation in seed set

In order to assess temporal v ariation in seed set. 1 collected achenes (thiits) from

flowering indiv iduals everv- year from 1997-2001. Achenes were collected from plants

located along Sliding Sands Trail (2700 m). near Silversword Loop (2400 m). near Puu

Kauaua (2400 m). and at Kalahaku (3050 m). For each plant. 1 measured rosette diameter

and collected three capitula. in order to quantity seed set. These naturally-pollinated

capitula were collected in late September, approximately 8-10 weeks after flowering,

when achenes were fully developed and close to dispersal. 1 stored all achenes in a

relrigerator. e.xamined them under a dissecting microscope, and used the proportion of all

dissected achenes (pooled from three capitula) that contained a filled embrvo as a

measure of percent seed set for that plant.

Pollen Limitation and Self-Incompatibility Experiments

I conducted pollen limitation and self-incompatibility experiments on indiv iduals

located throughout Haleakala crater from 1997-1999. For ease of access and to limit

damage to cinder cones, the majority of study plants were located at Silv ersword Loop,

near Puu Kauaua. and on the volcano's outer slope near Kalahaku. In all years, access to

flowering plants limited sample sizes in these experiments. In 1997. 1998. and 1999. I conducted pollen limitation experiments on 5. 4. and 13 individuals respectively. Self- 32

incompatibilit> experiments were conducted in 1998 and 1999. on 5 and 10 indi\ iduals

respecti\ely.

In each experiment. 1 haphazardly selected experimental capitula. although

capitula exhibiting signs of lepidopteran (Rhynchephestia rhabdotis. Pvralidae)

infestation were replaced by nearby uninfested capitula. To determine if siK ersword

seed set was pollen-limited. I conducted a pollen augmentation experiment.

Experimentally increasing pollen load is a common method to test for pollen limitation; if seed production in pollen-augmented flowers is increased relative to naturally pollinated

flowers, the plant is considered to be pollen-limited at that place and time (Hainsworth et al. 19S5. Zimmerman and Pyke 1988). 1 selected six experimental capitula on each plant and randomly assigned each to one of tw o treatments, for a total of three capitula per treatment per plant: open-pollinated with no supplemental pollen added (OPEN), or open-

pollinated with supplemental pollen added (.AUGMENT). In the .AL'GVIENT treatment, the supplemental pollen was a mix of pollen collected trom at least three other indi\ iduals. 1 collected donor pollen in a small vial by gently brushing the vial against se\ eral pollen-bearing capitula. and applied pollen to recipient capitula using a paintbrush to co\ er all recepti\ e stigmas. This procedure was repeated twice for each capitulum. in order to pollinate the maximum number of stigmas. Each experimental capitulum was marked with a color-coded thread to distinguish treatment and permitted to develop until fruits matured. .Achenes were collected, stored, and analyzed as described above.

If seed production is limited by resources as well as pollen, seed set in pollen- augmented tlowers may occur at the expense of non-augmented flowers on the same plant, as resources are reallocated to flowers that receive more pollen (Lee 1988.

Zimmerman and Pylce 1988). In order to assess whether pollen augmentation affected

seed set in naturally pollinated capitula on the same plant. I compared seed set in open-

pollinated capitula on plants that received the augmentation treatment (N=9 plants) to

seed set in open-pollinated capitula on control plants that did not receive the

augmentation treatment (N=7 plants). For each plant, open-pollinated seed set was the

proportion of all dissected achenes (pooled trom three capitula per plant) that were tilled.

.•\chenes trom open-pollinated capitula on treatment and control plants were collected, stored, and analyzed as described above.

Pre\ ious e\ idence suggests that some species in the Hawaiian sih ersword alliance (i.e.. Argy roxiphium. Diibautia. and IVilkesia) are self-incompatible (Carr et al.

1986). To measure the degree of self-incompatibility in the sih ersword. I conducted a

pollinator exclusion e.xperiment. in which I used nylon mesh bags to pre\ ent pollinators

from \ isiting experimental capitula. This method effecti\ ely excludes insect \ isitors but does not alter the microclimate surrounding the developing capitulum (Keams and

Inouye 1993). I haphazardly selected nine capitula per study plant and randomly assigned each to one of the following three treatments, for a total of three capitula per treatment per plant: unbagged and pollinated naturally (OPEN); bagged, with no pollen added (B.AG); or bagged, with self-pollen added (SELF). BAG and SELF capitula were enclosed in mesh bags as soon as they were distinct trom the flowering stalk. Self-pollen was collected trom at least three other capitula on the same plant and applied to receptive 34 stigmas as described abo\ e. Experimental capitula were collected alter achene maturation, and all achenes were stored and analyzed as previousK' described.

Statistical Analyses

Percent seed set data were logit transformed for statistical analyses. .Among-year

\ ariation in seed set was examined with a one-way analysis of \ ariance: Tukey-Kxamer tests were used to e\ aluate signiticant ditferences between all pairs of years. To examine the relationship between flowering plant abundance and percent seed set. I plotted the a\ erage percent seed set (= 1 SE) for each of the five years against the number of plants that flowered in that year. I used the transformation

V = -ln(l-f/fn,ax). (eq.l) where f equals the a\ erage percent seed set for each year and fma* equals the maximum fertility observ ed in the five-year period, or 0.45. in order to linearize the relationship. I then used linear regression to analyze the relationship between percent seed set and annual flow ering plant abundance.

In order to examine other factors potentially related to plant seed set. I used linear regression. Specifically. 1 tested whether individual seed set was dependent on plant size

(rosette diameter), and whether average annual percent seed set was correlated with annual precipitation. .Annual precipitation records for H.ALE were obtained from the

Western Regional Climate Center.

To anaK-ze the results of the pollen limitation and self-incompatibility experiments, I used two-way .\NOVAs. with treatment and year as the main effects. In the pollen limitation experiment. I compared two treatments (OPEN and AUGMENT) 35 and three years (1997-1999). and in the self-incompatibilit>- experiment. I compared three treatments (OPEN. BAG. and SELF) and two years (1998 and 1999). Open-pollinated seed set data from augmented and non-augmented plants were logit-transtbrmed and compared with a student's t-test.

All statistical analyses were performed with JMPin software (SAS 2000).

Results

From 1997-2001. the number of flowering silverswords varied greatly among years, ranging from a low of 167 (- O.33°'o of the total population) in 1998 to a high of

2.687 {- 5.37O0 of the total population) in 1997. Consistent with the annual variation in flou ering. percent seed set differed significantly among years (F4.4s=6.7S8. P=0.0002).

Seed set was significantly greater in 1997 and 2001. both high flowering years, than in

1998. 1999. and 2000. all low flowering years (Tukey-Kramer test, alpha = 0.05).

.•\\ erage annual percent seed set was positi\-ely correlated with flowering plant abundance, increasing as the number of tlowering plants increased and appearing to plateau around 40-45 percent seed set (Figure l.A). .\fter transformation (eq. 1). where fmax 0.45. the number of plants tlowering each year e.xplained 99.5°'o of the s anation in seed set among years (Figure IB).

There was no relationship berw een plant size (rosette diameter) and percent seed set. for all years combined, as well as for each year. 1997-2001 (Figure 2). Average percent seed set data for the five-year period were not correlated with annual precipitation (R" = 0.554. df = 4. P = 0.149). 36

In the pollen limitation experiment, treatment, year, and the treatment x year interaction were all significant effects (Table 1). Pollen augmentation significantly increased seed set in 1998 and 1999. but not in 1997 (Figure 3). This suggests that the siK ersword was strongly pollen-limited in 1998 and 1999. both low flowering years, but not in 1997. a high flowering year. The pollen augmentation treatment produced consistent results across years, yielding 35-40°o seed set in all years (1997: 38.92 = 3.63:

1998: 34.80 = 5.99; 1999: 36.72 = 4.87). Open-pollinated seed set did not differ between augmented and non-augmented plants (/ = 0.278. df == 14, P = 0.7854). indicating that the pollen augmentation treatment did not affect seed set in open-pollinated capitula on the same plant.

Results of the self-incompatibility experiment demonstrated that the sih ersword is strongly self-incompatible (Table 2. Figure 4). There was a very strong effect of treatment on seed set. but no effect of year and no treatment x year interaction (Table 2).

In both 1998 and 1999. percent seed set in bagged and selfed capitula were significantly lower than percent seed set in open-pollinated capitula (Figure 4). Seed set in the B.A.G and SELF treatments were statistically indistinguishable, averaging 0.31 = 0.12°o and

0.40 = 0.13°o across years, respectively, whereas seed set in open-pollinated capitula in these two years averaged 5.99 = 1.13°o.

Discussion

In the fi\ e-\ear study period, the number of silverswords flowering annually

\ aried greatly among years, with three low flowering years (1998-2000) bracketed by tw o high flowering years (1997 and 2001). A thirty-year flowering record collected by 37

Haleakala National Park suggests that this among-year variation in flowering is typical

for the sih ersword; relatively high flowering years are commonly separated by one to

three low flowering years, although there is no clear pattem in annual flowering (Figure

5). It is currently unknown what triggers silversword individuals to flower: attempts to

correlate annual flowering abundance with precipitation. El Nino, volcanic eruptions and other env ironmental factors ha\ e been unsuccessful (Loope and Cri\ ellone 1986, Rundel and Witter 1994. L.L. Loope. pers. com.). Svnchronous flowering at multi-year intervals

has been observ ed in other long-lived monocarpic species (Janzen 1976. Foster 197T.

Tav lor and Inouye 1985. Kelly 1994). and in general, the causes for such flowering s\nchron\ are rareK understood (Taylor and Inouye 1985).

\'ariation in flowering plant abundance was highly correlated with significant variation in percent seed set among years. Plants that flowered in high flowering years exhibited relatively high percent seed set (> 30" o). whereas plants that flowered in low flowering \ ears had low percent seed set (< 12°/o). .A.lthough this observed among-year

\ ariation in silversword seed set could be due to other, potentially confounding factors, attempts to correlate seed set with other variables were not successful. For example, seed set ma\ \ ar\ among individuals as a function of plant size, due to either differences in resource availability or pollinator attraction. In this study, however, there was no correlation between plant size and percent seed set, both when the data from the five

\ ears were pooled together (N= 49 plants), as well as when the data from each year were examined separateK'. In addition, although seed set may vary according to the a\ ailability of a variable resource such as water, annual precipitation was not correlated 38

with a\ erage annual percent seed set and does not appear to be a confounding factor in

this s\ stem. This result is strengthened by the consistency of the pollen augmentation

e.xperimental results, which confirm that the ability to set seed is independent of

precipitation. From 1997-1999. pollen augmentation treatments produced consistent seed

set lev els of about 35-40 percent, despite differences in annual precipitation among these

three >ears. This suggests that reproductiv e success is determined by factors related to

pollination, such as tlowering plant abundance, rather than by precipitation. Although it

w ould be ideal to manipulate tlowering plant abundance or density, to confirm that this

factor is responsible for annual variation in seed set. such experimental manipulation is

not feasible due to the conserv ation status of this species.

The strong dependence of seed set on the number of tlowering plants in a given

\ ear suggests density dependent seed set. or an .Allee effect, in this species. In addition, this .-Mlee effect is most likely pollinator-mediated. The siKersword is strongly self- incompatible. such that indiv iduals are essentially completely dependent on the receipt of compatible, outcross pollen. In addition, seed set was strongly pollen-limited in 1998 and

1999. both low tlowering years, but not in 1997. a very high tlowering year. Given the degree to which a small number of tlowering plants were spread out across both space and time in these low-flowering years (167 and 267 tlowering plants in 1998 and 1999. respectiv elv). it is not surprising that in these years, plants were limited by the amount of compatible pollen received.

Kunin (1993) suggested that most self-incompatible plants will have a critical minimum population density threshold, below which pollen limitation is likely to become 39 an imponant factor influencing reproducti\ e success. Pollen limitation in small or sparse populations can occur \ ia effects on the quantity and or quality of pollen receix ed (Kunin

1993. Lamont et al. 1993. Bosch and Waser 2001). In poor flowering years, low densities of flowering plants may attract fewer pollinators than larger tlowering displays, which can result in reduced \ isitation. and consequently pollen limitation (Sih and Baltus

198"'. Groom 1998. Ramsey and Vaughton 2000). In addition, individuals flowering in low flowering years are less likely to o\ erlap in time with nearby flowering plants. This is particularK' true for the sih ersword. for which the flowering season e.xtends across se\ eral months but the flowering period of an individual is only one to three weeks

(Forsvth. unpub. data). Flowering individuals, especially those tlowering at the beginning or end of the flowering season, may be isolated in both time and space from an> other flowering plant. In such cases, there is little outcross pollen available and the probability that recepti\ e stigmas will receive compatible outcross pollen declines as the number of tlowering plants decreases.

In addition to facing a reduction in the quantity of pollen recei\ ed. the siKersword's strong self-incompatibility mechanism makes this species particularly

\ ulnerable to an\- reductions in pollen quality. This incompatibility mechanism is most likel\ a sporoph\iic self-incompatibility (SSI) system, based on the previously obserx ed incompatibilit\ between related genotvpes in this species (Carr et al. 1986), as well as the pre\ alence of SSI in .Asteraceae (Vekemans et al. 1998). Individuals must therefore recei\ e genetically unrelated pollen in order to set seed: this requirement may be more difficult to fill fill in low-flowering years. In addition, if neighboring flowering plants 40 share SI alleles, these plants will likely exhibit \ erv' low seed set. particularly iflex els of intra-patch pollen transfer exceed levels of inter-patch pollination. This effect could be exacerbated if cohorts of related plants tend to flower in the same year.

Similarly, if flowering plants are sparsely distributed, pollinators are more likel\- to forage on multiple flowers within one plant, instead of visiting several different plants

(de Jong et al. 1993. Bosch and Waser 2001). This is particularly true for plant species exhibiting a "big bang" flowering habit, in which large numbers of flowers within a plant are on display simultaneously (.A.ugspurger 1980). Several studies have noted that pollinators tend to \ isit more flowers in larger inflorescences (KJinkhamer et al. 1989.

Mustajarv i et al. 2001). Such an increase of within-plant foraging would reduce the amount of outcross pollen deposited on a plant, while increasing the amount of geitonogamous (within-plant) self-pollination (de Jong et al. 1993. Harder and Barrett

1995. Bosch and Waser 2001). Given the silversword's strong self-incompatibility mechanism, geitonogamous pollination would lead to low seed set (reduced female fitness) as well as pollen discounting (reduced male fitness).

The analysis of among-year \ ariation in seed set and the pollen limitation experiment both suggest that pollen is not the only factor limiting reproduction in this species. When the average percent seed set for each year is plotted against the number of flowering plants in that year, seed set increases as number of flowering plants increases.

The cur\ e. however, appears to asymptote around 40-45 percent seed set. suggesting that seed set le\ els off at this point and that in years of even greater flowering (i.e.. >2700 flow ering plants), there would be very little, if any. increase in percent seed set. This 41

suggests that silversword seed set is limited by other factors, in addition to compatible

pollen, in all years. Given the harsh environment in which these plants li\ e. it is not

surprising that seed set may be resource limited as well as pollen limited. Resource

limitation of silversword seed set is also suggested by the pollen augmentation

experiment. In this experiment. I repeated the pollen augmentation treatment twice on each capitulum. in order to ensure that the maximum number of stigmas were pollinated.

1 also used donor pollen from se\ eral individuals, to increase the probabilit\' that compatible pollen would be present on the capitulum. Howe\er. although the pollen augmentation treatment produced consistent results across years, and significantly

increased seed set in both low-tlowering years, seed set in augmented capitula still av eraged only 35 -40 percent in each of the three years in which this experiment was conducted. These le\ els of seed set (< 40" o) suggest that silversword seed set is limited b> resources as well as by pollen.

The observ ed effects of flowering plant abundance on reproductive success, as mediated b\' pollinators, may help to explain the synchronized flowering pattem observed in this species. The evolution of flowering synchrony to maximize reproducti\ e success has been h\pothesized for other long-lived monocarpic species, including Sweriia rcuiiata. a long-li\ ed gentian (Taylor and Inouye 1985). In addition to its effects on pollination, hou ever. svnchronized flowering may also affect levels of seed predation. as predicted by the predator satiation hypothesis (Janzen 1976). This hypothesis, that sNTichronized flowering serv es to minimize seed predation by swamping seed predators w ith an abundance of seed in good flowering years, and starving them in poor flowering 42 years, has been proposed for other long-lived plant species (Janzen 1976. Augspurger

l^Sl. Kelly 1994). .Although not addressed in this study, previous obser\ ations suggest that this interaction may occur with the silversword. In some years, a large proportion of sih ersword achenes are lost to two predispersal seed predators. Rhynchepliestia rhabdotis (Lepidoptera: Pyralidae) and Tnipanea cratericola (Diptera: Tephritidae)

(Forsvth. unpub. data). In good tlovvering years, however, seed predation may be less than 50°'o (Kobayashi 1973. Loope and Medeiros 1994). Separating years of s\ nchronized flowering, in which seed predators are satiated, with low flowering years, in w hich seed predators starve, may help to minimize seed predation over the long term.

Consenation Implications

The presence of an .Allee effect in the Haleakala silversword has important implications for the persistence of this species, because at small population sizes, low- numbers of flowering plants will lead to reduced reproductive success for most indi\ iduals. Given that we occasionally see very low flowering years in the current population of approximately 50.000 individuals, it is likely that, if the population declined, fewer plants would flower each year and low-flowering years would be more common. These changes would have important consequences for the reproductive success of flowering individuals. In addition, the mechanism underlying this Allee effect suggests that population persistence is not only dependent on total population size, but also on the spatial distribution of flowering plants, annual flowering patterns, and pollinator activity and efficiency as well. This pollinator-mediated Allee effect could be 43 exacerbated by reduced pollinator abundance or efticiency. which in this system is a likely consequence of the current Argentine ant invasion (Cole et al. 1992. Appendix D).

Despite these possible outcomes, it is important to assess these potential effects in the larger context of the silversword's history at HALE. In the past century, the silversword successfully rebounded from a low of approximately 5.000 individuals to its current size of approximately 50.000 plants. This suggests that the population low achiev ed in the early part of the 20"^ century was still greater than the threshold population size below which extinction is nearly certain. If similar proportions of the total population tlowered at that time, as have been observed to tlower over the past twenty years, it follows that there were likely many years with very few flowering individuals. Given these conditions, as well as the strong effects of flowering plant abundance on reproductive success, this large increase in population size seems unexpected. However, although the historical data are limited, early records document some fairly good flowering years in the first half of the century, including 1935. in which at least 217 plants flowered, and 1941. in which 815 plants flowered (Loope and

Crivellone 1986). These relatively good flowering years, combined with protection from browsing and \ andalism. may have been sufficient for the silversword to rebound and persist. In addition, these data are presented as percent seed set. not total seed set per plant. Each flowering sih ersword has the potential to produce tens of thousands of seeds

(.Appendix B). such that even if an individual plant exhibits low percent seed set. it may still produce a substantial number of filled achenes. 44

In combination, results ot" this study provide strong support for a pollinator- mediated Allee etTect in the Haleakala silversword. .Allee effects may be prevalent in plants, particularly in self-incompatible species that rely on animal vectors for pollination. As plant population sizes begin or continue to decline, due to factors such as habitat fragmentation. har\ esting. or invasive species, e.xtinction risks may be heightened due. in part, to Allee effects. Such possibilities point to the need to better understand the factors influencing plant reproduction, particularly for rare and endangered species, including how reproductive success is affected by changes in population size. Evaluating

•Allee effects and determining threshold population sizes, below which individual reproduction is reduced, should be a critical step in the management and conservation of rare plant species. 45

References

Agren J (1996) Population size, pollinator limitation, and seed set in the self- incompatible herb Ivr/zn

Aizen MA. Feinsinger P (1994) Forest fragmentation, pollination, and plant reproduction in a chaco dr\' forest. Argentina. Ecology 75: 330-351

Allee WC (1931) Animal aggregations, a study in general sociology. L'ni\ ersity of Chicago Press. Chicago

.Allee W'C (1938) The social life of animals. W.W. Norton and Company. Inc.. New York

.Augspurger CK. (1980) Mass-tlowering of a tropical shrub (Hybanihus pnmifoliiis): intluence on pollinator attraction and movement. Evolution 34: 475-488

.Augspurger CK (1981) Reproductive synchrony of a tropical shrub: experimental studies on effects of pollinators and seed predators on Hybanihus pninifolius (Violaceae). Ecology 62: 775-788

Bosch M. Waser NM (1999) Effects of local density on pollination and reproduction in Delphinium nuttalliamim and Aconilum columbianum (Ranunculaceae). American Journal of Botany 86: 871-879

Bosch .VI. Waser NM (2001) Experimental manipulation of plant density and its effect on pollination and reproduction of two confamilial montane herbs. Oecologia 126: 76-83

Carr GD. Powell EA. Kyhos DW (1986) Self-incompatibility in the Hawaiian Madiinae (Compositae): an exception to Baker's Rule. Evolution 40: 430-434 46

Cole FR. Medeiros AC. Loope LL. Zuehlke WW (1992) Effects of the Argentine ant on arthropod fauna of Hawaiian high-elevation shrubland. Ecology 73: 1313-1322

Courchamp F. Clutton-Brock T. Grenfell B (1999) Inverse density dependence and the Allee effect. Trends in Ecology and Evolution 14: 405-410

Courchamp F. .Vlacdonald DW (2001) Crucial importance of pack size in the .^trican wild dog Lycaon piciiis. .Animal Conserv ation 4: 169-174.

de Jong TJ. Waser NM. KJinkhamer PGL (1993) Geitonogamy: the neglected side of selfmg. Trends in Ecology and Evolution 8: 321-325

Feinsinger P. Tiebout III HM. Young BE (1991) Do tropical bird-pollinated plants exhibit density-dependent interactions? Field experiments. Ecology 72: 1953-1963

Foster RB (19''7) Tachigalia versicolor is a suicidal neotropical tree. Nature 268: 624- 626

Gilpin ME. Soule ME (1986) .Minimum viable populations: processes of species extinction. In: Soule .ME (ed) Conserx ation Biology: The Science of Scarcity and Dix ersity. Sinauer .Associates. Sunderland. Massachusetts, pp 19-34

Groom MJ (1998) .Allee effects limit population viability of an annual plant. .American Naturalist 151: 487-496

Hackney EE. .VlcGraw JB (2001) Experimental demonstration of an .Allee effect in .American ginseng. Conservation Biology 15: 129-136 47

Hainsworth FR. Wolf LL. Mercier T (1985) Pollen limitation in a monocarpic species. Ipomopsis aggrcgata. Journal of Ecology 73: 263-270

Harder LD. Barrett SCH (1995) Mating cost of large floral displays in hermaphrodite plants. Nature 3 73; 512-515

Huenneke LF (1991) Ecological implications of genetic variation in plant populations. In: Falk DA. Holsinger K.E (eds) Genetics and Conservation of Rare Plants. Oxford L ni\ ersit\ Press. New "^'ork. pp 31-44

Janzen DH (1976) Why bamboos wait so long to flower. .Annual Review of Ecology and Systematics 7: 347-391

Jennersten O (1988) Pollination in Dianthus delioides (Caryophyllaceae): effects of habitat tragmentation on visitation and seed set. Conservation Biology 2; 359-366

Juvik SP. Juvik JO (1998) Atlas of Hawaii, third edition. University of Hawaii Press. Honolulu

Keams C.A. Inouye DW (1993) Techniques for pollination biologists. University Press of Colorado. Niwot. CO

Kell\ D (1994) The evolutionary ecology of mast seeding. Trends in Ecology and Evolution 9: 465-470

K.linkhamer PGL. de Jong TJ. de Bruyn G (1989) Plant size and pollinator visitation in Cynoglossum officinale. Oikos 54; 201-204 48

Kobav ashi. HK. (1973) Ecology of the silversword, Argy roxiphium sandwiccnse DC. (Compositae). Haleakala Crater. Hawaii. Ph.D. Dissertation. Dept. of Botany. Uni\ ersit\' of Hawaii. Honolulu

Kunin WE (1993) Se.\ and the single mustard: population density and pollinator beha\ ior effects on seed set. Ecology 74: 2145-2160

Kunin WE (1997) Population size and density effects in pollination: pollinator foraging and plant reproducti\ e success in experimental arrays of Brassica kaber. Journal of Ecology 85: 225-234

Kuussaari M. Saccheri 1. Camara M. Hanski 1 (1998) .-Mlee etfect and population d\Tiamics in the Glanville fritillary butterfly. Oikos 82: 384-392

Lament BB. Klinkhamer PGL. Witkowski ETF (1993) Population fragmentation may reduce fertilit\ to zero in Banksia goodii- a demonstration of the .Allee effect. Oecologia 94: 446-450

Lee TD (1988) Patterns of thiit and seed production. In: Lovett-Doust J. Lovett-Doust L (eds) Plant Reproducti\e Ecology: Patterns and Strategies. Oxford University Press. New \'ork. New ^'ork. pp 179-202

Loope LL. Crivellone. CF (1986) Status of the Haleakala silversword: Past and present. Cooperati\ e National Park Resource Studies Unit. University of Hawaii. Honolulu. Tech. Rep. 58

Loope LL. .Medeiros AC (1994) Biotic interactions in Hawaiian high ele\ ation ecosystems. In: Rundel PW. Smith -A-P. .Meinzer PC (eds) Tropical .A.lpine Environments: Plant Form and Function. Cambridge University Press. New York, pp 337-354 49

VIa\Taganis K.. Eckert CG (2001) Eftects of population size and isolation on reproducti\ e output in Aquilegia canadensis (Ranunculaceae). Oikos 95: 300-310

Moody-Weis JM. Hev-vvood JS (2001) Pollination limitation to reproducti\e success in the Vlissouri ex ening primrose. Oenothera macrocarpa (Onagraceae). American Journal ot'Botany 88: 1615-1622

Mustajar\ i K.. Siikamaki P. Rylkonen S. Lammi A (2001) Consequences of plant population size and density for plant-pollinator interactions and plant performance. Journal of Ecology 89: 80-87

Pedersen B. Hanslin HM. Bakken S (2001) Testing for positi\ e density-dependent perfomiance in four bryophyte species. Ecology 82: 70-88

Ramsey .N/I. V'aughton G (2000) Pollen quality limits seed set in Burchardia iimbellaia (Colchicaceae). .American Journal of Botany 87: 845-852

Roll J. Mitchell RJ, Cabin RJ. Marshall DL (1997) Reproductive success increases with local density of conspecifics in a desert mustard (Lesquerella fendleri). Conserx ation Biology 11: 738--'46

Rundel PW. Witter MS (1994) Population dynamics and flowering in a Hawaiian alpine rosette plant. Argyroxipfiium sandwicense. In: Rundel PW. Smith AP, Meinzer FC (eds) Tropical .Alpine Environments: Plant Form and Function. Cambridge University Press. New "\'ork. pp 295-306

S.AS Institute. Inc. (2000) JMPin statistical software. \'ersion 4.0.2 (academic) Schemske DVV (1980) Floral ecology and hummingbird pollination of Combretwn turinosiim in Costa Rica. Biotropica 12: 169-181

Shaffer ML (1981) Minimum population sizes for species conservation. Bioscience 31 131-134

Sih -A. Baltus .MS (1987) Patch size, pollinator behavior, and pollinator limitation in catnip. Ecology 68: 1679-1690

Stephens P.-\. Sutherland VVJ. Freckleton RP (1999) What is the Allee effect? Oikos 87 185-190

Taylor OR Jr.. Inouye DW (1985) Synchrony and periodicity of flowering in Frasera speciosa (Gentianaceae). Ecology 66: 521-527

U.S. Fish and Wildlife Service (USFWS) (1992) Determination of endangered or threatened status for 15 plants from the Island of Maui. HI. Federal Register 57: 20772- 20787

Vekemans Schierup MH. Christiansen FB (1998) Mate availability and fecundity selection in multi-allelic self-incompatibility systems in plants. Evolution 52: 19-29

Wolf .AT. Harrison SP (2001) EtTects of habitat size and patch isolation on reproductive success of the serpentine moming glory. Conservation Biology 15: 111-121

Zimmerman .M. Pyke GH (1988) Reproduction in Polemonium: assessing the factors limiting seed set. .\merican Naturalist 131: 723-738 51

Table 1. Two-way ANOV'A results for Argyroxiphium sandwicense ssp. macrocephalum seed set across pollen augmentation treatments (OPEN. AUGMENT) and years (1997-

1999). OPEN and AUGMENT treatments were performed on tive (1997). tbur(1998) and 13 (1999) indi\ idual plants. Treatment, year, and the treatment .\ year interaction were all siaiiticant effects.

Source of \ ariation df SS MS F P

Treatment 1 2.666 20.677 <0.0001

Year 2 2.431 9.426 0.0005

Treatment X Year 2 1.022 3.963 0.0273

Error 38 4.900 0.129

Total 43 11.972 52

Table 2. Two-way ANOV'A results for Argyroxiphium sandwcense ssp. macroccphalum

seed set across self-incompatibility treatments (OPEN. BAG. SELF) and years (1998-

1999). OPEN. BAG. and SELF treatments were performed on five(1998) and ten (1999)

indi\ idual plants. The effect of treatment on percent seed set was highly significant; year and the treatment year interaction were not significant effects.

Source of variation df SS MS F

Treatment 57.340 17.329 <0.0001

^'ear 2.63' 1.594 0.2140

Treatment X ^'ear 0.868 0.262 0.771

Error 39 64.523 1.654

Total 44 129.494 FIGURE LEGENDS

FIGURE 1. (A) Raw and (B) transformed (relative to fmax) percent seed set of open- pollinated Argyroxipluiim sandwicense ssp. macrocephaliim capitula for each year.

1997-2001. as a tiinction of the number of plants that flowered that year (N). Markers represent average percent seed set (= 1 SE) for each year. 1997: n = 6 plants: 1998: n =

5 plants: 1999: n = 15 plants: 2000: n = 7 plants: 2001: n = 20 plants. Transformed percent seed set = -In (1-f fma.x). w here f = the average percent seed set for each \ ear.

1997-2001. and fmax = the maximum percent seed set observed in the tive year period, or 0.45. -In (1 -f f^^tx) = 0.044 - 0.0009N: R- = 0.995: F = 602.380. df = 4. P < 0.0001.

FIGURE 2. Percent seed set of open-pollinated Argy roxiphium sandwiccnse ssp. macrocephaliim capitula (1997-2001). and plant size. Svmbols distinguish the fi\e

\ears. with clear svinbols indicating individuals that tlovvered in high-tlowering years

(1997 and 2001). and filled symbols indicating individuals that flowered in low- flowering \ ears (1998. 1999. and 2000). A\\ years combined: R' = 0.006. F = 0.277. df

= 48. P = 0.601. 1997: R" = 0.426. F - 2.974. df = 5. P = 0.160: 1998: R" = 0.359. F =

1.122. df=3./' = 0.40I: 1999: R'= 0.262. F = 3.904. df - 12. P = 0.074; 2000: R'=

0.301. F = 2.149. df = 6. P = 0.203: 2001: R" = 0.032. F = 0.544. df = 18. F = 0.467. 54

FIGURE 3. A\ erage percent seed set (= 1 SE) tor open-pollinated and pollen- augmented Argyroxiphium sandwicense ssp. macrocephalum capitula, 1997-1999.

1997: \ = 5 plants; 1998; N = 4 plants; 1999: N = 13 plants. The pollen augmentation treatment significantly increased seed set in 1998 and 1999. but not in 1997.

FIGURE 4. .As erage percent seed set (= 1 SE) for open-pollinated, bagged, and self- pollinated Argyroxiphium sandwicense ssp. macrocephalum capitula. 1998-1999. 1998:

N = 5 plants; 1999: N = 10 plants. Percent seed set differed significantly among the three treatments; in both years, seed set was significantly greater in the open-pollinated capitula than in the bagged and selfed capitula.

FIGURE 5. .A.nnual \ ariation in the number of flowering Argyroxiphium sandwicense ssp. macrocephalum individuals. Haleakala National Park. 1969-2001. Flowering sur\eys were conducted in all years e.xcept 1977 and 1981 (indicated by X"s). Zero plants flowered in 1970; two plants flowered in 1972. Flowering data are reprinted with permission from USGS-BRD. Haleakala National Park. .Maui. Hawaii. 1997 <•

2001

2000 r 1999

• 1998

0 500 1000 1500 2000 2500 3000

# of flowering plants FIGURE 1 80

"0 O 1997 hO ^ O • 199S 50 O ^ o • 1999 40 ® o • 2000 30 O ^ °

FIGURE 2 • Open-pollinated • Augmented

X

1997 1998 1999

FIGURE 3 14 • Open

12 • Bag

10 • Self

8

6

4

1998 1999

FIGURE 4 59

7000

6000

5000

4000

3000

— r^. I/". — r^. i/~, I— ^ — r^, T, r~~ vct^r-r^r^r-~3csc3cac5c3^s«3^3^

FIGURE 5 APPENDIX B:

MEASL RING PLANT REPRODUCTION FOR MATRIX

MODEL ANALYSES 61

MEASURI\G PLANT REPRODUCTION FOR

MATRIX MODEL ANALYSES

Stace\ A. Fors\th

Department of Ecology and Evolutionar\ Biology

University of Arizona. Tucson. AZ 85721

email: forsNthtou.arizona.edu

Key words: Haleakala sih ersword. matrix population model, monocarpy. seed bank, seed dormancy 62

Summan

1 The reproducti\ e biology of the monocarpic Haleakala sih ersword

(Argyroxipliium sandwiccnse ssp. macroccp/ialum) was studied in order to

quantity' reproducti\ e rates for use in a matrix population model. The data used

were collected annually from 1997 - 2002 at Haleakala National Park. Maui.

Hawaii.

2 The sil\ ersword seed dispersal cur\ e was highh' leptokurtic o\er a short distance,

indicating minimal dispersal. More than 60 percent of all collected achenes u ere

found within 20 cm of the parent plant.

3 See^s remained \ iable in the field for multiple years, suggesting that a separate

seed stage should be incorporated into a matrix model for this species. Seeds as

old as four years germinated in the laboratory, although \ iability declined with

seed age.

4 Capitulescence length, total number of capitula. and capitulum size (i.e.. number

of tlorets per capitulum) were strongly, positively correlated with rosette

diameter, enabling size-based estimates of reproductive output.

5 In de\ eloping matrix population models for plant species, assumptions regarding

seed dispersal and seed dormancy should be tested, to determine if a separate seed

stage is necessary. Calculating size-based estimates of reproduction, based on

demonstrated allometric relationships, may be a usefiil way to measure plant

reproducti\ e rates for matrix models while avoiding destructive sampling

techniques. 63

Introduction

In the past two decades, matrix modeling of demographic data has emerged as an effecti\ e \va\' both to e\ aluate the biological status of a population or species and to identif\ the stages in a species' life history that ha\ e the greatest impact on population growth rate (Schemske et al. 1994. Caswell 2001. Beissinger 2002). Population viability analyses (PV'As) based on matrix population models use age- or stage-based data to quantify' how indi\ iduals transition among different classes over time. These demographic \ ital rates are used to project how the population will change o\ er time, in terms of both size and stage distribution. .-Mthough PV'.A.s have the potential to accurateK' predict the future size and structure of populations and species (Brook et al. 2000). their precision depends on robust data. Ideally, the parameters used in the model should be estimated from data collected over a period of several years (Beissinger 2002). Due to the time, energy, and financial resources required for such long-term demographic monitoring, many studies are limited by the amount and quality of data available for such analyses (Beissinger 2002). In addition, it is frequently difficult to measure accurately the probabilities of all life history transitions, particularly if certain transitions are cryptic or otherwise difficult to measure.

In plants, it may be especially difficult to quantify accurately reproductive rates, due to certain aspects of plant life histories. It is difficult to follow the fates of indi\ idual seeds once the> ha\ e left the parent plant, and thus it may be impossible to determine the origins of newly recruited seedlings (Howe «S: VVestley 1986. Reed et al. 2002). Directly measuring seed production may require destructive sampling (.Menges 1986). which is 64 undesirable if plants are endangered or are part of a long-term demographic study. In addition, seed dormancy and the presence of a seed bank in some species can complicate calculations of plant reproductiv e success (Menges 2000a). Seed banks play an important role in the demography of some plant species, by preserv ing genetic \ ariation and buffering the effects of envirormiental \ ariation. thereby reducing the species" risk of extinction (Kalisz & .McPeek 1992. 1993. McCue & Holtstbrd 1998). However, because seed banks must be studied experimentally in order to quantity seed surv ival and germination rates, data on seed dormancy and seed banks are limited for many plant species (Menges 20006. Doak et al. 2002). Thus, in spite of their potential importance in plant life historv'. seed banks are frequently left out of plant PV.-\s (Menges 2000a).

In a recent paper. Doak et al. (2002) surveyed 70 plant demography studies to assess how plant demographers incorporate seeds into their analyses. Less than half of the studies included information about seed banks; of these, only four studies measured age-specific seed germination and. or seed survival rates and incorporated these results into a population model. In addition, the authors observed that available seed demograph\ data were biased toward agricultural weeds; they were unable to fmd any studies of rare plants that measured seed vital rates for use in a quantitative population model. If seed banks play a role in the persistence of a population or species, incomplete data on seed demography and seed bank dvTiamics may compromise estimates of a population's intrinsic rate of increase, stable stage distribution, and time to extinction

(Kalisz 1991. Kalisz & McPeek 1992. Doak et al. 2002). 65

When data on the reproductiv e biology and seed biology of a species are limited, researchers trequently rely on recruitment data to estimate plant reproductiv e success

(e.g.. Oostermeijer 1996). In these cases, reproduction is measured as the number of seedlings in year t divided by the number of flowering plants in year / - I. This calculation is based on two assumptions: that there is no net dispersal of seeds into or out of studv' plots, and that seeds do not remain viable beyond the first year in the soil. These assumptions, howev er, are rarely tested, which may lead to inaccurate demographic projections. Ev en if transitions from the seed stage make only minor contributions to a population's finite rate of increase, seed banks may still affect the demography of a population (Quintana-.A.scencio 1997).

In this study, I quantify reproduction of a threatened Hawaiian plant species, the

Haleakala silversword, Argyroxiphium sandwicense ssp. macroccphaliim {.A.steraceae:

.Madiinae). for use in a matri.x population model. The silversword population has been monitored since 1982, when concern for this species prompted researchers to initiate a long-term demographic study (Loope & Crivellone 1986). The primary goal of that study was to examine the changing size and stage distribution of the silversword population, in order to assess its long-term viability. The study monitored the fates of individual plants located in 11 permanent plots over time, but did not quantity plant reproduction. Later attempts to calculate plant reproduction as the number of seedlings in time t divided by the number of flowering plants in time f - 1 were unsuccessful; the many years in which seedlings appeared in plots following years of no flowering made it difficult to accurately estimate reproduction. In addition, the matrix model developed for the silversword 66

includes two ditferent tlovvering stage classes (small and large reproductive plants), and it was not possible, using this method, to accurately assign seedlings to one of the two reproductive stage classes.

Here. 1 use the results of a 5-year study (1997-2001) on the reproductiv e biologv of the Haleakala silversword to quantify- plant reproduction for use in a matrix model anaK sis. 1 measure seed dispersal and test the ability of achenes of different ages to germinate. In order to calculate the reproductiv e output of plants in two different size- based stage classes. 1 e.xamine allometric relationships between plant size and different components of reproduction. Specifically. I e.xamine relationships between rosette diameter and capitulescence length, the number of capitula (tlovverheads) per capitulescence. and the number of tlorets per capitulum. The primary goals of this studv are to (1) ev aluate seed dispersal, in order to test the assumption that there is no net dispersal into or out of study plots; (2) quantify germination rates of seeds of different ages, in order to determine if a seed stage should be incorporated into a matrix population model; and (?) calculate reproductive success as a fiinction of plant size, in order to estimate the reproductiv e output of plants in two size-based reproductiv e stage classes, for use in a matrix population model.

.Methods

STUDV SITE

1 conducted this research in the crater district of Haleakala National Park (H.A.LE).

Vlaui. Hawaii (20" 44" N. 156" 13" W). This area of H.A.LE is composed of alpine desert and subalpine shrubland habitats, which are characterized by low annual precipitation. 67 large diurnal \ ariation in temperature, trequent trost. and relatively bare cinder and ash soils (Juvik & Juvik 1998). Vegetation in the crater region of HALE is ver\- sparse and. in addition to the silversword. is comprised of a few dominant species, including

Diibauiia menziesii (Asteraceae). Styphelia lameiameiae (Epacridaceae). and Sophora clinsophylla (Fabaceae). .Annual precipitation in the silversword habitats is approximately 1000 - 1500 mm per year, with much of the precipitation arriving in the form of fog drip due to a tradevvind inversion (Loope & Medeiros 1994. Rundel & Witter

1994). Similar to other tropical alpine environments, diurnal temperature changes are frequently greater than the differences in av erage temperature between the warmest and coldest months of the year (Juvik & Juvik 1998).

STUDY SPECIES

The Haleakala sih ersword is a long-lived, monocarpic rosette plant endemic to

East -Maui. Hawaii (Figure 1). The species grows on cinder cones and lava flows throughout Haleakala crater (2000 - 3000 m). as well as on the outer slope near the v olcano's summit (3341 m). .After growing for many years as a single basal rosette, the si Iv ersword produces a tall flowering stalk (capitulescence) with hundreds of radiate flowerheads (capitula). and dies soon after setting seed. Silversword flowering occurs throughout the summer months, typically peaking in July. The Haleakala silversword is stronglv self-incompatible and requires pollination by insects, primarily native yellow- faced bees (Hylaeiis sp.). in order to set viable seed (Carr et al. 1986. Appendi.x A).

•Approximately eight to ten weeks after flowering, silversword achenes (fhiits) mature; achenes are 9.34 = 0.10 mm in length and have a highly reduced pappus (Forsvth. unpub. 68 data). As one of the few plant species commonly found throughout the western half of

Haleakala crater, the sih ersword is an important resource for many nativ e insect species, including two native seed predator species. Rhynchephestia rhabdotis (Lepidoptera:

Pvxalidae) and Tnipanea craiericola (Diptera: Tephritidae) (Loope & Vledeiros 1994).

.Although once widespread at Haleakala volcano, the silversword suffered severe declines in the late 19'*' and early 20'^' centuries, primarily due to grazing by introduced goats and cattle, as well as human vandalism (Loope & Crivellone 1986). These threats reduced the silversword population to a low of appro.ximately 5.000 individuals by the early 1920s (Loope & Crivellone 1986). Following federal protection from browsing and

V andalism. the population rebounded to its current estimated population size of approximately 50.000 individuals. Current threats to the Haleakala silversword include in\ asiv e insects such as the .Argentine ant (Linepithema hiimile) and western yellovvjacket

(I 'cspiila pennsylvanica). which prey on native insect pollinators (Cole et al. 1992. Loope

& Medeiros 1994).

SILVERSWORD DEMOGR.\PHV

In 1982. HALE researchers established eleven 5 x 20 m permanent plots on cinder cones throughout Haleakala crater in order to monitor silversword survival, growth, and flowering (Loope & Crivellone 1986). Individuals in the plots were placed into one of tive stage classes, defmed by rosette diameter and reproductive status. The plots were censused each year in the fall, immediately following the flowering season, from 1982-

1992 and from 1996-2001. Due to the steep slopes and loose substrate of many plots, all data were collected by observers standing beyond the plot boundaries in order to reduce 69 impact on the cinder cones and on study plants within the plots. To ensure that indi\ iduals were accurately followed over time, plants were mapped onto a detailed grid. rather than physically marked or tagged.

The monitoring study conducted from 1982 - 2001. with the exception of the three-year hiatus from 1993 - 1995. vielded data for 15 annual transitions. From these data, it is possible to calculate transition probabilities among the different vegetative stage classes, including rates of sur\ ival. grov\th. and flowering in this species. However, because demographic data were collected from beyond plot boundaries in order to minimize disturbance to the plants, reproduction (i.e.. fruit set or seed set) was not quanlitied.

SEED BIOLOGY

Estimates of plant reproduction based soleh' on tlowering and recruitment data assume that there is no net dispersal of seeds into or out of study plots, and that seeds do not remain dormant for multiple years. In order to test these rwo assumptions, 1 e.xamined silversword seed dispersal and dormancy. In the summer of 1998. I quantified seed dispersal from 13 plants that had flowered the previous year and that were located at least 10 m from any other flowering individual. All plants were located at Sih ersword

Loop, a relatively flat area within Haleakala Crater. I used a 20 cm diameter metal hoop and collected all achenes in a series of ten consecutive 20 cm diameter circles e.xtending out from the plant in a randomly chosen compass direction. I counted all achenes found within the circles from 0 - 2 m and returned them to the location from which they had been collected. 1 summed the number of achenes found at each distance for the 13 70 indi\ iduals, and used the proportion of all collected achenes that were found in each of the 10 distance categories to generate a seed dispersal cur\ e.

To e\aluate the ability ofachenes of different ages to germinate. I conducted a germination experiment using achenes produced from 1997 - 2001. In October 2001.1 identified dead plants that had flowered in each of the four previous years. I used maps of ttowering indiv iduals made in 1997 - 2000. as well as numbered tags placed on the plants in prev ious years, to determine the year in which a particular plant had flowered.

For each individual. I collected a sample of achenes located immediately below and within 0.5 m of the decaying rosette. Thus, collected achenes were exposed to natural tield conditions from the time they were produced until collection in 2001. a period of one to four years, depending on the year in which they were produced (1997 - 2000). In order to ensure that all collected achenes were produced by the focal plant. I collected achenes only from plants that were located at least 10 m from other plants that were flowering or that had flowered in the previous three years. I also collected achenes from plants that flowered in 2001; these achenes were collected directly from the capitulescence in early October, after achene maturation but prior to dispersal.

Between the time of achene collection and the start of the germination experiment

(approximately three weeks), all achenes were stored in a refrigerator. In late October. I placed achenes on moistened filter paper in Petri dishes sealed with parafilm. To ensure that I was testing the ability of filled achenes to germinate. 1 first soaked each sample of achenes in water. .Achenes that sink are typically tilled, whereas achenes that float on the surface of the water are typically unfilled, although occasional filled achenes float 71

(Fors\th. unpub. data). I excluded achenes that floated from the germination experiment.

I chose a sample of 40 filled achenes from each plant to germinate on filter paper.

Achenes were maintained in Petri dishes at room temperature on a 12 h light 12

h dark schedule. Plates were checked every other day for cotyledon emergence, and to ensure that the filter paper was still moist. The date of each seedling emergence was recorded, in order to quantity- both the total number of seedlings and the time to germination for each achene sample. I concluded the experiment after 30 days, one week after the last seedling emergence. Following the experiment. I calculated percent germination for each plant, and determined the average percent germination for each achene age class, ranging from zero (achenes produced in 2001) to four (achenes produced in 1997) years old. Among-year differences in germination success and time to germination were e\ aluated with .ANOV'A. followed by Tukey-K.ramer tests to determine significant differences between all pairs of years.

PL\NT SIZE .\ND REPRODUCTION

In order to determine the average rosette size of flowering plants. I measured a sample of flowering plants each year. 1997 - 2002. Plants were arbitrarily selected. primariK' based on accessibility. I measured the rosette diameter of each selected plant, generated a size distribution of flowering plants for each year, and calculated the average rosette size of flowering plants for each year. Because the matrix population model for this species includes two flowering stages, small reproductive plants (rosette diameter 5 -

20 cm) and large reproducti\e plants (rosette diameter > 20 cm). 1 also calculated the a\ erage rosette size of flowering plants in each of the two reproducti\ e stage classes. 1 72 measured rosette diameter and capitulescence length of all study plants that were in tiill tlower. i.e.. those plants for which the capitulescence had reached its full length. lndi\ iduals that were still bolting were not included in this sample. For a subset of indi\ iduals. 1 counted the total number of capitula on the capitulescence. In 2002. 1 e.\amined the relationship between plant size and capitulum size. For 20 plants. I recorded rosette diameter, capitulescence length, and the number of capitula on the capitulescence. 1 also counted the number of tlorets in three capitula on each plant, and used the a\ erage of these counts as an estimate of the number of achenes per capitulum for that plant. Floret counts were done before achene maturation in order to estimate potential seed production prior to losses due to predispersal seed predation. SiK ersword seeds are consumed by two native seed predators. Tnipanea cratericola (Diptera;

Tephritidae) and Rhynchephestia rhabdoiis (Lepidoptera; Pyxalidae). with annual le\ els of seed predation ranging trom less than 50° o to nearly lOO^ o of viable achenes being consumed (Kobayashi 1974. Loope &. .Medeiros 1994). .A.llometric relationships between rosette diameter and capitulescence length, number of capitula per capitulescence. and number of tlorets per capitulum were analyzed with linear regression. I used the equations defming these size relationships to calculate the potential number of achenes produced by different-sized plants, ranging trom 5 cm to 1 m in rosette diameter, and to estimate levels of achene production by plants in the small and large reproductive stage classes. Using the data collected here. I constracted a life cycle graph illustrating reproduction in the Haleakala sih ersword. and estimated the probabilities of all transitions for use in a matri.x model analysis. These transition probabilities were calculated using estimates of the following variables; Bsm. Big (achene production by

small and large reproducti\ e plants); F (percent seed set); G. Go (germination rate of

newly-produced and older achenes); and S. Sg (surv ival rate of seeds and newly-

germinated seedlings).

Results

SEED BIOLOGY

The seed dispersal cur\ e was highly leptokurtic (Figure 2). The majority of plants

that had flowered the previous year had large clumps of achenes immediately below, or

\ er\ close to. the decaying rosette. Si.xty-one percent of all collected achenes were

located within 20 cm of the parent plant, whereas less than 20 percent of all collected

achenes were found 21 - 40 cm from the parent plant. Only 21 percent of achenes were

found more than 40 cm from the parent plant. I obser\ed no animal seed dispersers in the

course of this study.

.•\chenes produced in all years (1997 - 2001) germinated under laborator>

conditions, but the proportion of achenes that successfiilly germinated differed

significantly among age classes (F4.17 = 38.641. P < 0.0001). Germination declined

markedly with achene age (Figure 3); achenes produced in 2001 (age 0) e.xhibited

significantly higher germination success than did achenes produced in all other years

(Tukey-Kramer test, alpha = 0.05). The germination rate of newly produced, filled

achenes averaged 73° o. whereas the germination rate of one-year old filled achenes dropped to 15%. Germination rates of 2-. 3-. and 4-year old filled achenes averaged 2%.

4''o. and 3° o. respectively, but these rates were not significantly lower than the ~4

germination rate of one-year old achenes. A\ erage time to germination for different-aged

achenes ranged from se\ en days (achenes produced in 1997 and 1999) to 15 days

(achenes produced in 2000 and 2001). Although younger seeds on a\erage took longer

to germinate, among-year differences in time to germination were not significant

(ANOVA; = 2.679. F = 0.101).

PLANT SIZE ANT) REPRODUCTION

In the si.x-year study period, the rosette size of flowering indi\"iduals ranged from

12.0 cm (in 1997) to 96.0 cm (in 199S; Figure 4). The average rosette size of tlowering

plants o\er the six years was 50.9 i: 0.9 cm (N = 190 plants). The average size of

tlowering plants differed significantly among years (F.s.isa = 7.243. P < 0.0001); flow ering indiv iduals were on average smaller in 2002 than in all other years (Tukey-

Kramer test, alpha = 0.05). Individuals in the small adult stage class (5 - 20 cm)

tlovvered in onl\ three of the six years. 1997. 2001. and 2002 (Figure 4). In all other

>ears. tlowering plants were at least 36 cm in rosette diameter. When individuals were separated into the small and large reproductiv e stage classes, the average size of small flow ering plants was 15.2 = 0.8 cm (N = 5 plants), and the average size of large flowering plants was 51.9 = 0.9 cm (N = 185 plants).

Rosette diameter was strongly and positively correlated with capitulescence length (Fim = 172.777. P < 0.0001; Figure 5). Rosette diameter was also strongly correlated with number of capitula on the capitulescence. with larger rosettes producing more capitula on the capitulescence (Fs- = 180.461. P < 0.0001; Figure 6). In addition to producing more capitula on the capitulescence. larger rosettes produced larger capitula containing more florets; rosette diameter was positi\ ely correlated with the number of

florets per capitulum (F|g = 15.840. P = 0.0009: Figure 7). Based on these allometric

relationships, it is possible to estimate the total number of achenes produced by flowerin

indi\ iduals of different sizes. Potential achene production for a given individual is

estimated as the product of estimated number of capitula and number of florets per

capitulum. based on plant size, as measured by rosette diameter (Figure S). Because the

relationship between rosette diameter and the number of florets per capitulum was only

established for plants 10 - 60 cm in diameter. I used the established relationships to

extrapolate potential achene production by plants larger than 60 cm in diameter. The

relationships between rosette diameter and reproductix e output predict that total achene

production will range tiom 306 achenes produced by the smallest flowering plant

measured in this stud\' (12 cm), to 140.854 achenes produced by the largest flowering

plant measured in this study (95 cm). Total achene production by an average-sized

flowering plant (50 cm) is estimated to be 41.815 achenes. These estimates of achene production, howex er. include florets that may not de\ elop into mature achenes due to predispersal seed predation or because of resource or pollen limitation.

Discussion

P\'.A.s based on matri.x models require demographic data for all parts of a species life c> cle. but for plant species some of this information may be difficult to obtain.

Reproducti\ e rates in particular are often hard to quantify due to cr\ptic aspects of plant life histories, such as seed dispersal and dormancy. In this study of the Haleakala sih ersvxord's reproductive biology, e.xamination of seed dispersal and dormancy lb suggested that a separate seed stage should be incorporated into a matrix model for this species. Strong correlations between rosette diameter and different components of reproducti\ e output enabled size-based estimates of reproduction to be calculated. These techniques ma\ provide an alternative way to quantity reproductive rates for matri.x model analyses, particularly when destructive sampling techniques are not an option.

SEED BIOLOGY

Sih ersword seed dispersal was minimal, indicating that there is likely to be no net dispersal of seeds into or out of study plots. .Appro.ximately 80% of all achenes dispersed less than 40 cm from the parent plant. This strongly leptokurtic seed dispersal pattern, seen at such a fine scale, is not surprising in this system, given the lack of animal seed dispersal, as well as the extremely reduced pappus on silversword achenes. Walker &

Powell (1995) presented similar results in a study on the .Mauna Kea silversword (.-I. sandwicense ssp. sanciwicense). in which achene dispersal was primarily limited to 1 - 2 m from the parent plant. .Although seeds could potentially disperse beyond plot boundaries if a parent plant was located near the edge of a plot, only 15% of plants in the plots are located within 40 cm of the plot boundary (Forsyth, unpub. data). It is also possible that dispersal of seeds out of the plots is balanced by dispersal of seeds into the plots from nearby flowering plants. In order to better understand silversword reproduction in the permanent plots, it may be usefril to note flowering and recruitment events that occur outside of, but very close to, the plot boundaries.

Achenes as old as four years germinated in the laboratory experiment, although

\ lability declined with achene age. These results are similar to those of Kobayashi 77

(19''3). who noted that Haleakala silversvvord achenes up to four years old still germinated, despite a marked reduction in v iability each year. Kobayashi's experiment, however, used achenes collected from the field immediately after tlowering and then stored in a refrigerator, and so did not test the ability of achenes to remain viable for multiple years under field conditions. In contrast, the results of this experiment suggest that achenes can remain in the field for several years, despite reduced viability with time.

This e.xperiment. however, tested the ability of achenes to germinate under laboratory conditions; age-specific germination rates in the field are unknown. It is likely that the results of the laboratory experiment, in which achenes were kept moist and were protected from temperature extremes, overestimate actual germination rates. Siegel et al.

(1970) found that silversword germination was heat sensitive, with no germination obser\ ed if achenes were exposed to temperature extremes (-15 or -35^C) for 8 hours or more. Due to the large range of soil surface temperatures observed at Haleakala. including freezing temperatures at night and davtime temperatures greater than 40'C

(Siegel et al. 1970. Kobayashi 1973), it is likely that germination rates are reduced in the field. For a matrix model designed to mirror conditions experienced by the natural population, it is reasonable to assume that the majority of recruitment is due to germination of newly produced and one year old achenes. and that rates of germination in the field are much reduced relativ e to those observed in the laboratory. Future studies of seed germination in the field should quantify germination rates relative to germination rates in the laboratory. 78

The results o*'this study suggest that a seed stage should be incorporated into a matrix model for the Haleakala silversword. Ho\ve\ er. the low rates of seed sur\ i\ al and seed germination of older achenes suggest that a seed bank is not as critical to sil\ ersword persistence as it is for some other plant species. This coincides well u ith predictions made by Doak et al. (2002). who estimated the relative importance of seed banks (and therefore the relati\ e importance of incorporating seed demography into

P\'.A.s) for different life histories. They predicted that seed banks are not important for long lived plants that experience minimal environmentally induced variation in adult performance. Silverswords li\ e for several decades before flowering and exhibit \ er\' little \ ariation in adult survival (Appendix C). In contrast, species that have shorter and more \ ariable life spans may rely hea\ ily on seed banks in order to persist (Thompson et al. 1998. Doak etal. 2002).

PLAST SIZE AND REPRODUCTION

Due to the strong correlations between plant size and reproductive output, it is possible to estimate the reproducti\ e rates of different-size plants. Nearly all plants that flowered in the six-year period were from the large adult stage class; only fi\ e of the 190 flowering plants included in this study were less than 20 cm in rosette diameter. The size distribution of flowering plants for each of the six years suggests that plants in the small reproducti\ e stage class make a minimal contribution to the following year's seed and seedling stage classes relative to plants in the large reproductive stage class. In addition to flowering less frequently, small adult plants produce many fewer achenes. The large difterence between the a\ erage size of small and large flowering plants exacerbates this

discrepancy in seed output.

A previous study on Haleakala silversword reproduction found no relationship

between plant size and percent seed set (Appendix A). Thus, although plant size has a

large etfect on the number of achenes produced, there is no effect on the proportion of

achenes that are tilled. This is in contrast to the prediction that larger plants will exhibit

disproportionatelv- higher seed set due to increased pollinator attraction (Brody &

Mitchell 1997, Ehrlen et al. 2002). .Although percent seed set was not correlated with

plant size. a\ erage percent seed set was significantly correlated with the number of plants

flow ering each > ear. with higher percent seed set observ ed in \ ears of greater flow ering

(.Appendix .A). In order to increase the accuracy of a matrix model analysis, size-

independent. density-dependent seed set can be incorporated into the sih ersword matrix

model, such that percent seed set is equal for plants in both flowering classes within a

year, but v aries among years as a tiinction of the number of flowering plants.

lNCORPOR.-\TrNG REPRODUCm'E BIOLOGY INTO .MATRIX .MODEL

The inclusion of a seed stage in the silversword matrix model makes it possible to quantity reproductive output by two size-based reproductiv e stage classes. The reproduction component of the silversword matrix model involves four life histor\- stage classes (small reproductive plants, large reproductive plants, seeds and seedlings) and six transitions among these stage classes. The six possible transitions include the contributions of each reproductive stage class to the seed and seedling stage classes: germination of seeds in the seed bank: and seed surv ival between years (Figure 9). 80

Within this model, each of these six transitions is described as the product of the

following variables: achene production (B). percent seed set (F). germination rate of

newly-produced (G) and older (Go) seeds, and survival rate of seeds (S) and newly

germinated seedlings (Sc) (Figure 9). Estimating reproductive transition probabilities as

the product of these separate components allows for easy manipulation of different

\ ariables in future analyses of the matrix model. For example. B can be altered to

incorporate variable levels of seed predation; F can be adjusted to vary according to the

abundance of flowering plants; and G and S may vary according to patterns of environmental variation, such as rainfall, that likely affect seed germination and seed and seedling surv ival rates. With this method, it is also possible to assess the relative effects of these separate components on population growth rate, rather than the total effect of each life history transition. For example, it would be possible to assess whether variation

in seed production is due to factors influencing seed set (F). such as pollination, or

factors influencing achene production (B). such as seed predation. Similarly, use of this

model, in conjunction with studies of germination in the field, could rev eal whether

recruitment is limited by germination rates (G or Go) or by the ability of new seedlings to surv ive to the following census (Sc).

The results of this study, combined with seed set estimates obtained elsewhere

(Appendix A), make it possible to estimate the values of these variables, in order to quantify plant reproductive success for matrix model analyses. For example, average- sized small reproductive individuals (rosette diameter = 15 cm) have the potential to produce approximately 3.000 achenes (Bjm). vvhereas average-sized large reproductive SI indi\ iduals (rosette diameter = 52 cm) have the potential to produce approximately

45.000 achenes (Big). These estimates, however, do not include achene loss due to two native predispersal seed predators. Rhynchephestia rhabdotis (Lepidoptera: Pyralidae) and Tnipanea craiericola (Diptera: Tephritidae). Seed predation has not been quantified here, but previous observations suggest that seed predation is variable among years and may reach \ ery high lev els, with up to 50 - 95° o of all viable silversword achenes consumed by the two seed predators in some years (Kobayashi 1974, Loope & Crivellone

19S6). Naturally occurring seed predafion therefore has the potential to drastically reduce these estimates of achene production, which are based on counts of florets prior to seed predation. For example, a 60° o level of seed predation. a reasonable estimate for this species, will reduce achene production by large reproductive individuals fi"om 45.000 to 1 S.OOO achenes. It is also important to note that within a year, levels of seed predation may v ary for plants of different sizes. Fermer et al. (2002) showed that larger capitula had higher rates of seed predator infestation, both within and among multiple species of

.•\steraceae. These impacts should be measured and incorporated into matrix models for increased accuracy of demographic projections.

In a stud\- conducted fi"om 1997 - 2001. percent seed set (F) ranged from 5°o to

45° o. with an average of 20° o seed set in a fair flowering year of approximately 1.000 flowering individuals (Appendix .A.). Seed vital rates, including germination (G, Go) and seed surv ival (S) probabilities, were found to be very low. particularly for achenes that are tw o or more vears old. Because the degree to which seed germination rates are reduced in the field is currently unknown, it is difficult to accurately estimate G and Go. 82

Ho\ve\ er. it is likely that G is between 5 and 60° o. with germination success \ ar\ing greath' among v ears. due to the influence of \ ar\ing environmental conditions. As seen in the germination experiment conducted here. Go is much lower, probably less than or equal to S^o. Due to limited information regarding seed survival rates, the seed stage has not been di\ ided into an age-structured seed bank. The only distinction made among different-aged seeds is between new ly-produced seeds and seeds that are already present in the seed bank. Thus. S. the proportion of seeds that surv ives in the seed bank, includes seeds of different ages and is weighted by the older seeds that have \ery low survival rates. Therefore, although the survival rate of newly produced seeds may be as high as

15°o. the very low survival rates of older seeds likely lowers this estimate to S^b or less.

Sc. the survival of newly germinated seedlings until the ne.xt census date, has not been measured here, but other work suggests that annual survival of established silversword seedlings is variable among years, ranging from 0 - lOO^o (Appendix C). However, this estimate is based on annual census data and therefore does not include seedlings that germinated but did not survive until the first census. Sc is likely lower due to the number of seedlings that germinate but that die prior to becoming well-established, possibly in the range of 5 - 10° o. The estimated values of these variables can be combined as shown in Figure 9. in order to estimate reproductive rates. For e.xample. in Table 1. we use the following estimates of the unknown variables in order to calculate the six reproductive transition probabilities: G = 0.05. Go = 0.03. S = 0.05. So = 0.04. Bsm = 3000. Big =

18.000. and F = 0.20. Based on these estimates, large reproductive plants produce 171 fertile seeds and 7 new seedlings, whereas small reproductive plants produce about 29 fertile seeds and 1 new seedling (Table 1). Future studies on the seed and seedling

biology of the Haleakala siK ersword will allow for a more detailed and accurate

demographic model for this species.

CONCLUSIONS

For many plant species, seed dispersal and seed dormancy make it difficult to

quantify- reproduction for use in matrix model analyses. The accuracy of these estimates.

howe\ er. may be crucial to the outcome of demographic projections. The inclusion of a

separate seed stage in a matrix model may be critical if seed dormancy plays a role in the

persistence of a population or species. A better understanding of species-specific patterns

of seed dispersal, as well as seed surv i\ al and germination rates, will help determine if a

separate seed stage is needed in a matrix population model. In addition, allometric

relationships between plant size and reproductiv e output prov ide a usefiil way to estimate

reproductiv e rates without having to use destructiv e sampling techniques. Reproductiv e

transition probabilities can be described as the product of their indiv idual components,

including seed production, seed set. and germination success, and this allows transition

probabilities to be estimated, even when data are limiting. Separating reproductiv e

transition probabilities into their individual components also adds flexibility to the matrix

model, and allows for easy manipulation of variables related to plant reproduction in

future stochastic simulations. These techniques can help elucidate the relative effects of different reproductive components on plant reproductive success, as well as on a population's growth rate and future persistence. 84

L1TER.\TURE CITED

Beissinger. S.R. (2002) Population viability analysis; past, present, future. Population viability analysis (eds S.R. Beissinger & D.R. McCullough). pp. 5-17. The University of Chicago Press. Chicago. IL.

Brody. .A..K.. & Mitchell. R.J. (1997) Effects ofe.xperimental manipulation of inflorescence size on pollination and pre-dispersal seed predation in the hummingbird- pollinated plant Ipomopsis aggregata. Oecologia. 110. 86-93.

Brook. B.W.. O'Grady. J.J.. Chapman. A.P.. Burgman. M.A.. .A-kcakaya. H.R. & Frankham. R. (2000) Predictive accuracy of population viability analysis in conservation biology. S'ature. 404. 385-387.

Carr. G.D.. Powell. E.A. & Kyhos. D.W. (1986) Self-incompatibility in the Hawaiian -Madiinae (Compositae): an exception to Baker's Rule. Evolution. 40. 430-434.

Caswell. H. (2001) Matrix population models, second edition. Sinauer .Associates. Sunderland. Massachusetts. US.A..

Cole. F.R.. Medeiros. .A.C.. Loope. L.L. & Zuehlke. W.W. (1992) Effects of the .•\rgentme ant on arthropod fauna of Hawaiian high-elevation shrubland. Ecology. 73. 1313-1322.

Doak. D.F.. Thomson. D. & Jules. E.S. (2002) Population viability analysis for plants: understanding the demographic consequences of seed banks for population health. Population viabilit}- analysis (eds S.R. Beissinger & D.R. McCullough). pp. 312-337. The University of Chicago Press. Chicago. IL. 85

Ehrlen. J.. Kack. S. & Agren. J. (2002) Pollen limitation, seed predation and scape length in Primula farinosa. Oikos. 97. 45-51.

Fenner. VI.. Cresswell. J.E.. Hurley. R..\. & Baldwin. T. (2002) Relationship between capitulum size and pre-dispersal seed predation by insect lar\ ae in common Asteraceae. Occologia. 130.12-11.

Howe. H.F. & Westley. L.C. (1986) Ecology of pollination and seed dispersal. Plant ecology- (ed M.J. Crawley), pp. 185-215. Blackwell scientific publications. Oxford. England.

Juvik. S.P. & Juvik. J.O. (1998) Atlas of Hawaii, third edition. University of Hawaii Press. Honolulu.

Kalisz. S. (1991) E.xperimental determination of seed bank age structure in the winter annual Collinsia \erna. Ecology. 72. 575-585.

K.alisz. S. & McPeek. M.A. (1992) Demography of an age-structured annual: resampled projection matrices, elasticity analyses, and seed bank effects. Ecology. 73. 1082-1093.

Kalisz. S. & McPeek. M.A. (1993) E.vtinction dynamics, population growth and seed banks. Oecologia. 95. 314-320.

Koba\ ashi. H.K. (1973) Ecology of the silversword .-irgyroxiphiiim sandwicense DC (Compositae). Haleakala Crater. Hawaii. Ph.D. Dissertation. University of Hawaii. Honolulu. Hawaii. 86

Kobayashi. H.K.. (1974) Preliminan" investigations on insects affecting the reproducti\e stage of the siKersword (Argyroxiphiiim sandwicense DC.) Compositae. Haleakala

Crater. Maui. Hawaii. Proceedings of the Hawaiian Entomological Society. 21. 397-402.

Loope. L.L. & Crivellone. C.F. {1986) Status of the Haleakala silversword: Past and present. Cooperati\ e National Park Resource Studies Unit. L'ni\ ersity of Hawaii. Honolulu, Tech. Rep. 58.

Loope. L.L. & Medeiros. A.C. (1994) Biotic interactions in Hawaiian high elevation ecos>stems. Tropical alpine environments: Plant form and function (eds P.\\'. Rundel. .A..P. Smith & F.C. .Vleinzer). pp. 337-354. Cambridge University Press. Cambridge. UK..

McCue K...A.. & Holtsford. T.P. (1998) Seed bank intluences on genetic diversity in the rare annual Clarkia spring\-illensis (Onagraceae). American Journal of Botany. 85. 30-36.

.Vlenges. E.S. (1986) Predicting the ftiture of rare plant populations: demographic monitoring and modeling. Satural Areas Journal. 6. 13-25.

Menges. E.S. (2000a) Population viability analyses in plants; challenges and opportunities. Trends in Ecology and Evolution. 15. 51-56.

Menges. E.S. (2000^) .Applications of population viability analyses in plant conservation.

Ecological Bulletin. 48. 73-84.

Oostermeijer. Brugman. M.L.. de Boer. E.R. & den Nijs. H.C..M. (1996) Temporal and spatial variation in the demography of Gentiana pneumonanthe. a rare perennial herb. Journal of Ecology. 84. 153-166. S"

Quintana-Ascencio. P.F. (1997) Population viability analysis of a rare plant species in patch\ habitats with sporadic fire. Ph.D. thesis. State L'ni\'. of New ^'ork at Stony Brook.

Reed. .Mills. L.S.. Dunning Jr.. J.B.. Menges. E.S.. .VIcKelvey. K.S.. Fr\'e. R.. Beissinger. S.R.. .A.nstett. .M.C. & Miller. P. (2002) Emerging issues in population viability analysis. Consenmion Biology. 16. 7-19.

Rundel. P.W. & Witter. M.S. (1994) Population dvnamics and flowering in a Hawaiian alpine rosette plant. Argyroxiphium sandwicense. Tropical alpine environments: Plant form and function (eds P.W. Rundel. .A..P. Smith & F.C. Meinzer). pp. 295-306. Cambridge L"ni\ ersit\' Press. Cambridge. UK..

Schemske, D.W.. Husband. B.C.. Ruckelshaus. M.H.. Goodwillie. C.. Parker. 1..M. & Bishop. J.G. (1994) Evaluating approaches to the conservation of rare and endangered plants. Ecology. 75. 584-606.

Siegel. S..M., Carroll. P., Com. C. &. Speitel. T. (1970) E.xperimental studies on the Hawaiian silvers words (Argyroxiphium spp.); some preliminary notes on germination. Botanical Gazette. 131. 277-280.

Thompson. K... Bakker. J.P.. Bekker. R..M. & Hodgson. J.G. (1998) Ecological correlates of seed persistence in soil in the north-west European flora. Journal of Ecology. 86. 163- 169.

Walker. L.R. & Powell, E..\. (1995) Factors affecting seed germination of the Mauna K.ea silversword in Hawaii. Pacific Science. 49. 205-211. ss

Table 1. Estimated probabilities of the six reproductive transitions. Transition probabilities were estimated as the product of the following variables: Bsm and Big

(achene production by small and large reproducti\e plants); G and Go (germination rates of nevv ly produced seeds and seeds already present in the seed bank; S and Sc (sur\ i\ al rates of seeds and seedlings); and F (percent seed set). The following estimates were

used in order to generate the si.x transition probabilities; G = 0.05. Go = 0.03; S = 0.05.

Sc = 0.04; = 3000. B,g = 18.000; F = 0.20.

t

Seed Sm. rep. Lg. rep.

1 Seed (1 - Go)S B,n,F(l-G)S Bi/(1 -G)S 0.049 28.500 171.000

I SeedUng GqSq Bs^FOSg BigFCSo

0.001 1.200 7.200 8Q

FIGURE LEGENDS

FIGL'RE I. The Haleakala silversword (Argyroxipliiim sandwiceiise ssp.

macroccphalum). Haleakala National Park. Maui. Hawaii.

FIGL'RE 2. Seed dispersal cur\ e for the Haleakala silversword. Bars represent the

proportion of collected achenes found in each 20 cm distance increment over 0 - 2 m

from each parent plant. N = 13 silversv\ ords that had flowered the pre\ ious year.

FIGLRE 3. Germination success of different aged Haleakala silversword achenes.

.A.chene age reflects the year in which achenes were produced (1997 - 2001). .A.11 achenes

were collected from the field and germinated in the fall of 2001. Bars represent the mean

(= 1 SE) percent germination for four (1997). five (1998-2000). and three (2001)

indi\ iduals. Percent germination is equal to the proportion of a 40-achene sample that

successfully germinated within the five-week trial. Germination success differed

significantly among the different achene age classes {.\NOVA; F4.1- = 38.641. P <

0.0001): letters above bars indicate statistically significant differences.

FIGL'RE 4. Size distribution of flowering Haleakala silverswords. Haleakala National

Park. .Maui. Hawaii. 1997 - 2002. Bars represent the proportion of all individuals measured that year that were in each rosette size class. 90

FIGURE 5. Correlation between rosette diameter (m) and capitulescence length (m) in tlovvering Haleakala sih erswords, Haleakala National Park. Maui. Hawaii. 1997 - 2002.

R- = 0.515. F = 172.777. P < 0.0001. N = 165.

FIGURE 6. Correlation between rosette diameter (m) and the number of capitula on tlowering Haleakala sih erswords. Haleakala National Park. Maui. Hawaii. Capitula were counted in 1997. 1998. 1999. and 2002. R- = 0.677. F= 180.461. P< 0.0001. N = 88.

FIGURE 7. Correlation between rosette diameter (m) and number of florets per capitulum. for flowering Haleakala sih erswords. Haleakala National Park. Maui. Hawaii.

Florets were counted in 2002 only. R" = 0.468. F = 15.840. P = 0.0009. N = 20.

FIGURE 8. Total achene production by different-sized Haleakala sih erswords. as estimated trom allometric relationships between rosette diameter and capitulescence length, number of capitula per capitulescence. and capitulum size (number of florets per capitulum). Estimates of achene production do not include achene loss due to predispersal seed predation.

FIGURE 9. Life cycle graph illustrating reproduction in the Haleakala silversword.

Reproduction in\ oh es four life history stages; small and large reproducti\ e plants, seeds, and seedlings. Light arrows indicate transitions to seed bank: dark arrows indicate transitions to seedling class. B = the number of florets produced by each small and large 91 reproducth e indiv idual: F = percent seed set; G = the germination rate of newly produced achenes; Go = the germination rate of achenes already present in seed bank:

S = the surv ival rate of achenes in seed bank until the following census; Sc = the survival rate of new seedlings from germination until census date. FIGURE 1 93

0.7

-y: 0.6 y I 0.5 0.4

.2 0.3

to.

~ 0.1

0

ri TI n riI n X. o ri

Distance from parent plant (cm)

FIGURE 2 Avg. % gcrniiniition _ — 4_

«—1—•

|— 1 C3-. rJ> O o nr c: m ni3 CO s ffQ Ui

CO 1/1"-I

- ^5

0.5 1997 X = 49.88. SD= 11.69 0.4 N = 65

-':yri 03

•yii

•sSftw 0.1 K-^ • 10 lo-iQ :o-:!Q 30-3Q 4o-;q 50-5Q "'o-^q SO-SQ qo-oo

0.5

1998 0.4 X = 56.92. SD= 13.81 N-26

0.3

OJ

0.1

'fj-

10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 Rosette diameter (cm) FIGURE 4 96

0.5 1999 .X = 54.63. SD= 10.83 0.4 N = :4

0.3

0.:

0.1

• m 10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99

0.5 2000 X = 59.78. SD = 8.87 0.4 N - 9

0.3

0.2

0.1 >•

10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99

Rosette diameter (cm)

FIGURE 4 (CONT'D) 97

2001 U 4 X = 51.1 l.SD= 13.95 N = 46

II 1

5Jj n u •

10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 >

2002 II 4 X = 37.60. SD= 12.18 N = 20

It;

I) I

10 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 Rosette diameter (cm)

FIGURE 4 (CONT'D) • 199" + 1998 A 1999 • 2000 x 2001 • 2002

1.6 . .

1.4

1.2IT •• ^ +•* + X * • • J-•• J^ > • 1 • + 5. -» A* O.S

0.6 •5 •• • +

0.4 • • +

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O.S 0.9 Rosette diameter (m)

FIGURES Q9

• 1Q97 + I9Q8 A IQOQ • 2002

400 • -

350

300 *4 -£= ^ A, • A • ^ -00 •5V ^ ' ++ 150 •*" V 10(1 ? •

50 •

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.^ Rosette diameter (m)

FIGURE 6 -UKI

350

3aT

250

200

150

100

50

0 0.1 0.2 0.3 0.4 0.5 0.6 Rosette diameter (m)

FIGURE 7 180.000

160.000

140.000

100.000

80.000

60.000

40.000

20.000

Rosette diameter (m)

FIGURES 102

Bi.FGS seedlms' BsmFGSc

Bsn.F(l-G)S C^(l-Go)S small reproductive seed bank

B,^F(1-G)S

large reproductive

FIGURE 9 APPENDIX C:

TE.MPOR.\L AND SPATIAL \ ARIATION IN THE

DEMOGR-APHV OF A THREATENED HAWAIIAN PLANT 104

TEMPOR.\L AND SPATIAL VARIATION IN THE

DEMOGR.A.PHV OF A THREATENED HAWAIIAN PLANT

Stacey A. Forsvth' and Lloyd L. Loope"

Department of Ecology & Ev olutionars Biology. The L'ni\ ersity of Arizona.

Tucson. AZ S5721

• L SGS-BRD. Haleakala National Park. P.O. Bo.x 369. Makawao. Maui. HI 9676S

Key words; demographic variation, elasticity analysis. Haleakala silversword. matri.x correlation structure, matrix population model, plant demography, population viability analysis (PV.A.). sensitivity 105

ABSTRACT

In the management of rare species, matrix population models are frequently used

to assess the v iability of populations and identify- the stages in a species' life histor%- that

have the greatest impact on its population growth rate. These models analyze parameters

estimated trom age- or stage-based monitoring data in order to better understand the

factors intluencing population growth and persistence. Here, we de\ elop a stage-based

matrix population model for the monocarpic Haleakala sihersword (Argyroxiphium

sandwicense ssp. macrocephaliim). a threatened Hawaiian plant species. We use 20

\ ears (19S2 - 2001) of demographic data trom eleven permanent plots located on fi\ e

cinder cones to examine temporal and spatial variation (at two spatial scales) in

demographic \ ital rates, population grow th rates, and sensitivit\' and elasticity

parameters.

The sih ersword's life history was described using seven life history stage classes: seed, seedling, juvenile, small adult, large adult, small reproductive plant, and large

reproducti\ e plant. From 1982 - 2001. the population in the plots declined by nearly

50" 0 (/. = 0.985). Sih ersw ord demography was characterized by very low mortality of adult plants, \ ariable seedling mortality, and high temporal and spatial variation in

flowering and seedling recruitment. Population growth rate (/.) varied over time and space, ranging from 0.88 (1998 - 1999) to 1.07 (1996- 1997). and from 0.93 in Plot 3 to

1.04 in Plot 5 over the entire census period. Reproductive value increased as individuals increased in size, with large adults and large reproductive plants having the highest reproductiv e \ alues. .Matrix model analyses predicted a stable stage distribution 106 dominated by seeds, with approximately 70" o of individuals predicted to be in the seed stage class. The observed and stable stage distributions (vegetative stage classes only) were similar, suggesting that the asymptotic analyses conducted here are relevant to the current dsnamics of this species.

Of all demographic transitions obser\ ed in the field, growth of small adults and seed germination had the highest sensitiv ities: population growth rate was also sensiti\ e to adult plant surv ival, tlowering of large adults, and juvenile growth. The highest elasticities were associated with stasis of small adult, large adult, and juvenile plants. In contrast, all elasticities associated with the seed and seedling stage classes were \ ery low.

This is similar to many other long-li\ ed species, for which adult sur\ i\ al often has the largest relative impact on population growth rate. .Although we observed quantitative

\ ariation in sensitivities and elasticities, the qualitative pattern remained fairly consistent o\ er time and space: adult plant growth and survival had the greatest relative impacts on

/. in all \ears and plots. Parameter sensitivity and elasticity were both strongly negativelv correlated with vital rate variability, such that the most variable transitions had the smallest impact on population growth rate. Temporal and spatial variation in /. was significantly correlated with variation in the elasticities associated with the seed. seedling, and large reproductive stage classes. Twelve pairs of transitions were significantly correlated, suggesting that different stage classes of the silversword life cycle respond similarly to environmental variation. This correlation structure should be incorporated into the silversword matri.x model for increased accuracy of fijture stochastic simulations. 107

rSTRODLCTION

Successful species management requires a thorough understanding of a species" biology, particularly the forces that influence population dynamics. Understanding both hou and why population numbers change o\ er time is critical regardless of whether the species in question is a rare or endangered species, in which case the goal is to increase the population growth rate; an invasive species, in which case the goal is to decrease the population growth rate and minimize or eradicate the population: or a resource species that is being har\ ested. in which case the goal is to maximize harvest and protit while simultaneously maintaining a viable population (Di.xon et al. 1997. Caswell 2001). In all cases, demographic analyses based on matrix population models are important tools that pro\ide useful and relevant information for species management (Schemske et al. 1994.

Casw ell 2001). These analyses describe how the number of individuals in a population or species changes o\ er time, and which life history stages have the greatest relati\ e impact on population growth rate (Schemske et al. 1994). Demographic analyses can determine the reproductive value of different age or stage classes, and provide insight into a population's stable age or stage distribution. In addition, matrix modeling of demographic data is the most appropriate way to identify the transitions in a species" life histor\- that are most critical to population persistence (Leslie 1945. Schemske et al. 1994.

Horx itz and Schemske 1995). This information is essential for determining which life historv' stages will be most effective to target for management, as well as for weighing the relatix e effectix eness of different management strategies. lOS

In the past uvo decades, increasing attention has been given to population

\ iability analyses (P\'As). and their potential to predict Hiture population size and e\ aluate extinction risk (Boyce 1992. Brook et al. 2000. Beissinger 2002). These studies use \ ital demographic rates obsen. ed in natural populations to estimate population growth rate and project future population size and structure under a \ ariety of scenarios.

Man\ of these studies also conduct sensiti\ ity and elasticity analyses, in order to weigh the relati\e contributions of different demographic transitions to the population growth rate. P\'.-\s based on matri.x models have been used to inform management decisions for a \ ariety of species, including loggerhead sea turtles (Crouse et al. 1987. Crowder et al.

1994). desert tortoises (Doak et al. 1994). cheetahs (Crooks et al. 1998). and various plant species (Oostermeijer et al. 1996. Ratsirarson et al. 1996. Gross et al. 1998).

In contrast to issues of species persistence, less attention has been gi\ en to the degree of temporal and spatial \ ariation in the demograph\' of natural populations (but see Horv itz and Schemske 1995. Oostermeijer et al. 1996). In part, this is due to the limited number of empirical demographic datasets that encompass multiple years and sites. Short time series are a common limitation of many demographic studies. .A recent sur\ e\ of plant PV.-\s found that the mean study length was five years and the median and modal study lengths were only four years (Menges 2000a). Only four of 99 plant studies were based on more than ten years of data (Menges 2000a). However. PVWs based on short-term datasets may fail to yield accurate results, particularly for long-lived species (Brault and Caswell 1993). There is some evidence that demographic parameters

\ar\ across both time and space (Mack and Pyke 1983. K.alisz and McPeek 1992. Horxitz 109 and Schemske 1995. Bender et al. 2000). and this \ ariation may ha\ e important implications for population stability and persistence (Vavxek et al. 1997). Gi\ en the potential effects of temporal and spatial variation in demographic \ ital rates. incorporating \ariation in demographic models may be critical (Schemske et al. 1994).

In this study, we used twenty years (1982 - 2001) of demographic data for the

Haleakala siKersword (Argy roxiphiim sanciwicense ssp. macrocephalum: Asteraceae:

Madiinae) to e.xamine the population dynamics of this threatened species and to assess the degree of temporal and spatial \ ariation in demographic parameters. We de\ eloped a stage-based matri.x population model for the siK ersword. with the following se\ en stage classes: seed, seedling. ju\ enile. small adult, large adult, small reproductive plant, and large reproducti\ e plant. Using a summarv' transition matri.x. in which data from all years and plots were pooled, we estimated population growth rate (/.). calculated the reproducti\ e \ alue of each life history stage, compared the stage distribution in 2001 to the predicted stable stage distribution, and calculated sensitivities and elasticities for all life histor\- transitions. To e.xamine temporal and spatial variation in silversword demography, we constructed transition matrices based on data trom 15 pairs of years and

11 plots. Using these matrices, we assessed variation in demographic vital rates, population growth rates, and sensitiv ity and elasticity parameters.

STUDY SITE ASD SPECIES

We conducted this research in the crater district of Haleakala volcano. Haleakala

National Park (HALE). Maui. Hawaii. US.A. (20° 44" N. 156° 13' W) (Figure 1). This area of HALE is comprised of alpine desert and subalpine shrubland habitats, which are 110 characterized b\- low annual precipitation, trequent frost, and large diurnal \ ariation in temperature {Ju\ ik and Juvik 1998). The cinder, ash. and lava landscape is dominated b\' a series of cinder cones that extends along the rift zone of Haleakala crater. Ele\ en permanent sih ersword demography plots are located on and among these cinder cones, at approximately 2300 m ele\ ation. Vegetation in this area of the crater is ver\' sparse and. in addition to the sil\ ersword. is comprised of a few dominant species, including

Diibaiitia menziesii (.A.steraceae). Sophora chrysophylla (Fabaceae). Sryphelia lameiameiae (Epacridaceae). and Vaccinium reticiilatum (Ericaceae). Precipitation in the siK ersword habitats av erages 1000 - 1500 mm per year, with much of this moisture arriv ing in the form of fog drip associated with a tradewind inversion present at about

2000 m (K.obayashi 1973. Loope and Medeiros 1994). Similar to other tropical alpine env ironments, diumal v ariation in temperature tvpically exceeds annual v ariation in mean dailv temperature (Juvik and Juvik 1998).

The Haleakala sihersword. shown in Figure 2. is a long-lived, monocarpic rosette plant endemic to East Maui. Hawaii. Plants of this species grow on cinder cones and lava flows within Haleakala crater (2000 - 3000 m). as well as on tlie outer slope near the volcano's summit (3000 - 3341 m). The Haleakala sih ersword is one of thirty species in three genera that comprise the Hawaiian sih ersword alliance, a monophyletic lineage descended from North .A.merican tarweed ancestors (Baldwin 1996). An excellent example of adaptive radiation in plants, this group displays a wide variety of growth forms, including trees, shrubs, rosette plants, and lianas (Carr 1985). The Haleakala sih ersword grows for many years as a single basal rosette, produces a tall flowering stalk (capitulescence) with hundreds of radiate flowerheads (capitula). and dies soon after

setting seed. Flowering within the population occurs over a period of several months,

typically peaking in July; each reproductive individual is in flower for about one to three

weeks (Forsyth, unpub. data). Previous studies have demonstrated that the sihersword is

highly self-incompatible and requires insect pollination, primarily by native yellow-faced

bees (Hylaciis sp.; Carr et al. 1986. .\ppendix A). As one of the few plant species found

throughout the western half of Haleakala crater, the sih ersword is an important resource

for man_v nati\ e insect species, including pollinators [Hylaeiis spp. (Hymenoptera:

Colletidae)]. seed predators [Tnipanea cratericola (Diptera: Tephritidae).

Rhynchephcsiia rhabdotis (Lepidoptera: Pyralidae)], and herbi\ores [.\'esodyne argyroxiphii (Hemiptera; Miridae). Plagithmysus fern.-/(Coleoptera: Cerambycidae)]

(Loope and Medeiros 1994).

.A.lthough once abundant at H.A.LE. the sihersword population suffered se\ ere declines in the late 19'^ and early 20'*^ centuries, primarily due to grazing by introduced goats and cattle, as well as human vandalism (Loope and Crivellone 1986). This combination of threats reduced the sih ersword population to a low of approximately

5.000 individuals in the 1920s (Loope and Crivellone 1986). TTie removal of these

threats, however, allowed the species to make a substantial recovery in the past several decades, with sih ersword numbers having increased to about 50.000 indi\'iduals by the

mid-1980s (Loope and Crivellone 1986). Population censuses initiated in 1971 and conducted e\ er\- ten years suggested an initial increase to more than 60.000 plants in

1991. followed by a subsequent decline to approximately 50.000 individuals in 2001 (F. 112

Starr, pers. comm.). Current threats to the siKersword include the in\asions of the

Argentine ant (Lincpithema humile) and western yellowjacket (I'espulapensytvanica). which pre\' on native insect species, including pollinators such as Hylaeus (Cole et al.

1992). In 1992. the Haleakala sih ersword was federally listed as a threatened species

(L'.S. Fish and Wildlife Service 1992).

METHODS

Haleakala sihersword demography and matrix model

In 1982. H.A.LE researchers established eleven 5 .\ 20 m permanent plots on cinder cones throughout Haleakala Crater. The four comers of each plot were marked b\' a short piece of P\'C pipe, as shown in Figure 3. The plots initially averaged 35-40 plants per

100 m". and combined, contained approximately l°o of the total sihersword population

(Loope and Crivellone 1986). Plots 1 and 2 are located near the top of Puu Nole. with

Plot 1 located slightly east of Plot 2; Plots 3.4. and 5 are located on Puu o Pele (northeast slope, northwest slope, and cinder cone crater, respectively); Plot 6 is east of Puu o Maui;

Plots 7 and S are located on the upper west slope of K.a-Moa-o-Pele. with Plot 7 located north of Plot S; and Plots 9. 10. and 11 are located on Puu Naue (northwest, northeast, and east slopes, respectively). Plot locations are shown in Figure 4.

In the first year of the study (1982). all of the plants in the plots were mapped onto a detailed grid and assigned to one of the following five stage classes, based on rosette diameter and reproducti\ e status: seedling. < 5 cm, 5-20 cm. > 20 cm. and flowering plant. The plots were censused in early October of ever\' year from 1982 -

1992 and from 1996 - 2001. All censusing was conducted by observers standing beyond 113 plot boundaries in order to minimize impact on the substrate and plants within the plots; thus, in all years, plot maps were used to identity- plants by their location. Each year, individuals were placed into one of the five stage classes, based on estimated rosette diameter and reproductive status. Dead and missing individuals were recorded, and the plots were thoroughly searched for new seedlings, which were then added to the plot map and dataset. In 2001. we estimated the rosette diameter of all individuals, in order to compare rosette diameter with plant age. as determined by the year in which each indi\ idual was first added to the study.

The plot surveys conducted fi-om 1982 - 2001. with the exception of the three- year hiatus from 1993 - 1995. vielded data for 15 annual transitions. To anal\7:e these data, we de\ eloped a stage-based matri.x population model (Letkovitch 1965) for the

Haleakala silversword. In plants, stage-based (Letko\ itch) models are typically preferred to age-based (Leslie) models because indi\'idual fates are often better correlated with size or stage than with age. and because it is often difficult, if not impossible, to determine the age structure of a plant population (Harper 1977. Werner & Caswell 1977. Schemske et al. 1994). Based on the data collected ft"om 1982 - 2001. we constructed a 7 x 7 matrix model, using the following stage classes, which were defined by rosette diameter and reproducti\ e status:

0. seeds, which are produced in abundance approximately 8-10 weeks after

tlov\ ering. Sih ersword achene (fiuit) production is positively correlated with

rosette diameter (.A-ppendix B). Percent seed set is positively correlated with

flowering plant abundance, but is independent of plant size, with small and large 114

reproducti\ e plants exhibiting similar percent seed set. Achenes have a highly

reduced pappus and very low dispersal, such that the large majority of achenes fall

\ er\' close to the parent plant (Appendix B). Although the ability to germinate

declines markedly with seed age. it is possible for seeds at least as old as four years

to germinate (.Appendix B).

1. seedlings. Newly-established indi\ iduals. By definition. indi\ iduals remain in

the seedling class for only one year following germination. If a seedling sur\ i\ es

to the following year, it is considered to have advanced to the juvenile stage class,

regardless of size.

2. juvenile rosettes. Non-reproducti\e plants less than 5 cm in diameter.

3. small adult rosettes. Non-reproductive plants 5-20 cm in diameter.

4. large adult rosettes. Non-reproducti\ e plants greater than 20 cm in diameter.

5.6. flowering plants. The Haleakala silversword is monocarpic and all flowering

plants die soon after setting seed. In this study, we distinguish between small

(stage class 5; 5 - 20 cm) and large (stage class 6; > 20 cm) reproducti\ e plants,

based on their rosette diameter prior to tlowering.

Vegetative rosettes were divided into three stage classes - juveniles, small adults, and large adults - in order to separate individuals e.xhibiting large differences in vital rates, but at the same time to maximize sample sizes widiin stage classes (Moloney 1986). The choice of these stage classes was based on the observation that 5 cm and 20 cm are key sizes influencing plant sur\ ival and tlowering. Plants < 5 cm do not flower and tvpically 115

ha\ e lower sur\ i\ al rates than larger plants: plants 5 - 20 cm rosette diameter rarely

flower, and have higher surviv al rates than individuals < 5 cm; plants > 20 cm commonK

flower and have very high survival rates. Although the large adult rosette stage class

includes a large range of rosette diameters (currently 21 - 50 cm), there is ver\' little

variation in the probabilities of flowering and surviving among plants in this stage class.

We used the Tabulation command in Systat (SPSS 1998) to obtain the

probabilities of ten transitions observed in the field, including growth, stasis, regression,

and tlowering. The probability of death for each stage class was not explicitly calculated

hut was equal to one minus the sum of all other transition probabilities trom each stage

class. We generated a summary transition matri.x for all years and plots combined, as

well as an average matrix, in which matrix entries represented the average transition

probability among years, with all plots pooled. We examined temporal variation in

transition probabilities, population growth rates, and sensitivity and elasticitv- parameters

b> generating a summar\' matrix for each armual transition, for a total of 15 annual

transition matrices, in which data trom all plots were pooled. We also examined spatial

variation in these parameters at two spatial scales, among plots and among cinder cones.

In these analyses, we examined demographic variation among 11 plot transition matrices, in which data from all years were pooled, and among five cinder cone transition matrices, in which data from all plots on each cinder cone (Puu Nole. Puu o Pele. Puu o Maui. Ka

Vloa o Pele. and Puu Naue) were combined and all years were pooled. The cinder cones represent separate geographic units within Haleakala crater, and pooling together data from the plots on each cinder cone allows to us to examine spatial variation in 1 16

sil\ ersvvord demography while minimizing the problems associated with small sample

sizes in the separate plots. Using the three sets of transition matrices (years, plots, cinder

cones), we calculated the variance and coefficient of variation (CV = SD mean x 100) of

each of the ten transition parameters quantified in the field across time (years) and space

(plots and cinder cones).

Estimating reproduction

population projection matrix A is comprised of two parts: T. which includes all

transitions to stage classes via growth, stasis, or regression, and F. which includes all

matrix entries related to reproduction (Caswell 2001). In this study. T was obtained b\' calculating transition probabilities observed in the permanent plots, as described abo\ e.

Hov\ e\ er. because we conducted all monitoring from beyond plot boundaries in order to minimize disturbance to the study plants, we did not collect fruits or directly measure

fecundity of reproductiv e individuals. We therefore do not have a direct measure of reproduction to include in the matrix model analyses. In order to estimate siK ersword reproduction, we first attempted to quantify' plant reproductive success as the number of seedlings observ ed in year t div ided by the number of reproductive adults in year r - \ .

However, in a number of years seedlings germinated in plots following years of no flowering in these plots. This indicated that this method did not accurately quantity- reproduction. In addition, seed germination trials demonstrated that siK ersword seeds can remain viable in the field for multiple years, suggesting the presence of a small seed bank (.A.ppendix B). We therefore incorporated a seed stage into our model, and estimated the six unknown transition probabilities among the reproductive, seed, and 1 r seedling stage classes as a function of the following variables; B5 and the number of achenes produced b\' small and large reproductix e plants, respectix ely; F. percent seed set; G and G„. the germination rate of new seeds and seeds already present in the seed bank, respectively; and S and Sc. the probability that seeds and newly germinated seedlings. respecti\ ely. will sur\ i\ e to the next census date. The reproduction component of the siK ersword life cycle graph, including all stage classes, transitions, and \ ital rate estimates, is shown in Figure 5. Of these variables. 85. Bo. and F were measured in a 5-

\ear stud\ on siK ersword reproductiv e biology; G. Go. S and Sg were estimated in germination expenments using different-aged achenes (.A.ppendix B). Achene production

(B) v\ as strongh' size-dependent, and B5 and Bh were estimated based on an established relationship between rosette diameter and achene production, in conjunction with data on the ax erage rosette size of plants in each reproductive stage class. In the germination experiments, seeds up to four years old germinated, although the ability to germinate declined with seed age. such that seeds two years old and older had \ ery lov\' rates of germination.

Silversword matrix model

\\'e used the following matrix model for all analyses:

nit + I) =\ \n(t) (eq. I) where n{t) is a vector of all indix'iduals in the population at time i and A is the matrix that describes how mdividuals transition among different stage classes within one time unit.

In this studv. the time unit is one year and .A is a 7 x 7 matrix (Table 1A and B). Each entn. of the matrix, a,,, represents the probability that an individual in stage class j (in 118 matrix column) will transition to stage class / (in matrix row) within one time interval.

Thus, when / > j. the transition is one of growth; when i = j. the transition is one of stasis, and when / < J. the transition is one of regression. In this study, the top row of the matrix represents contributions to the seed stage, either through seed surv ival (ami) or through seed production by small (ao^) or large (a^w) reproductive plants. The second row represents recruitment, with seedlings germinating from newly dispersed achenes from small {a:5) or large (air,) reproductive plants, or from seeds already present in the seed bank (am). In Table 1B. the matrix entries for all contributions to the seed and seedling stage classes (e.g.. ami) are shown as the product of their individual components (e.g.. B5.

. F. G. G,,. S. Sq). The third, fourth, and fifth rows of the matrix summarize plant survivorship. Stasis of juveniles (a;:), small adults (ai.;). and large adults (a.-j) is shown on the main diagonal, grouth (a:;, a;:, ajj) is on the sub-diagonal, and regression to smaller sizes (a; ,-. a ;j) is above the main diagonal. The bottom two rows of the matrix represent the probability that small (ass) and large (a^) adults will tlower. Because the transition matrix implicitly includes mortality rates, the sum of all transition probabilities from a given stage class may be less than one.

Matrix properties

The matrix population model summarizes how a population changes over time, in terms of both the number and relative distribution of individuals in different stage classes.

Certain mathematical properties of the matrix have valuable biological interpretations.

The dominant eigenvalue of the matrix corresponds to the asvmptotic population grou th rate. where In /. = r, the instantaneous grov^th rate (Caswell 2001). A stable 119

population, in which the number of individuals is neither increasing nor decreasing, is

represented by /. = 1. When a. is greater than 1. the population is increasing: when /. is

less than 1. the population is decreasing. Estimates of /. are often used to project ftiture

population size and evaluate extinction risk, but can also be used to compare the success or fitness of a population across time and space (Hor\ itz and Schemske 1995).

Researchers frequently use reproductive success as a measure of fitness, but it is more

useful to use population growth rate as currency; for many species, particularly long- li\ ed organisms, fecundity is not the most critical factor determining population \ iability

(Hor\ itz and Schemske 1995. Crone 2001). In addition to comparing /. across time and space, it is also possible to assess how changes in different vital rates affect in order to quantify- the relative impact of different threats or management strategies on the population growth rate (Ehrlen and Van Groenendael 1998).

The eigenvectors associated with /. also correspond to biological properties of the population. The left (row) eigenvectors correspond to the reproductive value, v. of each stage class (Caswell 1982). The reproductive value of each stage class is the predicted fijture contribution of an indi\ idual in that stage class as a parent. This value includes both estimated reproductive output, as well as the probability of surviving to reproduce.

The nght (column) eigenvectors correspond to the stable stage distribution, w. or the proportion of indi\ iduals in each stage class when the asymptotic population growth rate is realized (Caswell 2001). The stable stage distribution is independent of the initial population size or distribution; no matter what the starting frequencies, the relati\ e distribution of individuals among the different stage classes will converge on the stable 120 stage distribution. Comparisons berween the obser\ ed and stable stage distributions are useful in determining the relevance of the asvmptotic analyses to a population's current beha\ ior. If a population's stage distribution is substantially different from the stable stage distribution, its beha\ ior may differ from that predicted by the asvmptotic properties of the model (Hor\ itz and Schemske 1995).

Sensitivin- and elasticity- analyses

Further analyses of the left and right eigenv ectors produce sensitivity and elasticity values (Caswell 1978. de Kroon 1986. Caswell 2001). which assess the importance of each life history transition to the population growth rate. Sensitivity is the slope of/, with respect to a perturbation in a particular transition parameter (Caswell

1978). If a small perturbation in a particular transition probability has a large impact on

that transition parameter has high sensitivity. Sensitivities are calculated for all matri.x parameters and as a result, provide insight into the potential for selection to act on traits affecting different life histor\' transitions (Horvitz and Schemske 1995. Caswell and Kaye

2001). One drawback to sensitivity analysis is that sensitivities are affected by the scale of the demographic transition probabilities, and thus it may be difficult to compare the sensitivities of different types of transitions, particularly for transitions that have \ ery different values (Horvitz and Schemske 1995). For example, matrix entries related to reproduction may be very high (potentially » 1). whereas matrix entries describing survi\ al or growth are always less than or equal to one.

Comparisons across different life history stage classes, however, are readily done with elasticity analyses, which measure the proportional sensitivity of population growth rate to each transition parameter (de ICroon et al. 1986). Elasticity is the product of the sensiti\ it\' and the transition probability of each parameter divided by the population growth rate (de Kroon et al. 1986). Thus, unlike sensitivities, elasticities are only calculated for transitions that naturally occur and therefore have nonzero values in the matrix. Essentially, elasticities represent the relati\ e contribution of each life histor\- stage class and transition to the population growth rate. Transitions associated with high elasticities ha\ e relati\ ely large impacts on population growth rate, whereas transitions associated with low elasticities have relatix ely low impacts on population growth rate.

The elasticities of an entire matri.x sum to one. allowing for easy comparison of the elasticities associated with different transition parameters (Hor\ itz et al. 1997).

Matrix analyses

We used a deterministic model based on the summarv- matri.x (all years and plots pooled) to estimate the population growth rate (/.). calculate the reproducti\e \ alue of each stage class, and determine the stable stage distribution. .A-S is true for all subsequent matrix anaK ses described in this paper, these analyses were performed with L'L.M

(Legendre and Clobert 1995) and M.A.TLAB (The .MathWorks. Inc. 2001) software. We calculated the stable stage distribution for all stage classes (including seeds) and for

\ egetatix e stage classes only. We then performed a chi-square test to compare the stable stage distribution (\egetati\e stage classes only) to the stage distribution observed in

2001. We used the distribution without seeds for this analysis because the number of seeds in the seed bank was unknown. To measure the difference between the observ ed and stable stage distributions, we also calculated the proportional similarity inde.x (PS). 122

PS = L„'"' min (a,, bi)\ 100. (eq. 2) where n is the number of stages, a,- is the proportion of individuals in the i''' stage of the stable stage distribution, and A,- is the proportion of individuals in the i''' stage of the observed stage distribution (Horvitz and Schemske 1995). We also used the summar>- matrix to calculate the sensiti\ ities and elasticities of all matrix parameters: these were compared in order to determine which sih ersword life historv' transitions have the greatest impact on population growth rate. We compared the total elasticity associated with each stage (calculated as the sum of elasticities of all transitions from each stage class), as well as how the total elasticity was distributed among transitions of growth (G). sur\ i\ al (L: includes both stasis and regression), and reproduction (F). In order to estimate the number of years an individual lives prior to flowering and death, we used

MATL.A.B to calculate the a\ erage length of time spent in each stage class.

Matrix correlation structure

Pre\ ious studies ha\ e suggested that matrix parameters are frequently correlated with each other, and that this correlation structure has important implications for population dynamics (Doak et al. 1994. Nakoaka 1996. Fieberg and Ellner 2001. Morris and Doak 2002). However, short-term demographic studies are limited in their ability to address this issue. To examine the correlation structure of the silversword matrix model, we conducted correlation analyses betw een all pairs of transitions, for a total of 45 pairwise correlations. These correlations were based on transition probabilities from the

15 annual transition matrices (i.e.. N = 15 transition probabilities for each correlation). Temporal and spatial variation in silversn ord demography

We used the summary transition matrices constructed for each pair of years, each plot, and each cinder cone to examine temporal and spatial variation in demographic vital rates, population growth rates, and sensitivity and elasticity parameters.

I Ital rates. We estimated vital rate \ ariability by calculating the variance and coefficient of \ ariation (SD mean x 100) among years, plots, and cinder cones, for each of the ten transition parameters quantified in the field. We used these estimates to compare the degree to which different transition parameters \ aried across time and space. We also used correlation analyses to examine the relationship between parameter variability and parameter sensiti\ ity and elasticity.

Population growth rate. We calculated /. for each annual transition, plot, and cinder cone, and examined the degree to which population growth rate varied o\ er time and space. We compared the population growth rate predicted by the transition matrices for each annual transition, plot, and cinder cone, to the change in population size observed in the field and quantified by the following equation:

^ = |log(nq/no)|/tq (eq. 3) where n is the number of individuals at fime 0 and time q; t is time: q is the number of time intervals separating the two census dates: and = 1 - a. (Dennis et al. 1991). This approach, based on a stochastic model of exponential growth in age- or stage-structured populations, estimates population growth rates using time series data on population size

(Dennis et al. 1991). In calculating annual population growth rates, n = the total number of plants in all plots combined and q = 1 for each pair of years. The one exception to this 124

is the 1992 - 1996 transition, due to the three-year gap in plot surveys trom 1993 - 1995;

for this transition, q = 4. In calculating the population growth rates observ ed in the plots

and on the cinder cones, n = the number of plants in each plot, and in all plots combined on each cinder cone, respectively, and q = 19 (1982 - 2001).

Damping ratios. To assess the relevance of the asvmptotic analyses conducted here, we calculated the damping ratios for each annual, plot, and cinder cone transition matrix.

The damping ratio (/.| /.;. where }.\ is the dominant eigenvalue of the matrix and /-: is the matrix eigenvalue with the second largest magnitude) summarizes the rate of convergence of a population to its stable stage structure. The higher the ratio, i.e.. the larger the value of/.i relative to the other eigenv alues, the faster the population will converge on the stable stage distribution (Caswell 2001).

Scnsiriviry- and elasticity parameters. Using the matrices described abov e, we also examined temporal and spatial variation in sensitivity and elasticity parameters. W'e graphed the sensitivities and elasticities of all naturally-occurring transitions and examined how the distribution of sensitivities and elasticities varied over time and space.

For each set of transition matrices (years, plots, and cinder cones), we calculated the mean elasticity value and coefficient of variation of each transition parameter. We also calculated the total elasticity of each stage class for each annual transition, plot, and cinder cone, as well as the total elasticity associated with transitions of growth, survival, and reproduction. We used correlation analyses to evaluate relationships between

\ ariation in the total elasticity of each stage class and k, and between variation in the elasticity of each matrix entry and across both time and space. In order to assess how 125 the distribution of elasticit\- affects we graphically examined the relationship between these v ariables for all years and plots.

RESULTS

Demographic transitions

This twenty-year study followed the fates of 879 indiv idual plants. None of the indi\ iduals in this study passed through the entire life cycle (i.e.. seedling through flowering and death) in the twenty-year period. Plants trequently remained in the juv enile and adult stage classes for many years before advancing to the ne.xt stage class.

.•\\ erage rosette diameter was positively correlated with plant age. although there was much variation in size among plants of the same cohort (i.e.. individuals that germinated in the same year) (Figure 6).

The silversword life cycle graph depicts all demographic transitions observed from 1982 - 2001 (Figure 7). In total, there are sixteen possible transitions among the seven different stage classes. Ten of these are transitions among the different vegetative stage classes or trom v egetative to reproductiv e stage classes; growth of seedlings, juveniles, and small adults to the next stage class; stasis of juveniles, small adults, and large adults; regression of small and large adults to the previous stage class; and flowering of small and large adults. Individuals were never observed to skip a stage class, either through growth or regression, within one year. The probabilities of the ten transitions summarizing growth, survival, and tlovvering were quantified in the permanent plots. The remaining six transitions are from the reproductive stage classes and the seed 126 stage class to the seed and seedling stage classes. The probabilities of these transitions v\ ere estimated as prev iously described.

The summar\' and average transition matrices are shown in Tables 2 and 3. In general, the summarv' matrix is a better representation of a population's demographic transitions, because it weighs the transition probability of each year according to the number of individuals that made the transition each year (Horv itz and Schemske 1995).

In contrast, the average matri.x weighs the transition probabilities of all years equally, regardless of how many (or few) individuals made that transition each year. In this study, the summarv and average matrices are very similar. TTie largest discrepancy between the summary and average transition matrices is in the survival of the seedling class (a;/).

The number of seedlings present in the plots varied greatly among years, as did rates of seedling surv ival. For some seedling cohorts, the survivorship curve dropped dramatically within the tlrst year. v\ hereas other cohorts exhibited much higher rates of seedling survival, resulting in tlatter survivorship curves (Figure 8). Due to its equal weighting of all years, despite the large variability in the number of seedlings among

V ears, the av erage matrix predicts a higher probability of seedling survival (aj; = 0.690) than does the summarv- matrix (a:: - 0.588).

Stasis of small iay,) and large (a^) adults had the highest transition probabilities, followed closely by stasis of juveniles (azz)- Plant survivorship increased with increasing rosette size, such that large adult rosettes had close to a 100 percent chance of surviving to the next census date (Figure 9). Small and large adult plants occasionally regressed to the pre\ ious stage class, but these transitions were rare (2.2% and 2.5% of all transitions from these stage classes, respectively). Regression occurred most trequently in dr\' years, when outer rosette leaves died, causing the rosette to "shrink". The probability of transitioning to the ne.\t stage class was also much lower than the probability of stasis. a\ eraging 9. ["/o for juveniles (a:,;) and 4.0% tor small adults (<343)- Most tlowering plants reached this stage from the large adult stage class; plants in this stage class had a 7.0° 0 probability of tlowering, compared to a 0.3% chance of tlowering for plants in the small adult stage class.

Average duration of each stage class

Based on the observed demographic vital rates, we used MATLAB to calculate the a\erage time an individual silversword spends in each stage class (Figure 10). On a\ erage. an individual spends about 6 years as a juvenile, 12 years as a small adult, and

10 years as a large adult, before either moving to a different stage class (either through growth or regression) or dying. When the average time spent as a seed and as a seedling is also considered (one year in each stage class), a silversword may, on average, live for

20 years before tlowering as a small adult, or for 30 years before tlowering as a large adult. However, the estimates of stage class duration include individuals that died before ad\ ancing to the ne.xt stage class and may therefore underestimate the actual duration of each stage class. In addition, there is high variation among individuals in the number of years spent in each stage class (Figure 10); this suggests that there is substantial variation in the life span of an individual silversword, and that the silversword life span commonly e.xceeds several decades. 12S

Population growth rale

From 1982 - 2001. the total number of individuals in the 11 permanent plots

decreased trom 448 to 228 (Figure 11). This decline was not steady: there was much

fluctuation in the first half of the study, primarily due to years of high recruitment

followed by years of high seedling mortality. A portion of the decline can be attributed

to post-tlowering mortality, in which flowering plants died without replacing themseK es.

However, in the last fi\e years of the study, the majority of the decline was due to the

loss of juveniles and small adults. Although these stage classes typically have high

surv ival rates, larger numbers of individuals in these classes died between 1997 and 2001

than in other years of the study, most likely because of the drought conditions in these

\ ears. Based on the time series estimate of population gro\\th rate (eq. 3: Dennis et al.

1991). the decline fi'om 448 to 228 indiv iduals over a 19-year period corresponds to a

population growth rate (/.) of 0.985.

Reproductive value

Reproductive value increased as individuals grew and advanced to the ne.xt stage class (Figure 12). For the \ egetative stage classes, reproductive value ranged from 0.047

for seedlings to 0.309 for large adult plants. Reproductive value declined sharply if small adult plants flowered; the reproductiv e value of small reproductive plants was only slightly greater than that of seedlings (0.058). Large reproductive plants had the highest

reproductive \ alue. equal to 0.350. 12^

Stable stage distribution

In the stable stage distribution predicted by the summarv' matrix, the large majority of siherswords (- 70°o) were in the seed stage class (Figure 13A). The remaining indi\ iduals were dixided among the other six stage classes, with the largest proportion in the small adult and juv enile stage classes. In the stable stage distribution, a

\ er\ small proponion of indiv iduals were in the seedling and reproductiv e stage classes.

When the stable stage distribution was recalculated to include \ egetati\ e stage classes only, the observ ed and stable stage distributions were similar (PS = 89.34 "o; .V" = 9.90. df = 5. P > 0.05; Figure 13B). suggesting that asymptotic analyses are relevant for current silv ersword population dvnamics. The largest difference between the observed and stable stage distributions was in the proportion of individuals in the seedling stage class: only

2"o of plants in the plots were in the seedling stage class, compared to 9°o of plants in the stable stage distribution. The observ ed distribution also contained more large adults than did the stable stage distribution (Figure 13B). Proportions of individuals in thejuvenile. small adult, and reproductive stage classes were similar in the two distributions (Figure

13B).

Sensitivity analyses

The sensitivities of all matrix transitions are shown in Figure 14. Typically, transitions to the large adult and large reproductive stage classes had the highest sensitivities, indicating that these transitions have a large effect on /. (Figure 14A and B).

Of all naturallv -occurring transitions among the vegetative stage classes, growth of small adult plants had the highest sensitivity, followed by flowering of large adults, growth of ju\eniles. and stasis of large adults (Figure 14A). Transitions from both reproductive stage classes to all other stage classes had \ erv' low sensiti\ities (Figure 14A). All transitions to the seed stage class had very- low sensitivities, ranging from 0 to 0.0009. Of these transitions, the contribution to the seed stage class by seeds already in the seed stage class (i.e.. seed sur\ival) had the highest sensitivity. Transitions from the seed stage class had higher sensitivities than the sensiti\ ities from all other stage classes, ranging up to 5.24 for the seed to large reproductive transition (ow))-

Elasticity analyses

Elasticities indicate the proportional sensiti\ ity of population growth rate to different life history transitions. Stasis of small adults, large adults, and juveniles had the highest elasticities, suggesting that these transitions make the greatest relati\ e contributions to /. (Table 4). .A.11 parameters associated with reproduction (i.e.. all transitions to the seed and seedling stage classes) had very low elasticities (Table 4).

Small adult plants had the highest total elasticity (0.4514). followed by large adults

(0.3S39) and juveniles (0.2102; Figure 15.A). Seedlings and large reproductive plants had similar, much smaller total elasticities. 0.057 and 0.056. respectively (Figure 15A).

Seeds (0.0017) and small flowering plants (0.0009) had the smallest total elasticities

(Figure 15.A.). By far. the greatest total elasticity was associated with sur\i\al (0.8469). followed distantly by growth (0.0948) and reproduction (0.0583; Figure 15B).

Correlations among matrix parameters

Twehe pairs of matri.x transitions were correlated (Table 5). Of these, seven pairs of transitions were positi\ ely correlated and five pairs were negatively correlated 131 with each other. Matrix elements representing the same type of transition were often

positi\ ely correlated with each other. For e.xample. growth of seedlings [a:;) was

positi\ely correlated with growth of juveniles (aj.--) and small adults and growth of the latter two stage classes were positively correlated with each other. Regression of small (a:;) and large adults were also positively correlated. Flowering of the two adult stage classes ar,^) was strongly positively correlated (P < 0.001). Flowering of small adults {a>;) was negatively correlated with large adult survival (ajj). Howe\ er. negati\ e correlations were primarily found between transitions originating from the same stage class (e.g.. azz and a;;, az:- and axy. and ^44 and were negatively correlated).

This is not surprising, as transitions trom one stage class to another automatically reduce the number of individuals that can transition ft-om that same stage class to a different fate.

Temporal and spatial variation in silversword demography

Demographic vital rates. Of the ten demographic transitions measured in the field, stasis of ju\eniles (a;;), small adults (ay,), and large adults {^44) showed the least variation among years (Table 6A). The greatest among-year \ ariation in demographic vital rates was seen in the regression of large (034) and small (0:3) adult plants to the previous stage classes and the probabilit\' of flowering for both small (asi) and large (am) adult plants

(Table 6.A.). .A. similar pattern of \ ariation in demographic vital rates was seen among plots (Table 6B) and cinder cones (Table 6C). Temporal variation (Table 6A) exceeded the \ ariation among cinder cones for all demographic parameters (Table 6C). but only exceeded the variation among plots for half of the parameters (Table 6B). The greater amount of \ ital rate variation seen among plots than among cinder cones is likely an 132 artifact of the smaller sample sizes present in the plots. The number of individuals, as well as how these indi\ iduals are distributed among different stage classes, \ aries widely among plots, and this contributes to the observ ed \ ariation in demographic vital rates.

Despite the quantitative ditferences in vital rate variation, the qualitati\ e pattern of \ital rale variation was similar across both time and space. Stasis of juveniles, small adults and large adults always showed the least \ ariation. whereas regression of small and large adults and tlowering of small adults showed great variation among years, plots, and cinder cones (Table 6). The level of variation seen in the growth of seedlings, juveniles, and small adults was intermediate (Table 6).

Paramcier variabiliry vs. parameter sensitivity and elasticity. Among-year variability of demographic parameters was strongly and negatively correlated with the parameters" associated sensitivities and elasticities (Figure 16). In other words, of the ten matrix transitions measured in the tield. the transitions that had high sensitivities (Figure 16.A.) and elasticities (Figure 16B). all exhibited low variability among years. For example, transitions of stasis (by small adults, large adults, and juveniles) were the least variable among years and also had the highest sensiti\ ities and elasticities. Similarly, highly

\ ariable transitions, such as regression of small and large adults and flowering of small adults, were associated with much lower sensitivities and elasticities (Figure 16).

Population grow th rate (/.). The 15 annual transition matrices generated in this stud\' predicted much temporal variation in /. (Figure 17). In the course of the twenty-year period. /. fluctuated widely around 1. Eight of the armual transition matrices estimated a negati\ e population growth rate, whereas the remaining seven transition matrices 133 estimated a positiv e population growth rate. The lowest value for /. was associated with the 1998 - 1999 transition matrix (/. = 0.8812). The years immediately before and after this annual transition also had negative growth rates (/. = 0.9758 and 0.9689. respectively). Three years was the longest span of consecutive years e.xhibiting negative population growth rates; this occurred twice, from 1982 - 1985 and from 1997 - 2000.

Matrix model estimates of 'k were fairly accurate for most years, particularly for the span of \ ears between 1985 and 1992. The largest discrepancy between the predicted and observ ed population growth rates was seen in the 1983 - 1984 transition, in which the predicted /. of 0.955 greatly underestimated the observed /. of 1.069. This difference suggests that the asymptotic analyses may not be relevant for the population at this particular stage in time.

Examination of spatial variation in /. at the scale of the individual plot revealed much variation among plots (Figure 18). .A.nalyses of the 11 plot transition matrices estimated a positiv e population growth rate (/. > 1) for only two plots. Plot 5 and Plot 11. although the estimate of/, for Plot 8 was very close to 1 as well (Figure 18). Transition probabilities in Plot 3 vielded the lowest estimate of/., equal to 0.926. The number of indiv iduals in this plot declined from 10 individuals at the start of this study in 1982 to one large adult plant in 2001. .-Mthough the matrix analyses predicted a positive population grow th rate in two of the eleven plots, we observed a decline in the number of indiv iduals in all 11 plots. Observed changes in population numbers, as estimated by eq.

3. ranged from a low of 0.966 in Plot 3 to a high of 0.999 in Plot 5. In five of the plots

(2. 3. 6. 9. and 10). the matrix model underestimated population growth rate, whereas in the other six plots, the model ov erestimated population growth rate. The pattern of

predicted and observ ed population growth rates, however, was similar. For both

estimates of/.. Plot 3 had the lowest growth rate and Plot 5 had the highest growth rate.

In addition, for nine of the 11 plots, the model predicted a negativ e population growth

rate, which was also observ ed in the field.

Because the inter-plot variation in /. may in part be due to small sample sizes

within the plots, we also examined spatial variation in /. at the scale of the cinder cone.

When the data from the plots on each cinder cone were pooled together, the population grow th rates predicted for all cinder cones were similar, ranging from 0.957 at Puu o

Maui (Plot 6 only) to 1.013 on Puu o Pele (Plots 3. 4. and 5; Figure 19). Puu o Pele contained both the fastest growing plot (Plot 5) and the most rapidly declining plot (Plot

3). The remaining three cinder cones exhibited similar, negativ e population growth rates;

0.970 (Puu Naue). 0.981 (Puu Nole). and 0.988 (K.a Moa o Pele). WTien /. was calculated for each cinder cone based on the observed change in population numbers from 1982 -

2001. /. at Puu Nole was 0.981. the same growth rate predicted by the matrix model

(Figure 19). We observed a lower population growth rate at Puu o Pele (0.986) and Ka

Moa o Pele (0.980) than was predicted by the model. .At the other two cinder cones, the matrix model underestimated Puu o Maui, predicted to have the lowest growth rate of

0.957 actually had a fairly high growth rate, of 0.995. Puu Naue exhibited a k of 0.989. much higher than the predicted 0.970.

Damping ratios. Table 7 presents the damping ratios for all years, plots, and cinder cones. For eight of the 15 annual transition matrices, the dominant eigenvalue was much 135 greater than all other eigen\ alues (/-i > 1.20; Table 7A). The damping ratio was also high for an additional four annual matrices, with /.i kz ranging from 1.100 to 1.199.

However, in the 1983 - 1984. 1984 - 1985. and 1987 - 1988 transitions. /.| /.; was only slighth greater than one. suggesting that these distributions were not close to con\ erging on the stable stage distribution. This may in part explain the large difference in predicted and obserN'ed population growth rates in the 1983 - 1984 transition. With the exception of Plot 7. the damping ratios for all plots were high, ranging from a low of 1.172 in Plot

11 to a high of 1.357 in Plot 1 (Table 7B). When the data were grouped by cinder cone, all damping ratios were high, ranging from 1.177 to 1.268 (Table 7C). .A.mong years.

/.i was positi\ely correlated with /. (F = 6.057. df = 14. P = 0.029). suggesting that faster growing populations converge on the stable stage distribution more rapidly

(Caswell 2001).

Sensiiiviries. Sensitivities \ aried among years, plots, and cinder cones, but the qualitati\ e pattern of sensiti\ ity was similar across time and space (Figure 20). The highest sensiti\ ities were typically associated with the seed, juvenile, small adult, and large adult stage classes (Figure 20). In general. sensiti\ities increased with descent down a matrix column, i.e.. as a stage class transitioned to larger and larger stage classes, .^mong years and plots, the highest sensitivities were usually associated with transitions of growth (G) and sur\ i\al (L). although in some years and plots, reproduction (F). particularly by large adults, also had high sensitivity (Figure 20.A and B). When the data were pooled to examine \ ariation among cinder cones, the five cinder cones all e.xhibited the same pattern in sensitivity (Figure 20C). The highest sensitivities were associated with transitions of growth, followed by surv iv al and then reproduction. Overall, population growth rate on the cinder cones was most sensitiv e to the seed, small adult and large adult stage classes (Figure 20C).

Elasticities. Elasticities \ aried among years and plots, but the greatest total elasticities were always associated with the same three stage classes; juv eniles, small adults and large adults (Figure 21 .A. and B). The relative order and magnitude of elasticities associated with these three stage classes, however, varied over time and space, with each of the three stage classes exhibiting the greatest impact on /. in different years and plots.

\'ariation among cinder cones showed a similar trend, although the total elasticitv- associated v\ ith the juv enile stage class nev er e.xceeded that associated with the small and large adult stages (Figure 21C). The high total elasticities associated with these three stage classes were always due to the very high elasticities associated with stasis. .A.11 contributions to the seed and seedling stage classes had very low elasticities, ranging trom 0.0000 to 0.0018 for seeds, and from 0.0000 to 0.0640 for seedlings. In all \ ears. plots, and cinder cones, the greatest total elasticity was associated with survival (L). followed by grouth (G) and reproduction (F) (Figure 22).

For nearly all stage classes and transitions, temporal variation in elasticity exceeded spatial variation (Table 8). The pattern of variation in the elasticities associated with all matrix entries, however, was the same across both time and space. Elasticities associated with the regression of small and large adults, flowering of small adults, and the contribution of small reproductive individuals to the seedling stage class were the most variable, whereas the elasticities associated with stasis of juveniles, small adults, and 13" large adults, as well as growth of juveniles and small adults, were the least variable among years and plots (Table 8A and B). The elasticities associated with all demographic transitions were much less variable among cinder cones than among years or plots (Table 8). Patterns of \ ariation in elasticity, however, were similar to those seen among years and plots, with stasis of juveniles, small adults, and large adults showing low \ ariation and regression of small and large adults exhibiting the greatest \ ariation among cinder cones (Table SC). In terms of the total elasticity associated with each stage class, the elasticities associated with juveniles, small adults and large adults were the least \ ariable. whereas the elasticity associated with the small reproductive stage class was the most \ ariable among years, plots, and cinder cones.

Correlations betw een elasticity and population growth rate. Among years. was significantly correlated with the total elasticity of the seed (Fu = 27.600. R" = 0.680. P =

0.0002). seedling (Fu = 31.044. R" = 0.705. P < 0.0001). juvenile (Fu = 7.048. R" =

0.352. P = 0.020). and reproductive (small: F\4 = 5.654. R" = 0.303. P = 0.033: large: Fu

= 30.027. R- = 0.698. P = 0.0001) stage classes. .Among plots. /. was significantly correlated with the total elasticity of the seedling (Fui = 7.122. R" = 0.442. P = 0.026) and large reproductive (Fu, = 6.901. R" = 0.434. P = 0.028) stage classes: the correlation between /. and the total elasticity of the seed stage class was marginally significant (Fid =

4.829. R" = 0.349. P = 0.056). WTien plots were grouped according to the cinder cone on which the\' were located. /. was significantly correlated with the total elasticity of the seed (F4 = 26.002. R* = 0.897. P = 0.015) and large reproductive (F4 = 11.120. R' =

0.788. P - 0.045) stage classes, and marginally correlated with the elasticity of the seedling stage class (F4 = 9.697. R" = 0.764. P = 0.053). Table 9 presents the correlation coefficients between the elasticities of all matrix transitions and among years (Table

9.\). plots (Table 9B). and cinder cones (Table 9C). In all sets of transition matrices. /. was significantly correlated with the growth of seedlings, the tlowering of large adults, and the contributions of large reproductiv e indiv iduals to the seed and seedling stage classes (Table 9). These correlations were particularly strong among years (P < 0.0001).

Variation in >. was never correlated with seed survival, stasis of small and large adult plants, regression of large adult plants, or the contribution of the small reproductive stage class to the seed stage class (Table 9).

In years exhibiting positive population growth rate, elasticities were more evenly distributed among the seven different stage classes than in years exhibiting negati\ e population growth rate (Figure 23.^). In these years (/. < 1). elasticity was much less e\ enly distributed, such that a large proportion of the total elasticity was solely distributed among one or a few stage classes only. In Figure 23 A. this is illustrated by tall peaks representing very large elasticities for certain stage classes, typically the small and large adult stage classes. .A similar pattern is seen among the 11 plots: in plots exhibiting the highest population growth rates, elasticities were more evenly distributed among the different stage classes than in plots with lower population growth rates (Figure 139

DISCUSSION

Sih ersword life history

Results from the twenty-year silversword monitoring study at Haleakala National

Park prov ide us with new insights about the natural history of this threatened species.

One of the most striking results of this study is how slow growing and long-li\ed these

plants are. In the twenty-year period, no individuals in the study plots passed through the

entire life cycle, from the seedling stage through flowering and death. This highlights the

need for long-term demographic studies, particularly for such long-lived species (Brault

and Caswell 1993. Doak et al. 1994). In general, individuals remained in the juvenile and

adult stage classes for many years before advancing to the ne.xt stage class. The

relationship between plant age and rosette diameter (Figure 6) shows that 15-18 year old plants still only average 10 - 20 cm rosette diameter. Elsewhere, we have shown that

the av erage rosette diameter of flowering individuals is 51 cm. and that very few

individuals smaller than 30 cm flower (.A.ppendi.\ B). Thus, it is evident that the majority of plants require many more years than are covered in this study in order to grow large enough to flower. Estimates of the average time spent in each stage class predict an a\ erage of 20 years for a small plant to flower and 30 years for a large adult plant to

flower; however, there is much variation in these estimates, and plants may spend much more time in one or more stage classes. In addition, estimates of stage duration include individuals that transitioned to a different stage class without advancing to a larger class

(i.e.. through regression or death), and so may underestimate the actual time that a growing individual spends in each stage class. Although it was previously known that 140 the sil\ ersword is a long-li\ ed plant species, early estimates of the siK ersvvord life span were in the range of 7 - 20 years (Ruhle 1959). Results trom this study suggest that the sil\ ersword life span is much longer, and that it is likely closer to the flowering age predicted by Rundel and Witter (1994) of 40 - 50 years.

Variation in stage class duration is also suggested by the age - rosette size comparison, which re\ eals a large degree of within-cohort \ ariation in rosette growth rate. Occasionally, we saw large discrepancies in rosette growth rate among multiple plants that had germinated in the same year and that were located close to each other in the same plot. .A.lthough this study did not directK' examine the issue of whether such differences are due to genetic or en\ ironmental factors, it is clear that large differences in growth rate do exist within cohorts. This \ ariation may reduce the probability that indi\ iduals w ithin a cohort, which are potentially genetically related, will flower in the same year.

The siK ersword life historv' was characterized by slow growth rates, low mortalitN' of adults, and higher, more variable mortality of seedlings; this type of life histor\- is common in long-lived perennial plants (Harper 1977. Pinero et al. 1984. Moloney 1988.

Ratsirarson et al. 1996). Recruitment in the plots varied greatly among years, ranging from one seedling in 2000 to 100 seedlings in 1984, and occasionally occurred in plots tbllov\ ing years of no tlowering. This suggests that silversword seeds either remain

\ iable in the field for multiple years and can germinate two or more years after ha\ ing been produced, or that seeds disperse into the plots (.A.ppendix B). Elsewhere, seeds were show n to remain \ iable for multiple years (.Appendix B). suggesting the presence of a 141

seed bank and justifying the addition of a separate seed stage into a matrix model for this

species. Seed dispersal. howe\er. was minimal (Appendix B). reducing the likelihood

that seeds produced outside of the plots disperse into the plots. Seedling sur\ i\ al was

also \ er\ \ ariable: in some years, we obserxed ver\' high seedling mortality rates (up to

100 percent), whereas in other years, all seedlings survived to the following year (Figure

S). Seedling surv ival was sensitiv e to rain: in both very wet and very dry years. fev\-

seedlings survived (Forsvth and Loope. unpub. data). Because the majority of the

permanent plots are located on steep cinder cone slopes, strong rains have the tendencv' to

uproot seedlings and wash them downslope. Silversvvord individuals had the potential to

"shrink" in size under adverse conditions or stress, to the point where they actually-

regressed to the previous stage class. The data from the permanent plots suggest that

regression is not a common occurrence; howev er, the ability to shrink rather than die

under unfavorable envirormiental conditions may help individuals persist in the harsh

environment of Haleakala crater.

Silvcrsword matrix model

The use of a stage-based matrix population model to analyze the demography of a

population or species requires that a continuous life historv' be divided into a series of separate life historv' stage classes. The choice of such stage classes is somev\ hat arbitrary , but is guided by the goal of maximizing sample sizes within stage classes (i.e.. not dividing the population too finely into too many stage classes), while at the same time separating individuals that exhibit very different vital rates into different stage classes

(.Moloney 1986). Our choice of stage classes in the Haleakala silversvvord matrix model 142 fulfilled this goal. Individuals were divided into stage classes for seeds and seedlings, three size-based vegetative stage classes, and Uvo size-based reproductix e stage classes.

The seed and seedling stage classes are biologically distinct. The division of vegetati\ e rosettes into three difterent stage classes is based on the difterences in demographic \ ital rates exhibited by each class. The juvenile stage class contains individuals that are not large enough to reproduce, and the small and large adult rosette stage classes contain indi\'iduals with different probabilities of sur\ ival. and very different probabilities of flowering. Reproductive individuals are separated into rwo stage classes based on their rosette size prior to tlovvering: this division makes it possible to distinguish between the different levels of seed production by different-sized plants. Thus, the dix ision of the

Haleakala silversword life cycle into these seven stage classes separates individuals exhibiting different \ ital rates and different levels of reproductix e output, while simultaneoush maximizing sample sizes within stage classes.

The division of a continuous life cycle into distinct stage classes should not lead to an incorrect interpretation of how indix iduals progress through the life cycle. For example, the stage-based matrix analyses conducted here separate the transitions among

\ egetative stage classes into transitions of stasis, growth, and regression. In this study, transitions of stasis were found to be the least variable over both time and space, and had the greatest impact on relative to other types of transitions. However, defining transitions in this way may be misleading. For example, the term "stasis" implies that indix iduals remain the same size over time, when in reality, individuals are likely growing (or shrinking), but are simply not crossing the established size boundary between stage classes. This effect mav' be exacerbated by the fact that the range of sizes

encompassed by the different stage classes are not equivalent. For example, the large

adult stage class (i.e.. all plants greater than 20 cm in rosette diameter) includes a \ ery

large range of sizes, relative to the ju\ enile and small adult stage classes. This effect.

hou e\ er. is inherent to analyses based on stage-based matrix models and does not alter our results. It is important to note, though, that consideration of the true meanings of

"stasis." "growth." and "regression" will contribute to a more accurate understanding of the results presented here.

The matrix model analyses were based on demographic v ital rates measured in the

tield (probabilities of growth, stasis, regression, and flowering), as well as reproductive rates (contributions to the seed and seedling stage classes) estimated by the available data on silversword reproduction, seed germination, and seed survival. We had very complete data tor the first set of transition probabilities, including the degree of vital rate variation.

Howev er, our understanding of seed germination and seed and seedling survival rates, including how these vital rates vary over time and space, was limited. This is not uncommon in population viability analyses; typically, data are limiting for at least some part of a species' life cycle (Beissinger 2002). Howev er, we were able to use the av ailable information regarding silversword seed production, seed set. and germination in order to estimate the unknown transition probabilities for matrix model analyses. In addition, the results of our elasticity analyses demonstrated that the life history transitions for which we have the least amount of data, namely transitions from the seed, small reproductive, and large reproductive stage classes to the seed and seedling stage classes. 144

are also the transitions that have the smallest relativ e impact on k. Each ot" these six

transitions had a \ ery low elasticity, relative to other demographic transitions in the sil\ ers\vord life cycle. As a result, small alterations to these estimated transition

probabilities will have \ erv" little impact on the resulting population projection.

Population growth rate

Within the permanent plots, the silversword population declined by nearly 50° o in the twenty-year period. It is unclear, however, whether the decline observed in the plots is representative of the silversword population as a whole. The 11 plots comprise a total area ot 1100 m". a small fraction of the entire silversword range, and now only contain about 0.5° 0 of the entire silversword population. In addition, nearly all plots are located on \ er\' steep cinder cone slopes. The population dynamics observed in these areas may differ trom those in other habitat tvpes within Haleakala crater, as well as on the v olcano's outer slope. For example, there are large groups of silverswords in other areas of the crater, including Sliding Sands Trail and Silversword Loop, and groups of plants in these flatter regions may exhibit different growth rates than those located on the steep slopes. In addition, it has been suggested that cinder cone populations experience much turnover, even while the total population size remains fairly constant (Kobayashi 1973.

Loope and Crivellone 1986). If this is the case, the large fluctuations we have observed in some plots (e.g.. Plot 3) may not be indicative of a crater-wide population decline. The decrease in plot population size, however, is somewhat matched by the total population censuses that are conducted every ten years. .Although the 1982 (48.000 plants) and 1991

(63.000 plants) censuses depicted a growing population, the 2001 census showed a drop 145

in siK ersvvord numbers, with an estimated population size of 50.000 plants (F. Starr, pers.

comm.). This apparent decline may in part be due to a severe drought on Maui in the late

1 '-)90s; in these dry v'ears we observ ed reduced flowering and seedling recruitment, as

well as increased adult mortality rates (Fors\th and Loope. pers. obs.).

Rcproduclive value and stable stage distribution

Of the seven stage classes, the seed stage class had the lowest reproductive value,

due to the \ erv small probabilit\' that an individual in this stage class will sur\ i\ e to

reproduce. Not surprisingly, reproductive \ alue increased as plants increased in size and

therefore had a higher probability of surv iv ing to reproduce, ranging up to 0.35 for large

reproductive plants. Reproductive value of small adults declined if plants flowered as

small adults instead of advancing to the large adult stage class before flowering. This is

likely due to the fact that small adult plants ha\ e greatly reduced reproductive output

relativ e to large adult plants, because seed production is highly size-dependent (.A-ppendix

B). In addition, adult surviv al rates are v er\ high, such that a small adult plant has a v erv-

high probability of surviving to reproduce as a large adult, if it delays flowering.

Combined, these factors help e.xplain the very low number of plants that flower as small

adults. In a sample of flowering plants measured from 1997 - 2002. onlv' flv e of 190

flowering individuals were in the small adult stage class.

The stable stage distribution predicted by the summary- matri.\ was heavily dominated bv- seeds, with appro.\imately 70° o of all individuals in this stage class. Given that the number of viable seeds present in the seed bank carmot be quantified, it is unclear

if this prediction is accurate for this species. However, a similar seed-dominated stable 146 stage distribution was found for Calathea ovandensis. a perennial understorv' herb

(Hor\ itz and Schemske 1995) and Hiidsonia montana. a threatened shrub (Gross et al.

1998). When the silversword stage distribution is re-calculated to include only the non- seed stage classes, the stage distribution observ ed in 2001 was ver\- similar to the predicted stable stage distribution (PS = 89.34°o). This is an important finding because the beha\'ior of populations that are far from the stable stage distribution may differ substantialK from the predicted asymptotic dvnamics (Hor\itz and Schemske 1995). The similarity between the observ ed and stable stage distributions suggests that analyses of the asvTnptotic dynamics (i.e.. analyses of the dominant eigenvalue. and its associated eigen\ ectors) are relevant to the current dvnamics of the silversword population. This conclusion is also confirmed by the high damping ratios (Xi /.;). which indicate that the dominant eigenvalue has a large impact on population dynamics, relative to the other eigenv alues (Caswell 2001). On average, the dominant eigenvalue was more than 20" o greater than the next dominant eigenvalue. These ratios suggest that the asymptotic dynamics are important relative to the transient dynamics, and that transient dynamics will not greatly impede the approach of the population to the stable stage distribution

(Horvitz and Schemske 1995).

Sensitivity- and elasticity analyses

Population growth rate was most sensitive to transitions from the small adult and ju\ enile stage classes, followed by transitions from the large adult stage class (Figure 14).

Other studies of long-lived organisms have found similar patterns; population growth rate is frequendy sensitiv e to the fates of small adults (Grouse et al. 1987. Horvitz and 147

Schemske 1995). All transitions from the reproductive stage classes had ver\' low- sensitivities. as did all transitions to the seed stage class.

Total elasticity was highest for small and large adults, followed by juveniles. In contrast, all stage classes related to reproduction, including seeds, seedlings, and reproducti\ e plants, had verv' low elasticities. This suggests that survi\ al and growth of ju\ enile and adult plants have large effects on relative to other life history transitions, and that maintaining high sur\ i\ al and growth rates of these stage classes may be crucial for sih ersword persistence. .A. similar pattern of elasticity has been found in other demographic studies representing a \ ariety of ta.\a. including the killer whale (Brault and

Caswell 1993). desert tortoise (Doak et al. 1994). cheetah (Crooks et al. 1998). and a

\ ariet\' of plant species (Horvitz and Schemske 1995. Ratsirarson et al. 1996. Gross et al.

1998. Caswell and K.aye 2001). For these and other long-lived species, surv ival rates ha\ e the largest impact on population growth rate. The high elasticities associated with the ju\ enile and adult stage classes are due to the high elasticities associated with stasis; this is contirmed when total elasticity is di\ ided among transitions of growth. sur\ i\ al. and reproduction. 0\ er 80° o of the total elasticity was associated with transitions of survival, followed by \ er\' low elasticities associated with growth and reproduction. A recent re\ iew of elasticity analyses suggests that this is a common pattern among a

\ ariety of different ta.\a; surv ival commonly has the greatest total elasticity, tvpicalh' followed b\- growth; fecundity rarely has the highest elasticity (Crone 2001). Similarly.

SiK ertown et al. (1993) found that in woody plants and iteroparous herbaceous plants. sur\ i\ al had the highest elasticity. Semelparous herbaceous plants exhibited a different 14S pattern, with growth hav ing the highest elasticity, followed by fecundity and then sur\i\al.

Matrix correlation structure

Recent examination of demographic v ariation has suggested that matrix parameters do not necessarily vary independently, but that certain transition probabilities are instead correlated with each other (Doak 1994. Morris and Doak 2002). The presence, direction (positive versus negative), and strength of matrix correlations \ aries among species and is not well understood (Kaye and Pyke 2001. Morris and Doak 2002).

Howe\ er. the presence of such correlations has important implications for matrix model anahses and the outcomes predicted by stochastic models (Kaye and Pyke 2001. Caswell

2001. Morris and Doak 2002). For example, if vital rate variation is correlated among different matrix parameters, allowing transition probabilities to vary independently in stochastic simulations may lead to inaccurate population projections.

The 20 years of demographic data included in this study allow us not only to examine temporal variation in demographic vital rates, but also to explore existing correlations among different matrix parameters. Multiple correlations among \ ital rates, both positi\ e and negative, emerged. Similar types of transitions, including growth and flowering of different stage classes, were often positively correlated, suggesting a similar response by different stage classes to environmental variation. Opposite types of transitions (i.e.. positive transitions such as growth and flowering \ ersus negative transitions such as regression) were frequently negatively correlated, again suggesting a similar response to environmental variation by different stage classes. Comparisons of 149

\ ariation in these \ ital rates to \ ariation in en\"ironmental factors, such as precipitation,

may pro\ ide insights into the factors most responsible for the obser\ ed \ ariation in

sil\ ersword demography. One third of all significant correlations were negati\ e

correlations between transitions originating from the same stage class. These correlations

are an artifact, occurring because transitions from one stage class to another

automatically- reduce the number of individuals that can transition from the same stage

class to a different fate.

Temporal and spatial variation

Despite the recognized importance of long-term demographic studies, many

P\'.As. particularly for plants, are limited by the number of years of data they include

(Menges 2000a. 20006. Fieberg and Ellner 2001). A major problem of short-term demographic studies is that they may not include the fiill spectrum of en\ ironmental conditions experienced by the population, and as a result, they are less likely to capture

rare e\ ents. As a result, demographic \ ariation cannot be accurately assessed or

incorporated into a matri.x model, and population projections may differ from what actually occurs in the field.

Relati\ e to other plant demographic studies, this twenty-\ ear study on the

Haleakala silversword is unique in terms of its longevity, and because of this, presents a v aluable opportunity to examine temporal variation in demographic vital rates. population growth rates, and sensitivity and elasticity parameters. In addition, this study examined multiple plots located on different cinder cones throughout the subspecies" range, and so prov ides the opportunity to assess spatial variation in demography at two 150 spatial scales as well. Our ability to pool together data from different plots on the same cinder cone allows us to examine spatial variation in demographic parameters, while at the same time minimize the variation that may simply be due to small sample sizes within the plots. Although temporal and spatial \ ariation in demography has been obser\ ed in other species (Kalisz and McPeek 1992. Hor\'itz and Schemske 1995. Oostermeijer et al.

1996). a thorough understanding of this variation has been limited in part due to the short duration and limited spatial scale of most demographic studies. Measuring demographic

\ ariation and incorporating this variation into matrix models will greatly improve the accuracy of population \ iability estimates (Fieberg and Ellner 2001).

Demographic vital rates. We observed much variation in demographic vital rates o\ er time and space. .Although some studies have assumed equal variability of demographic parameters, analysis of silversword vital rates shows that different demographic parameters \ ary to different degrees over time and space, but that the pattern of v ariation is similar among years, plots, and cinder cones. Of the ten demographic vital rates quantified in the field study, transitions of stasis were the least variable over both time and space, whereas transitions of regression and reproduction were the most variable.

X'ariability of all growth transitions was intermediate. Variation among plots was greater than \ ariation among cinder cones, suggesting that some of the spatial variation observ ed among plots may be an artifact of the small sample sizes within the plots. In fijture PVAs based on the silversword matrix model, it will be critical to take into account this v ariability in demographic vital rates (Reed et al. 2002). Correlations between parameter

\ ariabilitv and sensitivity and elasticity showed that the least variable parameters were 151 associated with the highest sensitivities and elasticities. Thus, k is most sensitive to changes in the demographic transitions that are the least variable over time. The negati\ e correlation between variability of demographic parameters and sensitivity and elasticity is a pattern that has been obser\ ed for many different life histories (Pfister 1998. de Kxoon et al. 2000).

In the twenty-year period, the number of plants tlowering in the plots \ aried widely, ranging trom zero tlowering plants (in 1984. 1998. and 2000) to 16 tlowering plants (in 1991). Long-term tlowering surveys of Haleakala Crater conducted by the L'.S.

Geological Surv ey. Biological Resources Di\ ision. suggest that these data are representativ e of the annual flowering \ ariation that occurs crater-wide. The number of sih erswords tlowering throughout the crater varies widely among years, and despite efforts to ascertain the cause of tlowering. no clear pattern has emerged and the cause of tlowering remains poorly understood (Loope and Cri\ ellone 1986). Howe\ er. \ ariation in the abundance of tlowering plants has been shown to affect plant reproductive success, such that plants tlowering in high tlowering years e.xhibit significantly higher percent seed set than do plants tlowering in low tlowering years (Appendi.x .A). Such density- dependent seed set has implications for individual reproductive success, as well as the long-term persistence of this species.

Population growth rate (/.)• Temporal and spatial variation in demographic vital rates resulted in \ ariable population growth rates, with estimates of /. fluctuating around 1 in different years, plots and cinder cones. Comparisons between the observed variation in /. and \ ariation in environmental factors, such as precipitation, across both time and space. 152

will help clarify the suite of envirotunental conditions most conducive to silversword

growth and persistence. Similarly, it is possible to compare among-plot variation in /. to

\ ariation in plot characteristics such as substrate, slope, or aspect. For example, the

fastest growing plot (Plot 5) and the most rapidly declining plot (Plot 3) are located on

the same cinder cone. Puu o Pele. Plot 5 is in the crater of the cinder cone, whereas Plot

3 is on the steep northern slope of the cinder cone. Physical differences between these

two sites may contribute to the large difference observ ed in the population growth rates

between these two plots.

In all plots, the number of plants decreased from 1982 - 2001. with much of the

decline occurring in the second half of this study. However, it is unclear if this observed

population decline accurately reflects what is happening in the silversword population

crater-wide. Because the Haleakala siK ersword is also very abundant in areas quite

different from the cinder cone en\ ironment. it might be useful to establish permanent

plots in other, flatter areas of the crater. Such plots might provide an interesting

comparison to the cinder cone plots, if demographic monitoring continues over the long

term.

Sensirivities and elasticities. We observed temporal and spatial variation in parameter

sensitivities and elasticities but. qualitatively. se\eral general patterns remained

consistent across both time and space. Juveniles, small adults, and large adults typically

made the greatest contributions to although the relative importance of these three stage

classes \ aried temporally and spatially. The high sensitivities of these stage classes were due to the combined transitions of stasis and growth, whereas the high elasticities of these 153 stage classes were due to transitions of stasis. Population growth rate was trequenth' sensiti\ e to seed germination, although the elasticity associated with this transition was

\ er\ low. Seedlings and reproducti\ e plants had low sensitivities and elasticities, regardless of year. plot, or cinder cone. When total elasticity was di\ ided among transitions of growih. surv iv al, and reproduction, the highest elasticity by far was always associated with plant surv ival. These results suggest that although the actual \ alues of sensiti\ ir\- and elasticity parameters \ ary among years, plots, and cinder cones, the relative effect of different stage classes and transitions on /. is qualitatively similar o\ er time and space.

In contrast, other smdies have observ ed important qualitati\ e differences in the contribution of different life histor>' stage classes and transitions to o\ er time and space. Kalisz and VlcPeek (1992) found that the importance of a seed bank in Collinsia vcnict drastically increased in a poor year (/. « 1). relati\e to a good year (/. > 1). In a rare perennial herb (Gcntiana pneumonanthe). Oostermeijer et al. (1996) determined that sur\ i\ al was most important in stable and declining populations, but that growth and fecundity were more important in growing populations. Vavxek et al. (1997) observ ed seasonal differences in elasticities, although the highest elasticities were always associated with the surv ival and reproduction of the smallest stage class.

Implications for consen-alion

In addition to enhancing our understanding of a species' natural historv' and population dynamics, matrix population models are an important tool in species conser\ ation and management (Casw ell 2001. Fieberg and Ellner 2001). Matri.x model 154 analyses clarify- the current dynamics of a population and provide insight as to where in a species' life cycle to focus management efforts. Such analyses enable biologists to assess

the relati\ e effecti\ eness of different management strategies and to compare the tliture

population size and strucmre resulting from different management scenarios.

Results of this study demonstrate that the Haleakala sih ersword population in the

permanent plots has declined over the past 20 years. .Although it is currently unclear

w hether this observed change in population size is representative of the sih ersword

population as a whole, the decline observ ed in the plots on the cinder cones may be a cause for concern. Matri.x analyses of these demographic data identify the stage classes in the Haleakala sih ersword life cycle that are most critical to /.: small adults, large adults, and juveniles have the highest elasticities, suggesting that these stage classes make the greatest relati\ e contribution to and that small changes to the sur\i\ al and growth rates of these stage classes may ha\ e large impacts on the population growth rate. Thus. conser\ ation of indix iduals in these stage classes is crucial to the maintenance of a health\ sihersword population. .-Mthough these classes typically have \ er\' high sur\i\al rates, these rates are reduced in very dr\' years (Forsyth and Loope. unpub. data). It is likely that these reduced surv ival rates (corresponding with dry years) translate into reduced population growth rates.

It is important to note, however, that while elasticity analyses identify the stage classes most critical to population growth rate, they do not take into account our ability to actuallv- manipulate matri.x transition probabilities in the field (de Kjoon et al. 2000). For example, in this study, stasis of small and large adult plants had the highest elasticities. 155 suggesting that small changes in these transition probabilities will ha\ e relati\ ely large effects on However, in reality, it may be more difficult to alter stasis transition probabilities by a small amount than it is to alter other transition probabilities, such as the production of \ iable seeds, by a larger amount. Thus, management decisions informed b\' elasticit\- analyses should be grounded in an understanding of the species" natural histor>. as well as the managers" ability to alter demographic vital rates in the field.

Despite this shortcoming. howe\ er. elasticity analyses greatly enhance our understanding of how different life histor\- stage classes affect /.. Subsequent analyses can use this information to project future population size under a \ ariety of scenarios, in which \ ital rates are neuati\ el\- affected by different threats and or positi\ ely affected b\' different management regimes.

In addition to providing useful information for the conservation of the Haleakala siK ersword. results of this study may be usefiil in the management of the related subspecies, the critically endangered .Mauna K.ea siK ersword (Argxroxiphiiim sandw icensc ssp. sandwicense). The Mauna Kea siKersword is endemic to the high ele\ ation alpine deserts and subalpine shrublands of .Mauna Kea on the Island of Hawaii

(2600 - 3800 m). and is v ery similar to the Haleakala siK ersword in terms of its life c\cle. lndi\ iduals are long-lived and typically monocarpic. although an outplanted population of Mauna Kea siK erswords contains a disproportionately high number of multiple rosette individuals. Following a drastic decline in population size during the

and 20^ centuries, primarily due to consumption by introduced sheep {Oris aries) and goats (Capnis hirius) (Walker and Powell 1999). the Mauna Kea siKersword is 156

currenth' the focus of an intense reintroduction effort. Because of the similarities in the

natural histories of these two subspecies, it is possible to use the matri.x model developed

here to predict the relati\e impacts of different threats to the Mauna Kea silversword. as

u ell as weigh the relati\ e effectiveness of different management and restoration

strategies. SpeciticalK'. results of this study suggest that maintaining or increasing adult

sur\ i\ al rates will be critical in ensuring the persistence of the .Vlauna K.ea silversword

population.

Conclusions

.Vlatrix modeling of demographic data is a powerful tool that can be used both to

better understand population dynamics, as well as to inform conser\ation and

management decisions. These analyses clarify how a population changes o\ er time,

compare the relati\ e fitness of populations among different years or locations, and

contribute to our understanding of how different transitions in a species" life cycle

contribute to an o\ erall population growth rate. This long-term demographic study of the

Haleakala sih ersword suggests that the population of this threatened species may be in

decline. The obserxed temporal and spatial variation in demographic \-ital rates,

population growth rates, and sensitivity and elasticity parameters highlights the need for

longer demographic studies, particularly for long-lived species. Such studies will be

more likely to encompass the ftill spectrum of environmental conditions e.xperienced by a

population or species. .Measurements of demographic vital rates and how they \ ary o\ er time and space can be used to project tliture population size and structure under a \ ariety of scenarios. Such analyses will help consen ation biologists better target management efforts, as uell as assess the relative effectiveness of different management strategies. 15S

LITER-\TLRE CITED

Baldwin. B.G. 1996. Phylogenetics of the California tarweeds and the Hawaiian silversword alliance (Madiinae; Heliantheae sensu late). Pages 377-391 in D.J.N. Hind and H.J. Beentje. editors. Compositae: systematics. Proceedings of the International Compositae Conference. Royal Botanic Gardens. Kew.

Beissinger. S.R. 2002. Population viability analysis; past, present, ftiture. Pages 5-1" in S.R. Beissinger and D.R. McCullough. editors. Population viability analysis. The L'ni\ ersity of Chicago Press. Chicago.

Bender. .M.H.. J..VI. Baskin. and C.C. Baskin. 2000. Ecological life histor\- of Polymnia canadensis, a monocarpic species of the North .American temperate deciduous forest: demography. Plant Ecology 147:117-136.

Bo\ ce. .M.S. 1992. Population viability analysis. .Annual Review of Ecology and Systematics 23:481-506.

Brault. S. and H. Caswell. 1993. Pod-specific demography of killer whales (Orcinus area). Ecology 74:1444-1454.

Brook. B.W.. J.J. O'Grady. A.P. Chapman. M..A. Burgman. H.R. .Akcakaya. and R. Frankham. 2000. Predictive accuracy of population \-iability analysis in conservation biology. Nature 404:385-387.

Carr, G.D. 1985. Monograph of the Hawaiian .Madiinae (Asteraceae): Argyroxiphium. Diibautia. and Wilkesia. .Allertonia4:l-123.

Carr. G.D.. E..A. Powell, and D.W. Kyhos. 1986. Self-incompatibility in the Hawaiian Madiinae (Compositae): an exception to Baker's Rule. Evolution 40:430-434. 159

Caswell. H. 1978. A general formula for the sensitivit\' of population growth rate to

changes in life historv' parameters. Theoretical Population Biology 14:215-230.

. 1982. Stable population structure and reproductive \ alue for populations with comple.x life cycles. Ecology 63:1223-1231.

. 2001. Vlatri.x population models, second edition. Sinauer .Associates. Sunderland. Massachusetts. L'S.A..

Caswell. H. and T.N. K.aye. 2001. Stochastic demography and conserv ation of an endangered perennial plant (Lomanum bradshawii) in a dNTiamic tire regime. .A.d\ ances

in Ecological Research 32:1-51.

Cole. F.R.. .A..C. Medeiros. L.L. Loope. and W.W. Zuehlke. 1992. Effects of the -Argentine ant on arthropod fauna of Hawaiian high-ele\ ation shrubland. Ecology

73:1313-1322.

Crone. E.E. 2001. Is surv ivorship a better fitness surrogate than fecundity? Ev olution 55:2611-2614.

Crooks. K.R.. .VI..A. Sanjayan. and D.F. Doak. 1998. New insights on cheetah

conserv ation through demographic modeling. Conservation Biologv 12:889-895.

Crouse. D.T.. L.B. Crowder. and H. Caswell. 1987. .A. stage based population model for

loggerhead sea turtles and implications for conservation. Ecology 68:1412-1423.

Crowder. L.B.. D.T. Crouse. S.S. Heppell. and T.H. Martin. 1994. Predicting the impact of turtle e.xcluder devices on loggerhead sea turtle populations. Ecological .Applications

4:43 "-445. 160

de Kjoon. H.. A. Plaiser. J. van Groenendael. and H. Caswell. 1986. Elasticity: The relati\ e contribution of demographic parameters to population growth rate. Ecolog\- 67:142"-1431.

de kroon. H.. J. \ an Groenendael. and J. Ehrlen. 2000. Elasticities: a re\ iew of methods and model limitations. Ecology 81:607-618.

Dennis. B.. P.L. MunhoUand. and J.M. Scott. 1991. Estimations of growth and extinction parameters for endangered species. Ecological Monographs 61:115-143.

Dixon. P.. N. Friday. P. .\ng. S. Heppell. and M. Kshatriya. 1997. Sensitivity analysis of structured-population models for management and conserv ation. Pages 471-514 in S. Tuljapurkar and H. Caswell, editors. Structured-population models in marine, terrestrial, and freshwater systems. Chapman & Hall. New \'ork. L'S.A..

Doak. D.. P. K.arei\ a. and B. Klepetka. 1994. Modeling population viability for the desert tortoise in the western .Mojave desert. Ecological .A-pplications 4:-M6-460.

Ehrlen. J. and J. Van Groenendael. 1998. Direct perturbation analysis for better conserv ation. Conservation Biology 12:470-474.

Fieberg. J. and S.P. Ellner. 2001. Stochastic matrix models for conservation and management: a comparative review of methods. Ecology Letters 4:244-266.

Gross. K.. J.R. Lockwood III. C.C. Frost, and W.F. .Morris. 1998. .Modeling controlled burning and trampling reduction for conserv ation of Hiidsonia montana. Conserv ation Biology 12:1291-1301. 161

Harper. J.L. 1977. Population biology of plants. Academic Press. New ^'ork. New York. USA.

Hor\ itz. C.C. and D.W. Schemske. 1995. Spatiotemporal variation in demographic transitions of a tropical understory herb: projection of a matri.v analysis. Ecological Monographs 65;155-192.

Hor\ itz. C.. D.W. Schemske. and H. Caswell. 1997. The relative "importance" of life- historv stages to population growth; Prospective and retrospective analyses. Pages 247- 2"2 in S. Tuljapurkar and H. Caswell, editors. Structured-population models in marine, terrestrial, and freshwater systems. Chapman & Hall. New York.

Ju\ ik. S.P. and J.O. Juvik. 1998. .\tlas of Hawaii, third edition. University of Hawaii Press. Honolulu. Hawaii. USA.

Kalisz. S. and M.A. .McPeek. 1992. Demography of an age-structured annual: resampled projections matrices, elasticity analyses and seed bank effects. Ecology 73:1082-1093.

Kaye. T.N. 2001. Population viability analysis of endangered plant species: an evaluation of stochastic methods and an application to a rare prairie plant. Ph.D. Dissertation. Oregon State University. Cor\allis. Oregon. US.A.

Kobayashi. H.K. 1973. Ecology of the silversvvord, Argyroxiphiiim sandwicense DC. (Compositae). Haleakala Crater. Hawaii. Ph.D. Dissertation. Dept. of Botany. University of Hawaii. Honolulu.

Letkovitch. L.P. 1965. The study of population growth in organisms grouped by stages. Biometrics 21:1-18. 162

Leuendre. S. and J. Clobert. 1995. L'LM. a softw are for conserv ation and e\ olutionar\' biologists. Journal of .A.pplied Statistics 22:817-832.

Leslie. P.H. 1945. On the use of matrices in certain population mathematics. Biometrika 33:183-212.

Loope. L.L. and C.F. Crivellone. 1986. Status of the Haleakala silversword: past and present. Cooperati\ e National Park Resource Studies L'nit. L'ni\ ersity of Hawaii. Honolulu. Tech. Rep. 58.

Loope. L.L. and .\.C. Medeiros. 1994. Biotic interactions in Hawaiian high elevation ecosystems. Pages 337-354 in P.W. Rundel. .A..P. Smith, and F.C. Meinzer. editors. Tropical alpine environments: Plant form and function. Cambridge University Press. New \'ork. L'S.A.

.Vlack. R.N. and D.A. Pyke. 1983. The demography oiBromiis lecronim: variation in time and space. Journal of Ecology 71:69-93.

Vlathworks. Inc. 2001. M.-\TL.A.B 6.0 (Release 12). South Natick. Massachusetts. L'S.A..

Menges. E.S. 2000^z. Population viability analyses in plants: challenges and opportunities. Trends in Ecology and Evolution 15:51-56.

. 20006. .Applications of population viability analyses in plant conservation. Ecological Bulletins 48:73-84.

.Moloney. K. 1986. .A generalized algorithm for determining categor\- size. Oecologia 69:176-180. 163

. 1988. Fine-scale spatial and temporal \ ariation in the demography of a perermial bunchgrass. Ecology 69:1588-1598.

VIorris. W.F. and D.F. Doak. 2002. Quantitativ e conserv ation biology: Theorv and practice of population v iability analysis. Sinauer Associates. Inc.. Sunderland. .Vlassachusetts.

N'akoaka. .M. 1996. Dvmmics of age- and size-structured populations in fluctuating env ironments: applications of stochastic matri.x models to natural populations. Research in Population Ecology 38:141-152.

Oostermeijer. J.G.B.. M.L. Brugman. E.R. de Boer, and H.C..VI. den Nijs. 1996. Temporal and spatial v ariation in the demography of Gentiana pneiimonanihe. a rare perennial herb. Joumal of Ecology 84:153-166.

Pfister. C..A. 1998. Patterns of v ariance in stage-structured populations: ev olutionarv' predictions and ecological implications. Proc. Natl. .A-cad. Sci. L'S.A. 95:213-218.

Ratsirarson. J, J..A.. Silander. Jr.. and .A.F. Richard. 1996. Conservation and management of a threatened Madagascar palm species. Xeodypsis decary-i. Jumelle. Conserv ation Biology 10:40-52.

Reed. J.M. L.S. Mills. J.B. Dunning Jr.. E.S. .Menges. K.S. .McKelvey. R. Frve. S.R. Beissinger. M. .Anstett. and P. .Miller. 2002. Emerging issues in population vibility analysis. Conservation Biology 16:7-19.

Ruhle. G.C. 1959. Haleakala guide. Hawaii Natural History Association. 164

Rundel. P.W. and M.S. Witter. 1994. Population dynamics and flowering in a Hawaiian alpine rosette plant. Argyroxiphium sandwicense. Pages 295-306 in P.W. Rundel. .A..P. Smith, and F.C. .Vleinzer. editors. Tropical alpine environments: Plant form and function. Cambridge L'ni\ ersit\- Press. New York, L'S.A..

Schemske. D.W.. B.C. Husband. .M.H. Ruckelshaus. C. Goodwillie. I..M. Parker, and J.G. Bishop. 1994. Ev aluating approaches to the conserv ation of rare and endangered plants. Ecology 75:584-606.

Sih ertown. J.. M. Franco. I. Pisanty. and .A.. Mendoza. 1993. Comparative plant demographv - relative importance of life-cycle components to the finite rate of increase in woody and herbaceous perennials. Journal of Ecology 81:465-476.

SPSS. Inc. 1998. Systat Version 9 for Windows.

U.S. Fish and Wildlife Service (USFWS). 1992. Determination of endangered or threatened status for 15 plants from the Island of .Maui. HI. Federal Register 57:20772- 20^87.

Vavrek. M.C.. J.B. McGraw. and H.S. >'ang. 1997. Within-population variation in demography of Taraxacum officinale: season- and size-dependent surviv al, growth, and reproduction. Joumal of Ecology 85:277-287.

Walker. L.R. and E..A.. Powell. 1999. Regeneration of the Mauna Kea silversword Argy roxiphium sandwicense (Asteraceae) in Hawaii. Biological Conservation 89:61-70.

Werner. P.A. and H. Caswell. 1977. Population growth rates and age versus stage- distribution models for teasel (Dipsacus sylvestris Huds.). Ecology 58:1103-1111. 165

Table 1. Matrix model for the Haleakala sih ersword (Argyroxiphium sandwicense ssp. macrocephalum). Matrix entries represent the probability of transitioning trom the stage listed in the column (time t) to the stage listed in the row (time / - 1). Table lA describes the t\pe of transition for each matrix entry; Table 1B notes the probability of each matrix transition. In Table IB. transition probabilities noted as a,, were quantified in the 20-year demographic study. The probabilities of all other transitions (i.e.. all contributions to the seed and seedling classes) were estimated as the product of the following variables:

G. Gi, = germination rates of new. old seeds; S. Sg = seed, seedling sur% i\ al rates; F = percent seed set; B = achene output.

A Seed Seedling Juvenile Small Large Sm. rep. Lg. rep.

Seed Seed Fecundity Fecundity Nurxival

Seedling Seed Fecundity - Fecundity - termination germination germination

Juvenile Grouih Stasis Regression

Small Growih Stasis Regression

Large Growih Stasis

Sm. rep, Flowering

Lg. rep. Flowering 16(1

Table 1 (cont'd)

B 0 1 2 3 4 5 6 Seed Seedling Juvenile Small Large Sm. rep. Lg. rep.

0 (l-Go)S B5F(1-G)S Bf,F(l-G)S Seed

GqSQ B5FGSG Bf,FGSG Seedling

•> m 0--y\ ^•>•5 Juvenile

3 a,, a.34 Small

^44 Large

J ^53 Sm. rep.

6 Lg. rep. 167

Table 2. Summary matrix for the Haleakala silversword. Matrix entries represent

transition probabilities when all years (N = 15) and plots (N = 11) are pooled. Transition

probabilities marked with an asterisk were calculated as described in Table 1. using the

following estimates of reproducti\ e \ ital rates; G = 0.05. Go = 0.03; S = 0.05. Sg = 0.04;

Bv = 3000. Bf, = 18.000; F = 0.20. Estimates of reproductive \ ital rates are based on

germination experiments, rosette size - achene production relationships, and assessments

of percent seed set \ ariation among individuals and among years (Appendix B).

Seed Seedling Juvenile Small Large Sm. rep. Lg. rep.

Seed 0.049* 28.500* 171.000*

Seedling 0.001* 1.200* 7.200*

Juvenile 0.588 0.800 0.022

Small 0.091 0.895 0.025

Large 0.040 0.893

Sm. rep. 0.003

Lg. rep. 0.070 168

Table 3. A\ erage matrix for the Haleakala sih ersword. Matrix entries represent the average (standard deviation) transition probabilities among years (N = 15). when all plots

(N = 11) are combined. Transition probabilities marked with an asterisk were calculated as described in Tables 1 and 2. using the following estimates of reproducti\e vital rates:

G = 0.05. Go = 0.03; S = 0.05. Sq = 0.04; Bs = 3000. B,, = 18.000; F = 0.20. The remaining \ alues were calculated as part of the long-term sih ersw ord monitoring study.

Seed Seedling Juvenile Small Large Sm. rep. Lg. rep.

Seed 0.049* 28.500* 171.000*

Seedling 0.001* 1.200* 7.200*

0.690 0.800 0.027 Juvenile (0.315) (0.087) (0.040) 0.093 0.888 0.025 Small (0.070) (0.056) (0.043) 0.042 0.S95 Large (0.027) (0.085) 0.003 Sm. rep. (0.005) 0.068 Lg. rep. (0.078) 169

Table 4. Elasticities of all transitions in the Haleakala silversword lite cycle. Elasticities are generated by the summary transition matri.x (all years and plots pooled). Transitions with the largest relative impact on population growth rate are shown in bold.

Seed Seedling Juvenile Small Large Sm. rep. Lg. rep.

Seed 0.0001 0.0001 0.0008

Seedling 0.0008 0.0005 0.0274

Juvenile 0.0287 0.1437 0.0045

Small 0.0332 0.3758 0.0046

Large 0.0328 0.3183

Sm. rep. 0.0005

Lg. rep. 0.0282 170

Table 5. Matrix of coaelation coefficients among all transition parameters in the

Haleakala silversword life cycle. N = 15 annual transitions; asterisks indicate level of statistical significance. For each transition parameter, the notation a,, indicates the probability of an individual in stage class j transitioning to stage class /" within one year.

Numbers correspond to the following stage classes: (1) seeding. (2) juvenile. (3) small adult. (4) large adult. (5) small reproductive plant. (6) large reproductive plant.

a:! a22 as: a23 ass a4s ass as4 a44

0.025 as: 0.479* -0.548** -0,095 -0.275 a23 -0.228 an -0.132 0.481* -0.079 -0.849*** 0.657*» a43 -0.210 0.507** -0.001 -0.426* 0.357 0.285 ass 0.120 -0.448* 0.360 0.142 a}4 0.125 -0.332 0.012 0.600** -0.419 -0.245 -0.319 au -0.05" 0.168 -0.112 0.129 0.251 0.262 -0.582** -0.228 a6j 0.102 0.081 0.160 -0.412 0.445* -0.052 0.804*** -0.2" 1 -0.S47***

* <0.10. ** < 0.05. *** < 0.001 Table b. Coet'ficients of\ariation (SD mean x 100) among (A) years. (B) plots, and (C) cinder cones of the ten transition parameters quantified in the field for the Haleakala sih ersword. Values greater than or equal to 100 are shown in bold.

Seedling Juvenile Small Large

A Juvenile 46 11 148

Small 75 6 172

Large 64 9

Sm. rep. 167

Lg. rep. 115

B Juvenile 54 20 85

Small 52 7 128

Large S3 5

Sm. rep. 270

Lg. rep. 51 c Juvenile 25 3 59

Small 25 2 100

Large 51 3

Sm. rep. 100

Lg. rep. 36 172

Table 7. Population growth rate (/.) and damping ratio (/-i /,:) tor the Haleakala sihersvvord tor each (A) pair of years. (B) plot, and (C) cinder cone.

A

^ ear /. >.2

1982-1983 0.991 1.334 1983-1984 0.955 1.027 1984-1985 0.968 1.051 1985-1986 1.020 1.288 1986-1987 1.024 1.155 1987-1988 0.952 1.022 1988-1989 1.050 1.290 1989-1990 1.036 1.184 1990-1991 0.960 1.336 1991-1992 1.028 1.211

1996-1997 1.072 1.396 1997-1998 0.976 1.100 1998-1999 0.881 1.127 1999-2000 0.969 1.199 2000-2001 1.012 1.284 173

Table 7 (Cont'd).

B

Plot A ^2

1 0.978 1.357 0.976 1.238 :> 0.926 1.274 4 0.988 1.262 5 1.042 1.274 6 0.957 1.177 7 0.977 1.091 8 0.988 1.235 9 0.951 1.214 10 0.956 1.195 11 1.010 1.172

c

Cone /. A] / /vT

Puu Nole 0.981 1.251 Puu 0 Pele 1.013 1.268 Puu 0 Maui 0.957 1.177 Ka .Moa o Pele 0.988 1.189 Puu Naue 0.970 1.186 174

Table 8. Coefficients of \ ariation of elasticities associated with all transitions in the

Haleakala silversword life cycle. Tables show variation among (A) years. (B) plots, and

(C) cinder cones. Values greater than or equal to 100 are shown in bold.

Seed Seedling Juvenile Small Large Sm. rep. Lg. rep. A Seed 0 0 83 Seedling S3 167 91 Juvenile 91 94 197 Small 77 73 125 Large 75 69 Sm. rep. 167 Lg. rep. 91

B Seed 0 0 57 Seedling 57 160 50 Juvenile 50 47 100 Small 41 44 121 Large 46 58 Sm. rep. 160 Lg. rep. 51 c Seed 0 0 25 Seedling 25 100 29 Juvenile 29 21 70 Small 19 10 116 Large 29 21 Sm. rep. 125 Lg. rep. 29 175

Table 9. Correlation coefficients between the elasticities of all matrix entries and predicted population growth rate (/.) for the Haleakala silversword for all (A) years (N =

15). (B) plots (N = 11). and (C) cinder cones (N = 5). Asterisks indicate level of statistical significance.

seed seedling juvenile small large sm rep Ig rep

seed 0.230 0.108 0.6S8*** seedling 0.706*** 0.307* 0.698*** ju\enile 0.705*** 0.284* -0.360* small 0.463** -0.080 -0.165 large 0.591** -0.047 sm rep 0.303* Ig rep 0.698***

B seed 0.249 0.001 0.372* seedling 0.336 0.019 0.436* juvenile 0.442* 0.120 -0.012 small 0.405* 0.137 0.022 large 0.443* -0.259 sm rep 0.016 Ig rep 0.432*

seed 0.000 0.000 0.811* seedling 0.770* 0.035 0.787* ju\enile 0.764* -0.053 -0.758* small 0.408 0.041 0.009 large 0.669 -0.173 sm rep 0.047 Ig rep 0.783*

* < 0.05. ** < 0.005. *** <0.0001. 176

FIGURE LEGENDS

FIGURE 1. Haleakala crater. Haleakala National Park. Maui. Hawaii.

FIGURE 2. The Haleakala silversword in bloom.

FIGURE 3. Silversword Plot =9. Puu Naue. Haleakala crater. Haleakala National Park.

Maui. Hawaii.

FIGURE 4. Satellite image of Haleakala crater. Haleakala National Park. Maui. Hawaii.

Filled circles indicate the locations of 11 permanent sih ersword demography- plots.

FIGURE 5. Reproduction in the Haleakala sih ersword. Light arrows indicate transitions to the seed stage class; dark arrows indicate transitions to the seedling stage class. B = the number of achenes produced by small and large reproducti\ e plants; F = percent seed set; G = germination rate of newly produced seeds; Gd = germination rate of seeds one y ear old or older; S = surv ival rate of seeds in seed bank; Sg = survival rate of new seedlings.

FIGURE 6. Correlation between Haleakala silversword age and rosette diameter (cm).

Rosette diameters were measured in 2001; individuals that died prior to 2001 are not included in this sample. Markers represent average current rosette diameter of each 177 seedling cohort (= I SE). The absence of a marker for a given age means that either no seedlings germinated in that year, seedlings were not censused in that year (i.e.. 1993-

1995). or seedlings germinated but all individuals in the cohort died prior to 2001.

R- = 0.675. F = 20.729. dt'=\\.P = 0.001.

FIGL'RE 7. Life cycle graph for the Haleakala siU ersword. The seven stage classes, defmed by rosette diameter and reproducti\ e status are; seed, seedling, juvenile (< 5 cm), small adult (5-20 cm), large adult (> 20 cm), small reproductive plant, and large reproducti\ e plant (see te.xt). .A.nro\vs indicate all possible transitions among the life histor\' stage classes.

FIGL'RE S. Surv ivorship curves for tlve Haleakala silversword seedling cohorts. Only annual cohorts with more than 25 seedlings were included in this figure.

FIGL'RE 9. Annual surv ival probabilities for the four vegetative stage classes of the

Haleakala silversword. Survival probabilities are from the summary matri.x (all years and plots pooled) and represent the summed transition probabilities of stasis, growth, and regression for each of the four stage classes.

FIGL'RE 10. A\ erage time in years (= 1 SD) that an individual plant spends in each stage class of the Haleakala silversword life cycle. PS

FIGURE 11. Change in the number of Haleakala silverswords in 11 permanent plots.

1982-2001. The decrease in the number of sih erswords corresponds with a /. = 0.985.

FIGL'RE 12. Reproducti\ e \ alue of each of the se\ en life history stage classes of the

Haleakala siK ersword. Reproducti\ e \ alue is equivalent to the left eigen\ ectors associated with the dominant eigenvalue (/.). based on the summary- matri.x (all \ ears and plots pooled).

FIGURE 13. Stable stage distribution predicted by the summary' matri.x (all years and plots pooled) for the Haleakala silversword. (A) The relative proportion of individuals in the seed and \ egetative classes in the stable stage distribution. (B) Stable stage distribution (hatched bars) \ ersus stage distribution observed in 2001 (clear bars), for

\ egetati\ e classes only. In (.\). bars represent the proportion of all indi\ iduals in each of the se\ en stage classes in the stable stage distribution; in (B). clear bars represent the proportion of all plants in each of the six \ egetative stage classes in the stable stage distribution.

FIGURE 14. Sensiti\ ities of all demographic transitions in the Haleakala silversword life cycle, based on the summary matrix (all years and plots pooled). (A) Sensitivities of all transitions from the vegetative and reproductive stage classes {i.e.. seedling, juvenile, small adult, large adult, small reproductive, and large reproductive) to all other stage classes. Lines represent the sensiti\'ities associated with transitions from the stage listed 179 in the legend to the stage listed on the .v axis. (B) Sensitivities of transitions from the seed stage class to all other stage classes.

FIGURE 15. Total elasticitv associated with (A) the seven life histor\' stage classes and

(B) the three t\pes of transitions in the Haleakala silversword life cycle, based on the summar>- matri.x (all years and plots pooled). In (A), the total elasticity of each stage is the sum of elasticities for all transitions from that stage {i.e.. column sum). In (B). bars represent the elasticity associated with transitions of growth, surv ival, and reproduction.

FIGURE 16. Correlation between the variability of each matri.x entrv' and its corresponding () sensitivity (R" = 0.807. F| - = 29.285. P = 0.0010) or (B) elasticity

(R" = 0."33. F| > = 21.936, P = 0.0016). Variability of matri.x entries is among 15 annual transition matrices (all plots pooled); sensiti\ ities and elasticities are deri\ed from the a\erage transition matrix (all plots pooled).

FIGURE 17. Temporal \ariation in population growth rate (/.) for the Haleakala sil\ ersword. The dotted line represents the predicted asymptotic population growth rate for each pair of years, based on each annual transition matrix, all plots pooled. The solid line represents the observ ed change in population size between each pair of years. 1982 -

2001. The hea\ y dashed line indicates a stable population growth rate (/. = 1). 180

FIGURE 18. Spatial variation (among plots) in population growth rate (/.) for the

Haleakala silversword. Hatched bars represent the predicted asNinptotic population growth rate for each of the 11 permanent plots, based on the transition matrices generated for each plot, all years pooled. Open bars represent the obser\ ed change in population size in each plot. 1982 - 2001. The heavy dashed line indicates a stable population growth rate. (/. = 1).

FIGURE 19. Spatial variation (among cinder cones) in population growth rate (/.) for the

Haleakala siKersword. Hatched bars represent the predicted asymptotic population growth rate for each of the five cinder cones, based on the transition matrices generated for each cinder cone, plots combined and all years pooled. Open bars represent the observ ed change in population size on each cinder cone. 1982 - 2001. The heavy dashed line indicates a stable population growth rate. (/. = 1).

FIGURE 20. \ ariation in sensitivity parameters across (A) years. (B) plots, and (C) cinder cones. Lines represent the sensitivities associated with transitions of growth (G; diamonds), survival (L; stasis - regression; squares), and reproduction (F; triangles) from the stage class listed on the .v axis. ISl

FIGURE 21. Variation in elasticity parameters across (A) years. (B) plots, and (C) cinder cones. Lines represent the elasticities associated with transitions of growth (G; diamonds), survival (L; stasis - regression; squares), and reproduction (F; triangles) from the stage class listed on the .v axis.

FIGURE 22. Total elasticity associated with transitions of growth (G). surv ival (L). and reproduction (F) for (A) 15 annual transition matrices (all plots pooled). (B) 11 plot transition matrices (all years pooled), and (C) the cinder cone transition matrices (plots combined and all years pooled).

FIGURE 23. Distribution of total elasticity among the seven stage classes of the

Haleakala silversword life cycle for (.A) the 15 annual transition matrices and (B) the 11 plot transition matrices. In (A), solid lines represent years e.\hibiting a positive population grov\ th rate (/. > 1; N = 7 years) and dotted lines represent years e.xhibiting a negative population growth rate (/. < 1; N = 8 years). In (B). solid lines represent plots e.vhibiting relatively high population growth rates (/. > 0.99: N = 4). and dotted lines represent plots exhibiting relatively low population growth rates (/. < 0.98; N = 7). The total elasticity of each stage class is the sum of elasticities for all transitions from that stage {i.e.. column sum). 182

FIGURE 1 FIGURE 2 184

FIGURES 185

FIGURE 4 B5F(1-G)S (^d-Gc small reproductive seed bank

B6F(1-G)S

large reproducti\e

FIGURE 5 0 2 4 6 8 10 1 Age (years)

FIGURE 6 seed

sdIg

JUV

sm sm rep

Igrep

FIGURE 7 1S9

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Age (years)

FIGURE 8 Annual survival 191

23

20

15

10

seed sdlg ju\ sm Ig smrep Igrep

Staae class

FIGURE 10 192

500

450

400

350

300

250

200

150

100

50

0

FIGURE 11 0.4

0.35

0.3

0.25 > 0.2 r -. •'. I

£ 0.15 !r,i^=V-j y ,-': •- ' : J"

0.1

0.05

seed sdlg ju\' sm Ig sm rep Ig

Stage class

FIGURE 12 0.8

ppf ."* v„ *

seed sdlg ju\ sm Ig sm rep Ig rep

Stage class

FIGURE 13A • Obsened El Stable Distribution

X- = 9.90, P > 0.05 PS = 89.34%

JZl

sdlu ju\- sm Ig sm rep Igrep

Stage class

FIGURE 13B • " • sdig juv — — sm Ig sm rep Ig rep

I

0.8

0."

0.6

0.5

0.4

0

seed JUV sm smrep ig rep

Stage class

6

4

0 seed sdlii ju\ sm sm rep Ig rep

Stage class

FIGURE 14 seed sdliz ju\ sm Ig sm rep Ig rep Stage class

0.8 B -<41 0.7

0.6

0.5 'ti. -TiSSfe 0.4

0.3

0.2 —- - .if-rtK

0.1

0 Grouth Sur\i\al Reproduction

Type of transition

FIGURE 15 19S

B log (variance)

0 r 0 0.5 2;5 -0.5 • i

-1 O 1 - ^ -l.D

<» ' -1 - Ufi Q -J

-3.5

-4 log (CV) 199

-Predicted • Observed Stable

I.I

1.05

=ij 0,')5

0.^

0.S5

O.S

FIGURE 17 Population growth rati

t-H o c s

00 i.o:

l.OI

1

0.99

0.98

0.9"

0.96

0.95

0.94

0.93

0.92 202

1983 1987

1988 1984 I 5

1989 1985 I 5

•

1990 1986 15

Staae class Staae class

FIGURE 20A 203

1 .5 1991 < 1999

0 5

1992 I 5 2000

1997 15 2001

Staae class

1998

FIGURE 20A (Cont'd)

Stage class Stage class Stage class

FIGURE 20B 205

11

10

,< II

ZL CCi

Stage class

FIGURE 20B (Cont'd) 206

Puu Nole I 5 Ka Moa o Pele

Puu o Pele Puu Naue 1 5

Stage class

Puu 0 Maui

^ ^ ^ p- ^

FIGURE 20C Stase class 207

1 I -

OS. 1987 08 1983

06 I) b •

04 0 4

02

0 I)

1 - - 1984 OS 1988

» ty I) 6

" 4 I) 4

1 1985 OX 1989 0 6

4 U 4

I) 2

0

I 1 • 1986 ,)8 1990 o h U 6 •

0 4 0 4

0 2

() ZL I) •f r.

FIGURE 21A 208

I

I) s D.S • 1999

II 6

o 4 II 2

1992

ns 1997 2001 I) n

II 4

II

I

II s Staae class

11 h

II 4 It 2 II

FIGURE 21A (Cont'd) Stage class 209

FIGURE 2IB 210

FIGURE 2IB (Cont'd) 211

1 • - - - Puu Noie 0 s Ka Moa o Pele 0 0

U 4

(i

1 1 • " Puu o Pele " ^ Puu Naue I' U t>

U 4 4

0 Zlj Zi]

I Stage class " X Puu o Maui

' 4

ctt

Stage class

FIGURE 2IC 0.0»1.0

0.1 \0.9 0.2/ } NO.8 0.3/ \0.7 0.4/ \p.6 F 0.5/ \0.5 0.6/ - \0.4 \ 0.7/ ' •0.3

0.8/ \0.2

0.9/ • - . \0.1

1.0' •0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 G

V\0.9

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 G

FIGURE 22 0 .0 -,10 0.1 ' ^\p.9 0.2/ •• \0.8 0.3 - \0.7

0.4 ....\o ,6 ^ 0.5 \0.5 ^ 0.6- kOA 0.7 \0.3

0 8 \p.2 0.9' \0.1 10 -0.0 0.0 0.1 0.2 0 3 0.4 0.5 06 0.7 0.8 0.9 1 0 G

FIGURE 22 (CONT'D) 0.800

0.600

0.400

0.200

0.000 seed sdlg juv sm Ig sm rep Ig rep

1.200

1.000 B

0.800

0.600

0.400

0.200

0.000 seed sdlg ju\' sm Ig sm rep ig rep

Stage class

FIGURE 23 APPENDIX D:

DEMOGR-APHIC MODELING OF HAWAIIAN SILVERSVVORDS

(ASTER.\CEAE): IMPLICATIONS FOR CONSERVATION AND

MANAGEMENT 216

DEMOGRAPHIC MODELING OF HAWAIIAN SILVERSWORDS (ASTERACEAE):

IMPLICATIONS FOR CONSERVATION AND MANAGEMENT

Stacey A. Forsyth and Robert H. Robichaux

Department of Ecology & Evolutionary Biology.

The University of Arizona. Tucson. AZ 85721

email: [email protected]

Key words: Argentine ant, elasticity, population viability analysis (PVA), matrix population model. Haleakala silversvvord. Mauna Kea silversvvord 217

Abstract

Population \ iability analysis (PV^A.) is currently recognized as an important tool in the management of rare and endangered species. P\'A provides a quantitati\ e assessment of population dvnamics. and can be used to project a population's fiiture size and structure, as well as to evaluate extinction risk. Through such analyses, it is also possible to determine the stages in a species" life historv' that are most critical to population growth rate (/.). and to assess the relative effects on of different disturbance or management regimes. In this study, we used a stage-based matri.x population model de\ eloped for the Haleakala siKersword (Argyroxiphiiim sandwicense ssp. macrocephalum) to better understand factors influencing the persistence of this species.

W e also e.xtrapolated tirom the model to assess the \ iability of a closely related subspecies, the .Mauna Kea sihersword (Argy roxiphium sandwicense ssp. sandwicense). under different disturbance and management scenarios. With elasticity and perturbation analyses. v\ e determined that siK ersword population growth rate was most sensiti\ e to changes in adult sur\ival rates. Similarly, a series of deterministic and stochastic models re\ ealed that factors influencing surv ival rates, such as browsing or outplanting. had much larger effects on /. than did factors influencing seed set. Greenhouse rearing, which raises germination and seedling survival rates, also had very large impacts on /.. Our results suggest that management strategies aimed at increasing either germination rates or adult sur\ i\ al rates will be most effective in ensuring the persistence and growth of sih ersword populations. 218

Introduction

In the past two decades, population viability analysis (PVA) has developed into

an important tool for the conservation and management of rare and endangered species

(Brook et al. 2000. Reed et al. 2002). PVAs are based on field-collected demographic data, and can be used to project future population size, evaluate extinction risk and a\ erage time to extinction, and compare the persistence of a population under a range of different scenarios (Menges 2000a). Certain components of PVA. such as sensitivity and elasticity analyses, provide insight into the relative importance of different life history stages and transitions for a population's growth rate (de Kroon et al. 1986. Schemske

1994). .Although the accuracy and reliability of PVAs are sometimes limited by incomplete demographic data (Beissinger and Westphal 1998. Bierzychudek 1999).

PVAs based on robust data are povverftil tools for comparing the relative effects of different disturbance or management regimes on population persistence (Menges 20006.

Reed et al. 2002).

PVAs are frequently based on analyses of age- or stage-based matrix population models (Caswell 2001). Such models have been used to inform conservation decisions for a variety of species. For example, analysis of a stage-based demographic model for the loggerhead sea turtle {Caretta careita) demonstrated that large juvenile sea turtles made the greatest contribution to population growth rate (Crouse et al. 1987). This finding suggested that the most common management practices, including protecting eggs on nesting beaches and "headstarting" turtles by rearing hatchlings in captivity for se\ eral months, were actually targeting the least responsive life history stages, and that 2U)

management strategies targeted at the juvenile stage, such as turtle excluding de\ ices.

would be much more effective (Crouse et al. 1987. Crowder et al. 1994. Heppell et al.

1996). Similar contributions to management were made by demographic studies of the desert tortoise (Gophenis agassizii) and cheetah (Acinonyxjubatiis). which revealed that,

for both species, population growth rate was more sensitive to adult sun ival than to an\ other life history- transition (Doak et al. 1994. Crooks et al. 1998). In both cases, these

findings helped shift conser\ ation efforts trom less effective actions targeting juvenile stages to more effective measures aimed at maintaining or increasing adult sun'i\ al rates.

.Additional studies have used matri.x modeling of demographic data to determine \ iable le\ els of harvesting (Ratsirarson et al. 1996). compare reserv e design strategies

(.Andersen and Mahato 1995). evaluate the effectiveness of predator control techniques

(Harding et al. 2001). and determine the most effective frequencies of controlled bums

(Burgman and Lamont 1992. Gross et al. 1998. Caswell and Kaye 2001).

In this study, we use matrix modeling techniques to evaluate the consequences of different disturbance and management regimes for the persistence of two federally-listed

Hawaiian plants. The threatened Haleakala silversword (Argyroxiphium sandwicense ssp. macrocephalum) and the critically endangered Mauna Kea silversword

(Argy roxiphium sandwicense ssp. sandwicense) exhibit very similar life histories and are of much interest to both evolutionary and conser\ ation biologists. The Haleakala siK ersword successfully rebounded from a substantial decline in the late 19'^' and early

20''' centuries, but a recent study suggests that this population may once again be in decline (.Appendix C). The remnant natural population of the Mauna Kea silversword 220 currently contains only 34 indi\ iduals. with an additional 4.000 individuals outplanted on

Mauna Kea in the past three decades. Both subspecies currently face the in\ asion of alien social insects, including the .Argentine ant and western yellowjacket. which prey on nati\ e pollinators; in addition, the Mauna K.ea sih ersword faces the ongoing threat of alien ungulates, especially mouflon sheep.

Here, we use a stage-based matrix population model of the Haleakala sih ersword. based on 20 years of demographic data, to assess the relative impacts of these threats on sil\ ersword population viability. We also use the model to weigh the relati\ e effecti\ eness of different management strategies for maintaining or increasing sil\ ersword population growth rate. Specifically, we use a combination of deterministic and stochastic models to (1) determine which life historv- transitions ha\ e the greatest relati\ e impact on population growth rate; (2) compare the relative effects of alien social insects and ungulates on population growth rate; and (3) assess the relative effectiveness of three management strategies; managed breeding (i.e.. increased seed set), greenhouse rearing (increased germination and early seedling survival rates), and outplanting

(increased survival and growth rates of all vegetative stage classes). .A.lthough our models are based on data from the Haleakala silversword population, we use these data to model the v iability of the Mauna Kea silversword population as well, due to the very- similar life histories exhibited by these two subspecies. 221

Species Background

The Haleakala and Mauna Kea silverswords are closely related subspecies in the

Hawaiian siK ersword alliance (Asteraceae). a monophyletic lineage descended trom

North American tarvveed ancestors (Baldwin 1996). A premier example of adapti\ e radiation in plants, this lineage displays a wide variety of growth forms, including trees, shrubs, rosette plants, and lianas (Carr 1985). The two subspecies are endemic to the alpine and subalpine regions of Hawaii, and exhibit ver>' similar life histories. The

Haleakala silversword is endemic to the Island of Maui, growing on the cinder cones and la\ a tlows within the crater of Haleakala volcano (2000 - 3000 m). as well as on the outer slope near the volcano's summit (3000 - 3341 m). The Mauna Kea silversword is endemic to the upper slopes of Mauna K.ea (2600 - 3800 m) on the Island of Hawaii.

Indi\ iduals of both subspecies grow for many years as basal rosettes and produce tall tlouering stalks (capitulescences) bearing hundreds of radiate flowerheads (capitula).

Flowering occurs throughout the summer months, tvpically peaking in July. The

Haleakala silversword is monocarpic: individuals grow as a single rosette and reproduce only once before they die. In contrast, the Mauna Kea silversword displays a higher incidence of multiple-rosette individuals, which are potentially polycarpic. In the remnant natural Mauna Kea silversword population, approximately 25° o of individuals ha\ e multiple rosettes, whereas in the outplanted population, more than 90° o of indiv iduals ha\ e multiple rosettes. This discrepancy may be due to a genetic bottleneck that occurred in the initial reintroduction of this species. It has also been noted that greenhouse-raised individuals (that are later outplanted) frequently grow multiple rosettes (Robichaux. unpub. data). Previous studies have demonstrated that the two silversword subspecies are both highly self-incompatible and require insect pollination, primarily by nati\ e yellow-faced bees (Hylaeiis spp.; Colletidae). in order to produce viable seed (Carr et al. 19S6. Powell 1992. .A.ppendi.x A).

The Haleakala and Mauna Kea sih erswords both suffered population declines in the late 19'"'' and early 20^ centuries, primarily because of browsing by alien ungulates.

.At Haleakala. browsing by introduced goats and cattle, combined with human collection and \ andalism. reduced the silversword population to a low of approximately 5.000 individuals by the 1920s (Loope and Crivellone 1986). This subspecies was federally listed as threatened in 1992 (U.S. Fish and Wildlife Service 1992). The Mauna Kea silv ersword population suffered an even more precipitous decline due to browsing by alien ungulates, especially sheep, which were introduced in the late 1700s (U.S. Fish and

Wildlife Service 1994). The only sih erswords that survived on .Mauna K.ea were those located on steep rocky clitf faces, the only terrain inaccessible to alien ungulates. Thus, browsing disrupted the continguous population and created a fragmented population in which surviving individuals were frequently isolated from other conspecitics. Due to the silversword's strong self-incompatibility mechanism, this fragmentation likely caused the population to decline even ftirther. By the late 1970s, only a small remnant population of the Mauna K.ea sih ersword remained (Robichaux et al. 1997). This subspecies was federally listed as endangered in 1986 (U.S. Fish and Wildlife Service 1986).

At Haleakala. the recovery of the silversword was aided by the formation of

Haleakala National Park, which provided the species with federal protection from human 223

\ andalism (Loope and Cri\ ellone 19S6). The subsequent eradication of alien ungulates and the fencing of the park removed the threat of browsing. This protection allowed the

Haleakala sih ersword population to make a substantial recovery, increasing to about

50.000 individuals by the mid-1980s (Loope and Crivellone 1986). Population censuses begun in 1971 and conducted ever>' ten years suggested an initial increase to more than

60.000 plants in 1991. followed by a subsequent decline to approximately 50.000 plants in 2001 (F. Starr, personal communication).

On Mauna Kea. concern for the silversword population led the Hawaii

Department of Land and Natural Resources. Division of Forestrv' and Wildlife, to initiate an outplanting program in the 1970s, in order to promote the recoverv' of this subspecies

(Robichaux et al. 1997). .A.s part of this program, \ iable seeds were harv ested trom two plants that tlowered in the remnant natural population in 1973. Seedlings were grown in greenhouses, and outplanted as small plants into fenced exclosures on Mauna Kea

(Robichaux et al. 1997). Subsequent outplanting efforts, in fenced and unfenced areas. ha\ e increased the outplanted population to more than 4.000 individuals. Key elements of the current .Mauna Kea silversword reintroduction program include managed breeding, in which hand-pollinations are performed in order to augment outcross pollen loads and increase the number of genetic founders: greenhouse rearing, in which seeds are germinated in greenhouses and newly-germinated seedlings are maintained in the greenhouses for approximately 9-12 months; and outplanting indixiduals at 9-12 months, when the\' are approximately 7-10 cm in diameter. 224

CurrentK'. a primarv" threat to the Haleakala and Mauna Kea sih erswords is the spread of alien social insects into Hawaiian alpine and subalpine areas. The Argentine ant (Lincpiihema humile) and western yellowjacket (Vespula pensylvanica) are two alien

predators that ha\ e been shown to reduce populations of native insect species, including

pollinators such as Hylaeus (Cole et al. 1992). Due to their strong self-incompatibilit\' mechanism, the two siK ersword subspecies are extremely vulnerable to factors that affect pollinator abundance or efficiency, .^.ny reductions in pollinator populations could lead to se\ ere pollen limitation and subsequently, greatly reduced seed set and reproductive success. Honeybees (Apis mellifera) may also affect seed set by silverswords. through competition with native pollinators and or disruption of native plant-pollinator interactions, but the effectiveness of honeybees as silversword pollinators is currently unknown.

In addition to the effects of alien social insects, the Mauna Kea silversword continues to be vulnerable to browsing by alien ungulates, especially moutlon sheep, which still occur on the volcano. Though a court-mandated hunting program was begun in the 19S0s. alien ungulates have not yet been eradicated from Mauna K.ea. and their presence continues to impact the persistence of native plants (U.S. Fish and Wildlife

Ser% ice 1994). Browsing by even low numbers of ungulates has large effects on the sur\ ival and growth of all vegetative stage classes of silverswords. 225

Methods

Silversword matrix model

We assessed the relative effects of different factors on siK ersword population

\ iabilit\'. using a stage-based matrix population model constructed for the Haleakala

siK ersword. This model divided the Haleakala silversword life cycle into the following

seven stage classes, defined by rosette diameter and reproductive status: (0) seed. (1)

seedling. (2) juvenile rosette (< 5 cm). (3) small adult rosette (5-20 cm). (4) large adult

rosette (> 20 cm). (5) small reproductive individual, and (6) large reproducti\e

individual. Demographic vital rates (i.e.. stage-specific probabilities of growth. sur\'i\al.

and reproduction) were determined in a 20-year (1982 - 2001) field study, in which

indi\ iduals in ele\en 5 • 20 m plots were mapped and followed over time (see details in

.Appendix C). The probabilities of ten stage class transitions were quantified in this field study: grovuh of seedlings, juveniles, and small adults; stasis of juveniles, small adults, and large adults; regression of small and large adults to the previous stage classes; and

flowering of small and large adults (Figure 1). For these transitions, we used the 20-year dataset to calculate the mean and standard deviation of each vital rate among years, with data trom all plots combined (Table 1). The model included an additional six transitions related to reproduction: contribufions of the small and large reproducti\ e stage classes to the seed and seedling stage classes; seed survival between years; and seed germination

(Figure 1). The probabilities of these six transitions were esfimated using data fi-om a separate fi\ e-year stud\' on the reproductiv e biology of the Haleakala silversword

(.Appendix B). These six transition probabilities were calculated based on estimates of 226

achene production (B). percent seed set (F). germination rate of one year old or older (G„)

and newly-produced (G) seeds, and the surv ival rate of seeds (5) and newly-germinated

seedlings (So). We used a transition matrix comprised of the average vital rates (av erage

transition matrix) as the basis for multiple deterministic and stochastic analyses (Table 2).

Details on the construction and analysis of the silversword matrix model are presented

elsewhere (Appendix C).

Demographic data for the Mauna Kea silversword are limited, as is trequentlv- the

case for critically endangered species (Beissinger and Westphal 1998). Because of this,

we used the demographic model constructed for the Haleakala silversword to address

questions regarding both the Haleakala and Mauna Kea silverswords. This extension of

the model is possible due to the very similar life histories of the two subspecies. TTie two

sil\ erswords occupy similar habitats and both are very long-lived, growing for an estimated 40-50 years or more before flowering. Both are highly self-incompatible, and

rely on yellow-faced bees (Hylaeus spp.) for pollination (Powell 1992. Appendix .A).

The main distinction between the life histories of these subspecies is that the Mauna Kea sih ersword commonly produces multiple rosettes, at least in the outplanted population, such that a large proportion of individuals are potentially polycarpic. whereas the

Haleakala silversword nearly always produces a single rosette, such that all individuals

are monocarpic. As a result, flowering Mauna Kea silverswords can contribute to both the seed and seedling stage classes, as well as to the small or large non-reproductive stage classes (based on rosette sizes prior to flowering of one or more of the multiple rosettes), whereas flowering Haleakala silverswords can only contribute to the seed and seedling stage classes (Figure 1). The tendency ofMauna K.ea silverswords to reproduce multiple times was therefore incorporated into the matrix model for stochastic simulations for this subspecies.

Elasticity' and perturbation analyses

To evaluate the relative effects of different life history stages and transitions on sih ersvvord population growth rate, we conducted elasticity and perturbation analyses.

We analyzed a deterministic model based on the average transition matri.x. in order to calculate the elasticities of all matrix transitions. We also constructed "low" and "high" transition matrices to simulate the range of vital rates observ ed in the demographic stud\'. and calculated the elasticities of all transitions based on these matrices. Vital rates in the low growth rate matrix were equal to the average v ital rate minus one SD. v\ hereas the

\ ital rates in the high growth rate matrix were equal to the av erage vital rate plus one SD.

Elasticity analyses quantify the relative effects on of small modifications to demographic \ ital rates (de Kxoon et al. 1986. Caswell 2001). However. the\' may not accurately reflect the relative effects on /. when vital rates are modified by a larger degree

(Crouse et al. 1987, Doak et al. 1994). To examine the consequences for /. of larger alterations to demographic \ ital rates, we conducted perturbation analyses. Using the deterministic model based on the average transition matrix as a baseline, we s\ stematically altered each vital rate individually. Specifically, we increased and decreased each \ ital rate by 10% and 20° o of its initial value, and examined the effect on

/.. relativ e to the baseline a and to a stable population growth rate of /. = 1. 22S

For all demographic analyses, including elasticity analyses, perturbation analyses, and the simulations described below, we used ULM (Unified Life Models) sotrware

(Legendre and Clobert 1995).

Modeling the effects of altered vital rates

Negative impacts. Current threats to the sih erswords include the effects of alien social insects (Haleakala and .Mauna K.ea). and continued browsing by alien ungulates (Mauna

K.ea only). The past population declines of the two subspecies are attributed primarih' to predation b\ alien ungulates, as well as to collection by humans in the case of the

Haleakala sih ersword. Using data and obser\ations trom the field, we estimated the degree to which these threats would alter silversword vital rates. The effect of inx asive insects is \ ia pollen limitation, if alien insects indirectly impact sih ersword reproductive success b\ preving on or outcompeting native pollinators. In contrast, browsing by alien ungulates primarih' affects probabilities of growth. surv i\ al. and regression for all

\ egetati\ e stage classes.

Pollen limiiation. Previous studies have shown that the sih ersword is highly self- incompatible. with bagged or selfed capitula exhibiting 0 - 2''o seed set (Carr et al. 1986.

Pov\ ell 1992. Appendix A). .Alien social insects that prey on or outcompete native pollinators, without replacing their pollination services, may therefore ha\ e a large impact on silversword reproductive success via pollen limitation. To assess the potential effect of alien insects on silversword seed set. we examined the Argentine ant invasion at

Haleakala National Park and compared silversword seed set between ant-infested and non-ant-infested areas. 229

In October 1997. ue collected three open-pollinated capitula trom ti\ e

sil\ ersvvords located at Kalahaku. an .Argentine ant-infested area, and from six

sih ersvvords located either on Sliding Sands Trail or near Puu Kauaua. both non-ant-

infested areas. The limited overlap of the silversword and .Argentine ant ranges

prev ented replication of the ant-infested treatment. To ensure that any observ ed pollen

limitation in the .A.rgentine ant-infested area was due to reduced pollinator abundance or efficiencv'. rather than to pollen incompatibility among neighboring plants, we augmented

pollen loads on three capitula on each of five individuals at Kalahaku. using a mix of pollen from at least three other neighboring silverswords. Open-pollinated and pollen- augmented capitula were collected approximately 8-10 weeks after tlowering. when achenes (fruits) were dr\- and close to dispersal. .Achenes were stored in a refrigerator and examined under a dissecting microscope to determine the proportion of achenes that w ere tilled. The proportion of all achenes combined from the three capitula was used as a measure of percent seed set for each plant. Percent seed set data were logit transformed and analyzed with .ANOV.A to evaluate differences in percent seed set among the three treatments: open-pollinated with ants, pollen-augmented with ants, and open-pollinated without ants. Differences between each pair of treatments were analyzed with Tukey tests (alpha = 0.05).

Brousing. We used observations from Mauna Kea to estimate the potential effects of browsing ungulates on silversword demographic vital rates. In the past, the only sih ersvvords that survived the presence of sheep and other ungulates were those located on V ery steep rocky cliff faces, the only terrain inaccessible to browsing ungulates. Thus. 230 the impact of alien ungulates is severe, leading to highly reduced rates of surv ix al and grov\th. To model the effects of different le\ els of browsing, we decreased the survival and grouih rates of all \ egetative stage classes by 25%. 50° o. and 75° o. to simulate light, medium, and heavy levels of browsing, corresponding with different levels of ungulate abundance.

Positive impacts. We estimated the relative effectiveness of three key elements of the current reintroduction program for the Mauna Kea silversword. Specifically, we estimated the positi\e effects on silversword vital rates of (1) managed breeding, or augmenting pollen loads with compatible outcross pollen (i.e.. increased seed set); (2) germinating seeds and rearing seedlings in a greenhouse (increased germination and early seedling sur\'i\'al rates); and (3) outplanting individuals at 7-10 cm diameter (increased ju\ enile and adult survival and growth rates).

Managed breeding. We used data trom pollen augmentation experiments conducted on the Haleakala siK ersword from 1997-1999 (Appendi.\ A), as well as data from the

Mauna K.ea siK ersword reintroduction program (Robichaux. unpub. data), to assess the potential effect of managed breeding on silversword seed set. Pollen augmentation treatments performed on the Haleakala silversword produced, on average. 35.85°o seed set (N = 22). Similar treatments performed on Mauna Kea silverswords in 1997 produced an average of 36.84% seed set (N = 19). These results suggest that although sih ersword seed set can be enhanced with augmented pollen loads, seed set for both subspecies is resource limited, such that with a surplus of outcross pollen, individuals can. on average, only produce about 35-40% seed set. 231

Greenhouse rearing and outplanting. We used data from the greenhouse propagation

and outplanting program on Mauna Kea to estimate the potential etYects of improved

en\ ironmental conditions on seed survival (5). germination rates of newly produced (G)

and older {Gi,) seeds, and early seedling survival rates (Sc). as well as on the survival and

growth rates of all x egetative stage classes following outplanting. In the field,

germination and seed and seedling survival rates are low. each approximately equal to

(Appendix B). In the greenhouse, however, these rates are much higher. The

sur\ i\ al of seeds stored in a refrigerator is high between years, but declines as seeds age.

Of a sample of seeds collected in 1997.68'''o sur\'ived the tirst two years in storage,

whereas only 39'' o survived for three years in storage (Robichaux. unpub. data).

Germination rates (G) are typically higher than 90% in the greenhouse, as are the survival

rates of newly-germinated seedlings (Sc). Once outplanted. individuals have much

higher rates of survival and growth than plants that germinated in the field (Appendix C.

Robichaux. unpub. data). Out of a cohort of 482 seedlings outplanted on Mauna Kea in

1999. 98.0"0 survived the first year. 95.3% survived the first two years, and 93.8%

surv ived the first three years (Robichaux, unpub. data).

Impact ofpolycarpy. Although only 25% of individuals in the natural Mauna Kea sih ersword population are multi-rosette, more than 90% of individuals in the outplanted

population are multi-rosette and therefore potentially polycarpic. The majority of multi-

rosette indiv iduals have 2-5 rosettes, but some individuals have as many as 25 or more

rosettes. To evaluate the impact ofpolycarpy on the Mauna Kea silversvvord model, we

incorporated transitions from the small and large reproductive stage classes to the small and large non-reproducti\ e stage classes, respectively, in the matrix model. We examined the etfect of polycarpy on /. when the probability of reproducing again (Pj?.

Pjh. for small and large reproductive plants, respectix ely) was 0.00. 0.25. 0.50. and 0.75.

Modeling procedure. We used the results of deterministic and stochastic models based on the a\ erage transition matrix as a baseline against which other models were compared.

Using the data and observations described above, we constructed new transition matrices of altered demographic vital rates, which incorporated changes to seed set le\ els. germination and seedling sur\ ival rates, and juvenile and adult sur\ i\ al and growth rates.

\\'e pertbrmed deterministic and stochastic simulations based on these altered transition matrices, in order to assess the relative effects of different threats and management options on sih ersword population viability.

Dcicrminisiic models. We used deterministic models based on the altered transition matrices to compare the relative effects of moditled vital rates and incidence of polycarp\' on population growih rate. First, we examined the effect of seed set on when all other

\ ital rates were held constant, in order to assess the relative effects of reduced seed set. due to alien social insects, and increased seed set. due to managed breeding. Then, we examined the relati\ e effects on /. of reduced survival and growth rates (of all vegetative stage classes) due to browsing; of increased germination and seedling surv ival rates due to greenhouse rearing; and of increased survival and growth rates (of all vegetati\ e stage classes) due to outplanting. The consequences of altered vital rates were examined across a potential range of seed set levels (10- 50% seed set), in order to examine any interactions between seed set and other demographic vital rates. In addition, we incorporated different probabilities of polycarpy (P35. P46 = 0. 0.25. 0.50. and 0.75) into the deterministic model based on the average transition matri.\. in order to assess the impact on /. of multiple reproductive episodes per individual.

Stochastic models. In all stochastic simulations, we used a beta distribution defined by the mean and standard deviation of each vital rate. The stochastic simulations began with an initial population size of either 50.000 vegetative individuals plus 20.000 seeds (to simulate the Haleakala silversword population), or 5.000 vegetative individuals plus

1.000 seeds (to simulate the Mauna Kea silversword population). In all simulations, the initial population was distributed among the si.x vegetative stage classes as predicted by the stable stage distribution. We performed .Monte Carlo simulations, calculating 500 replicates of 100 years for each simulation. Based on these simulations, we projected the population size of both subspecies over the 100-year period and calculated the mean population growth rate, the growth rate of the mean population, the probability of extinction, and time to extinction (if applicable). We performed both density- independent and density-dependent stochastic simulations, using the average and altered transition matrices, in order to examine the relative effects of browsing, greenhouse rearing, outplanting. seed set. and polycarpy (Mauna Kea silversword only) on population persistence.

Densiry -dependence. Silversword seed set varies according to the abundance of flowering plants, with higher percent seed set observed in years of greater flowering

(Figure 2.A.: .Appendix This positive density-dependence was incorporated into a subset ot" stochastic simulations, in which percent seed set (F) varied according to the tbllovving equation:

F = Fmax Ml- exp(-A:{- flowering plants))). (1) where F„,a.x equaled 0.40. or the maximum percent seed set obser\'ed in this stud\'

(Appendix A), and k was the slope defining the relationship between the number of tlowering plants and percent seed set (Figure 2B). hi this paper, we define k as pollination efficiency, a product of the interaction between the abundance of both tlowering plants and pollinators. In order to model the effects of decreased pollination efficiency (resulting from reduced pollinator abundance), we used the relationship observ ed fi-om 1997 - 2001 as the baseline relationship, and re-calculated the relationship if efficiency declined to 50%. and 25% of its current level (Figure 2.A.). The slopes of the new relationships (Figure IB) were incorporated into density-dependent stochastic models for the Haleakala and Mauna K.ea sih erswords.

Results

The results of the elasticity analyses, perturbation analyses, and the deterministic and stochastic models were highly congruent. The analyses suggested that of all demographic transifions in the silversword life cycle, adult plant survival has the largest relati\ e impact on k. As a result, positive and negative factors that affect this transition v\ ill ha\ e large effects on k. In contrast, transitions related to reproduction had relatively small impacts on suggesting that factors affecting these transitions will have negligible effects on sih ersword population growth rate. Elasticity and perturbation analyses

Of all parameters in the average transition matrix. sur\ i\ al of small adults had the highest elasticity, followed by surv ival of large adults and juveniles (Table I). In the low transition matrix, nearly all of the total elasticity was associated with the sur\ ival of small adults (Figure 3A). However, as demographic vital rates increased, the distribution of elasticitv- among the different life historv' transitions became more e\en (Figure 3).

Speciticalh', the elasticities associated with the survival of juveniles and large adults greatly increased as vital rates increased (Figure 3B. C). For all transition matrices, regression of small and large adults and flowering of small adults had extremely low elasticities; growth of seedlings, juveniles, and small adults, and flowering of large adults, had slightly higher elasticities (Figure 3).

When indi\ iduai vital rates were perturbed by larger amounts (lO^o and 20" o). the effects on /. followed the predictions of the elasticity analyses. Changes to survi\ al rates had much larger effects on k than did equivalent changes to rates of growth, regression, and flowering (Figure 4). Effects on /. were largest for changes to the small adult sun. i\ al rate, followed b\' sur\ival rates of large adults and juveniles. Perturbations to rates of regression, as well as flowering of small adults, had virtually no effect on similarly, alterations to growth rates and flowering of large adults had small, but slightly more noticeable, effects on /. (Figure 4).

Argentine ant impacts on seed set

Plants that were open-pollinated in the Argentine ant-infested area had signiflcanth' reduced seed set. relative to plants that were open-pollinated in non-ant- infested areas (Figure 5). Average percent seed set in the ant-infested area was 2.3°o. compared to 40.8° o in the non-ant-infested area, and two of the five plants sampled in the ant-infested area e.xhibited 0°o seed set. The difference in percent seed set among the three treatments was highly significant (P < 0.001). The reduction in seed set observ ed in the .Argentine ant-infested area was not due to incompatibility among neighboring plants, as the pollen augmentation treatment produced levels of seed set comparable to plants located in non-ant-infested areas (Figure 5). The highly significant difference in seed set between ant-infested and non-ant-infested areas suggests that alien social insects that reduce populations of native pollinators have the potential to drastically reduce sih ersword seed set.

.Model results

Deterministic models. In a deterministic model based on average demographic vital rates and lev els of seed set (F) ranging from 2-50''b. /. e.xceeded one onlv' when seed set was 30°o or higher (Figure 6). Percent seed set had a substantial effect on with small reductions in seed set (e.g.. a decrease from 30 to 20°'o) causing the population to change from a growing population (/. > 1) to a declining population (/. < I) (Figure 6). When F u as 2° 0. similar to the level of seed set observed in Argentine ant-infested areas. /. dropped below 0.95.

Reduced survival and growth rates (simulating browsing) led to large reductions in /. (Figure 7). .Across a range of seed set levels, a 25% reduction in survival and growth rates caused /. to drop from appro.ximately 1 to appro.ximately 0.7. Increased levels of browsing, simulated by reductions in survival and growth rates of 50 and 75° b. led to 237 e\ en further reductions of population growth rate, with X equal to about 0.5 and 0.3. respectively. Relative to the effects of browsing on percent seed set had little effect on population grovuh rate (Figure 7). For each level of browsing. /. varied slightly over a large spectrum of seed set levels, with F ranging from 10 to 50° o seed set.

We also observed large effects on /. when survival and growth rates were positix ely affected by greenhouse rearing and outplanting. Increased germination success and early seedling surv iv al rates, due to greenhouse rearing, led to a large increase in population growth rate, with /. increasing from about 1 to more than 1.2. av eraged across seed set levels (Figure 8). In the absence of greenhouse rearing, increased juvenile and adult surviv al and growth rates, which tend to occur following outplanting. caused /. to increase by a smaller amount, from about 1.0 to about 1.1 (Figure 8). The combination of these two treatments led to very large increases in /., with }. increasing from about 1.0 to

1.3 and higher (Figure 8). Relative to the effects of increased germination, survival, and growth rales, the effect of seed set was minimal. However, when germination and seedling survival rates were increased to simulate the effects of greenhouse rearing

(shown as the dotted lines in Figure 8). the effect of seed set became more pronounced, w ith /- substantially increasing as vital rates were held constant but percent seed set increased (Figure 8).

The addition of polycarpy to the deterministic model led to higher population growth rates (Figure 9). At an average seed set level of 20%, the inclusion of polycarpy

(P.-i5. P4^ = 0.50 or higher) caused k to shift from a negative (/. < I) to a positive {). > 1) population growth rate. Increasing the probability- of multiple reproductive episodes led

to larger increases in /. (Figure 9).

In the deterministic model, altered rates of survival, growth, and tlowering. combined with varving levels of seed set. influenced not only the population growth rate,

but also the stable stage distribution. When the sur\ i\ al and growth rates of all

\ egetati\ e stage classes were reduced relative to the a\ erage transition matri.x. larger proportions of indi\-iduals were in the seed and seedling stage classes, and smaller

proportions were in the ju\enile and adult stage classes (Figure lOA and B). In contrast. v\ hen the same \ ital rates were increased relative to the average transition matrix, a much smaller proportion of individuals was in the seed stage class, and much larger proportions of individuals were in the seedling, juvenile, and small adult stage classes (Figure lOB and C). Within each "treatment" (low, average, and high vital rates), the proportion of indi\ iduals in the seed and seedling stage classes increased as F increased, whereas the proportion of indix iduals in the juvenile and adult stage classes decreased as F increased

(Figure 10). For all three transition matrices, the two reproductive stage classes comprised a ver>' small proportion of the stable stage distribution.

Density-independent, stochastic models. Density-independent, stochastic simulations based on a\ erage \ ital rates and varying levels of seed set yielded population projections with \ en,- different outcomes after a 100-year period (Figure 11). Population trends. howe\er. were similar for the Haleakala (Figure 11 A) and Mauna Kea (Figure 11B) sih erswords. Populations e.xhibiting lO^ o seed set declined over the 100-year period, whereas populations with 30—40'''o seed set increased in size. For populations with 30% 239 seed set. the increase u as a gradual one. whereas populations with 40° o seed set rapidly grew. When populations e.xperienced 20''o seed set. the Haleakala silversword gradually declined, whereas the Mauna Kea silversword population size remained fairly constant o\ er the 100-year period.

series of density-independent stochastic models was used to e.xamine the relative effects on /. of juvenile and adult survival and growth rates, germination and seedling sur\ i\ al rates, and percent seed set. Results of the stochastic models were qualitativeK \ er\' similar to the results of the deterministic model. Decreasing surv iv al and growth rates, to simulate browsing, drastically decreased the mean population growth rate for the 100-\ear period for both subspecies, with the mean /. ranging from 0.735 to

0.782 (Haleakala) and from 0.755 to 0.802. depending on seed set (Table 3. Figure 12).

These stochastic simulations, simulating browsing conditions, predicted a 100° o probability of e.xtinction within 100 years, with the predicted time to e.xtinction ranging from 36.7 to 46.3 years (Haleakala) and from 33.5 to 44.6 years (Mauna K.ea) (Table 3).

Similarly, increasing survival and growth rates, to simulate the effects of outplanting. significantly increased the mean population grovsth rate, with the mean /. ranging from

1.035 to 1.115 (Haleakala) and from 1.045 to 1.123 (Table 3. Figure 12). In all stochastic simulations based on average and high transition matrices, the probability of extinction was 0 (Table 3). Within the simulations based on low. average, and high transition matrices, percent seed set had very little effect on /.. relative to the effects of altered survival and growth rates (Figure 12). Increasing germination and seedling survival rates

(from 5°o to 50" o). to simulate the effects of greenhouse rearing, greatly increased the 240

mean /. (Fig. 12). Within the latter treatment, seed set had a relatively large effect on

with higher seed set leading to increases in the mean population growth rate.

Incorporating polycarpy into the stochastic model for the .Mauna Kea siK ersword

led to a \ er\' different outlook for the population's future (Figure 13). When the

probability of indiv iduals reproducing multiple times was 0 (i.e.. strict monocarpy). the

population mcreased for the first ten years, and then continually declined for the

remainder of the simulation. In contrast, when the probability of multiple reproductiv e episodes was 0.50 (i.e.. permitting polycarpy). the population rapidly increased in the first ten years, and then continued to increase, at a more gradual rate, for the remainder of the simulation. Thus, the higher incidence of polycarpy in the Mauna K.ea silversword significantly affected population growth rate, suggesting that polycarpy should be incorporated into models simulating the biology and population dynamics of this subspecies.

Densit>-dependent, stochastic models. Incorporating positively density-dependent seed set in the stochastic model produced ver\' different projections for the Haleakala and

•Vlauna Kea sih ersword populations. In the Haleakala simulation, the population experiencing current lev els of pollination efficiency grew rapidly within the first 10 - 20 years, and then gradually increased, remaining close to 150.000 plants for the duration of the simulation (Fig. 14A). However, as pollination efficiency dropped to 75%. 50" b. and

25° 0 of its current level, the population grew for the first ten years, but then declined more and more rapidly after this point. Although the probability of extinction within the

100-year period was zero for all simulations, the projected population sizes resulting 241 from reduced pollination etTiciency were very low. ranging between 16.628 (75° o) and

148 (25''b) individuals. In the Mauna Kea simulation, all populations exhibited declines, including the population experiencing current levels of pollination efficiency (Figure

14B). This population grew for the first ten years and then gradually declined, whereas populations experiencing reduced pollination efficiency did not grow at all and instead, sharply declined from the start of the simulation. Estimates of final population size alter

100 years ranged between 682 (100%) and 41 (25%) individuals. The results of both simulations suggest that even if other demographic vital rates, such as the probabilities of grow th. sur\ ival. and flowering, are held constant, reduced pollination efficiency may potentially lead to large population declines. The Mauna Kea simulation suggests that this population has the potential to drastically decline if vital rates or pollination success do not improve. However, this simulation was based on density-dependent seed set obser\ ed in the Haleakala silversword, and the relationship between flowering plant abundance and seed set may be slightly different in the Mauna Kea silversword.

Density-dependent stochastic simulations showed qualitatively similar effects of browsing and outplanting on k as did the density-independent simulations (Table 4).

Perturbations to survival and growth rates had very large impacts on k for both the

Haleakala and Mauna Kea silverswords (Table 4). Decreased vital rates led to very low population growth rates, with the mean k ranging from 0.700 to 0.705 (Haleakala) and from 0.718 to 0.719 (Mauna Kea) (Table 4). In all stochastic simulations based on reduced vital rates, the probability of extinction was 1.0, with the time to extinction ranging from 31.1 to 32.8 years (Haleakala) and from 25.7 to 26.0 years (Mauna Kea) 242

(Table 4). For both subspecies, increases in vital rates, to simulate the effects of outplanting. nearly always resulted in a positive mean population grouth rate, with the mean /. ranging from 1.019 to 1.077 (Haleakala) and from 0.991 to 1.096 (Mauna Kea)

(Table 4). Relativ e to the effects of altered survival and growth rates, changes in pollination efficiency had small impacts on the mean population growth rate, but o\er long periods of time these small changes in 'k led to large impacts on final population size. In all density-independent and density-dependent stochastic simulations, the growth rate of the mean population was larger than the mean population growth rate, as predicted by theorv (Nakaoka 1997. Caswell 2001; Table 3. 4).

Changes in pollination efficiency also resulted in changes to the stable stage distribution. .A.t the baseline level, the stable stage distribution of the Haleakala sil\ ersword population was dominated by the seed stage class, with a substantial proportion of individuals in the juvenile and adult stage classes as well (Figure 15A).

\'er\- few indi\ iduals were in the seedling and reproductive stage classes. .A.s pollination efticiencv dropped, the proportion of individuals in the seed stage drastically declined, whereas the proportion of individuals in the small and large adult stage classes greatly increased (Figure 15.'\). k similar pattern was seen in the Mauna Kea silversword population, although this population was never dominated by the seed stage class (Figure

15B). As pollination efficiency dropped, the proportion of individuals in the seed stage class decreased, whereas the proportion of individuals in the small and large adult stage classes greatly increased (Figure 15B). As was the case for the Haleakala silversword.

\ er\- few individuals were in the seedling and reproductive stage classes. 243

Discussion

The results presented here prov ide insight into the relative impacts of different

factors on silversword population growth rate. Elasticity and perturbation analyses

suggested that changes to adult surv ival rates would have the largest relative impacts on

This prediction was supported by a series of deterministic and stochastic simulations,

u hich produced highly congruent results. Overall, the most significant finding of this

study is that germination and early seedling survival rates, as well as adult survival rates.

ha\ e the largest relativ e impacts on Alterations to these vital rates will have important

consequences for the persistence of silversword populations.

Elasticity and perturbation analyses

Elasticity analyses demonstrated that adult survival had the highest elasticity,

followed by juvenile survival. This is a common pattern; survival trequently has a larger

impact on /. than either growth or fecundity, particularly in long-lived species

(Silvertown et al. 1993. Crone 2001). and for many different taxa. adult stage classes

ha\ e been shown to make the largest contribution to population growth rate (Doak et al.

1994. Horxitz and Schemske 1995. Chaloupka 2002. Rubin et al. 2002). Although

elasticities \ ary systematically with population growth rate (de Kroon et al. 2000), a comparison of elasticities for low. average, and high transition matrices revealed that the qualitativ e pattern of elasticity was consistent across a range of vital rates. Elasticities

V aried quantitatively as demographic vital rates increased, but adult survival had the

highest elasticity in each of the three transition matrices. This suggests that the adult stage classes consistently make the greatest contribution to population growth rate. 244 although the degree of this impact relative to that of other stage classes varies as \ ital rates \ ar>'.

Whereas elasticity analyses examine the relative effect on /. of \ ery small changes to demographic vital rates, perturbation analyses can examine the effects on /. of much larger changes (Doak et al. 1994). Perturbations of 10 and 20% to vital rates produced results consistent with the predictions of the elasticity analyses: changes to sur\ i\ al rates had noticeable effects on /.. whereas changes to rates of regression and tlowering had

\ery minimal impacts on Alterations to growth rates also had very small effects on A..

The elasticity and perturbation analyses showed that adult surv ival consistently has the largest relati\ e effect on However, these analyses involve the perturbation of one \ ital rate at a time. In reality, external factors may influence multiple vital rates simultaneously. In addition, elasticity and perturbation analyses do not incorporate the degree to which \ ital rates actually are. or can be. altered in the field, either by negative factors that threaten the species, or by positive factors, such as different management actions (Mills et al. 1999, de Kroon et al. 2000). In contrast, deterministic and stochastic models enable us to simultaneously vary multiple vital rates by amounts that are biologically meaningful. As a result, such models clarify the relative importance of different vital rates, and allow us to better understand the degree to which positive and negatix e factors influence population persistence.

Impacts of alien species

The primary factor implicated in the past decline of the Haleakala and Mauna Kea sil\ erswords was the removal of plants, due to either browsing by alien ungulates or 245 collection and \ andalism by humans. These factors affect the silversword population in a similar way. by drastically reducing the surv ival and growth rates of all \ egetati\ e stage classes. .-Mthough ungulates have been eradicated from Haleakala National Park and are no longer a threat to the Haleakala silversword. the Mauna Kea silversword is still

\"ulnerable to browsing by alien ungulates, especially moutlon sheep. .An additional factor thought to pose a threat to both subspecies in the near fiature is the current invasion of alien social insects, which greatly impact native pollinator populations (Cole et al.

1992) and in so doing, potentially alter silversword seed set levels. A comparison of seed set betw een .Argentine ant-infested and non-ant-infested areas reinforced this h\pothesis. with plants located in ant-infested areas e.x.hibiting negligible seed set relative to plants located in non-ant-infested areas. The models presented here enable us to compare the relati\ e impacts of these different alien species separately, as well as in combination.

Reduced surv ival and growth rates, simulating either browsing by ungulates or collection by humans, drastically reduced population growth rate. The lightest level of browsing reduced /. by about 20°'o. from approximately I.O to appro.ximately 0.8. Higher le\ els of browsing reduced k even fiirther. .Although the changes to these \ ital rates may seem e.\treme. it is likely that historic le\ els of browsing, particularly on .Mauna Kea. were in the medium to heavy range, given the number of ungulates recorded to have been on the \ olcano. In the 1930s, for e.xample. 40.000 sheep were estimated to be present on the upper slopes of Mauna Kea (U.S. Fish and Wildlife Service 1994). Given this very high density of alien ungulates, as well as the predictions made by our models in terms of the impacts of reduced survi\'al rates on population viability, it is not surprising that the 246

Vlauna K.ea sih ersword population declined so rapidly, and to such low numbers. The onl\ plants that sur\ i\ ed were those growing on steep cliff faces that were inaccessible to ungulates. It is likely that without the interv ention begun in the 1970s, the highly reduced sur\ i\ al and growth rates due to browsing would have led to extinction.

.-Mtered levels of seed set had important effects on population growth rate, but these effects were small relative to the effects of browsing. However, in the absence of browsing, reduced seed set le\ els had substantial effects on transforming a growing population into a declining population. For example, in the absence of other factors, decreasing seed set from 30% to 20° o caused /. to decrease from a positive {/. = 1.003) to a negative {/. = 0.990) \ alue. Over time, this apparently slight difference in /. translated into ver\' large differences in population size. Although reduced seed set also led to reduced population growth rates when sur\ i\ al rates were reduced b\' browsing, these effects were minimal relative to the effects of browsing. These results suggest that, in isolation, factors that affect seed set. such as alien social insects or managed breeding, can ha\ e important effects on the viability of a silversword population. Howe\ er. in the presence of factors that reduce juvenile and adult survaval and growth rates, such as brov\ sing or vandalism, these effects are swamped and become relatively unimportant.

Management implications

It is frequently assumed that management should target the life history stages and transitions associated with the largest elasticities. In the field, however, different transitions are not equally possible to manipulate with management practices (de Kroon et al. 2000). Thus, it is helpftil to combine elasticity analyses with demographic modeling, in order to assess the relative effects of different scenarios on a population's growth rate. The primary utility of PVA is not necessarily in a definitix e projection of

fiiture population size, but rather in the ability to compare the relative outcomes of different disturbance regimes or management scenarios (Beissinger and Westphal 1998.

Menges 20006. Fieberg and Ellner 2001. Reed et al. 2002). Here, we assess a uvo-part management plan that includes (1) control of alien species, including ungulates and social insects, and (2) sihersword reintroduction (Mauna K.ea only). The reintroduction program in\ol\es a combination of three separate components: managed breeding (i.e.. increased seed set), greenhouse rearing (increased germination and seedling sur\i\al rates), and outplanting (increased survi\al and growth rates of all \ egelative stage classes). In the actual reintroduction program, each of these components is performed in conjunction with the other two (i.e.. greenhouse rearing is always followed b\ outplanting. etc.): however, here we e\aluate the three components separately, in order to assess their relatix e effects on population grov\th rate.

.A.S part of ongoing sih ersword management, both Haleakala and Mauna K.ea are acti\ ely managed in order to minimize alien species impacts. Haleakala National Park is enclosed b\ fences, which are trequenth' maintained in order to pre\ ent the in\ asion of ungulates, such as .A-vis deer. Haleakala also controls yellowjacket populations, and annually distributes a formicide in order to limit the spread of two e.xisting .Argentine ant populations. On Mauna Kea. the state hunts mouflon sheep every 6 months, removing, on ax erage. about 200 animals each time. However, in areas where the state has not yet succeeded in eradicating ungulates, the sheep continue to hea\ ily impact local 248 sil\ ersword populations, even when sheep are only present in low numbers. Given the predicted large effects of alien species on it is clear that, in the absence of alien species control programs, the baseline silversword population growth rate would be much lower than in the models presented here. Current average demographic \ ital rates predict a baseline /. that is very close to one; in the absence of alien species control. howe\ er. this baseline would be greatly reduced. For e.xample. without hunting and/or fencing, the baseline /. would most likely be closer to that predicted for medium and heavy levels of browsing (as shown in Figure 7). Similarly, in the absence of alien insect control, the baseline /. would potentially resemble that predicted for populations experiencing reduced pollination efficiency (as shown in Figure 14. Table 4).

.•\lthough alien species control programs contribute to the persistence of the sih ersword populations, the resulting population growth rates are still occasionally less than one. Thus, these programs in and of themselves are not sufficient to guarantee a self-sustaining population, particularly on .Mauna Kea where the silversword population contains less than 5.000 individuals. Whereas the Haleakala silversword population appears to be self-sustaining, intervention is necessary in order to ensure the persistence of the .Vlauna Kea silversword population. This intervention is in the form of a reintroduction program that combines managed breeding with greenhouse rearing and outplanting.

Pollen augmentation treatments conducted on both the Haleakala and Mauna Kea siKerswords demonstrated that it is possible to increase seed set with hand-pollination, up to a maximum of approximately 35-40%. The benefits of managed breeding. 249

therefore, include higher seed set levels, as well as an increase in the number of genetic

founders. Howe\ er. although higher seed set le\ els lead to increased population growth

rates, the influence of seed set on /. is slight, relative to the influence of adult sur\ ival

rates. If sur\ i\ al rates are increasing, pollen augmentation can contribute to even larger

increases in but if surv ival rates are declining, due to factors such as browsing or drought, increased seed set attained through pollen augmentation will not be large enough to offset decreased survi\ al. Thus, managed breeding will be most effective either in

populations exhibiting high survi\ al rates or in conjunction with otlier management practices, including greenhouse rearing and outplanting.

.A.S part of the Mauna Kea silversword reintroduction program, seeds are collected from the tleld. germinated in the greenhouse, and the seedlings are raised until outplanting. Since 1997. these measures have resulted in greatly increased germination and seedling survival rates, relative to what is observed in the field. Germination rates ranged from 39-95° o. depending on the number of years since seed collection, and sur\ i\ al of newl\- germinated seedlings until outplanting was typically 90'' o or higher. In our models, much smaller rates of germination and seedling survival (equal to 50 percent) had large positi\ e impacts on population growth rate. Increased germination and seedling survi\ al rates, relative to typical values in the field, had larger impacts on /. than did increased rates of juvenile and adult survi\al alone.

Following rearing in the greenhouse, plants are outplanted on the east slope of

Mauna Kea. where mouflon sheep are not as abundant as in other areas. Early results show that outplanted individuals have \ er\' high sur\ival rates, on average greater than 250

'•)0"o. As seen in the models presented here, these high surv ival rates translate into large increases in population growth rate. When the benefits of outplanting are combined with the benefits of greenhouse rearing, the impact on /. is even larger. Thus, although greenhouse rearing and outplanting may be somewhat costly in terms of both time and mone\'. the resulting increases in germination and seedling survival rates, as well as in ju\ enile and adult survival and grov\th rates (which translate into ver\' large impacts on

/.) demonstrate that these strategies are highly effecti\e in enhancing population growth rate.

Together, these results suggest that an integrated management plan, in which alien species control is combined with managed breeding, greenhouse rearing, and outplanting. has the greatest potential for ensuring the persistence of endangered siK ersword populations. 251

L1TER.\TURE CITED

Andersen. M.C. and D. Mahato. 1995. Demographic models and reser\ e designs for the California spotted owl. Ecological .Applications 5:639-647.

Baldwin. B.G. 1996. Phylogenetics of the California tarweeds and the Hawaiian sih ersword alliance (Madiinae; Heliantheae sensu lato). Pages 377-391 in D.J.N. Hind and H.J. Beentje. editors. Compositae: systematics. Proceedings of the International Compositae Conference. Royal Botanic Gardens. K.ew.

Beissinger. S.R. and M.I. Westphal. 1998. On the use of demographic models of population viability in endangered species management. Journal of Wildlife .Management 62:821-841.

Bierzychudek. P. 1999. Looking backwards: assessing the projections of a transition matri.\ model. Ecological .Applications 9:1278-1287.

Brook. B.W.. J.J. O'Grady. .A.P. Chapman. M.A. Burgman. H.R. .Akcakaya. and R. Frankham. 2000. Predicti\ e accuracy of population \ iability analysis in conser\ ation biology. Nature 404:385-387.

Burgman. M..\. and B.B. Lamont. 1992. A stochastic model for the viability of Banksia cuneata populations: environmental, demographic and genetic effects. Journal of .Applied Ecology 29:719-727.

Carr. G.D.I 985. Monograph of the Hawaiian Madiinae (Asteraceae): Argyroxiphium. Diibautia. and Wilkesia. .Allertonia 4:1-123. 252

Carr. G.D.. E.A. Powell, and D.W. Kyhos. 1986. Self-incompatibility in the Hawaiian Madiinae (Compositae): an e.xception to Baker's Rule. Evolution 40:430-434.

Caswell. H. 2001. Matri.x population models, second edition. Sinauer .Associates. Sunderland. Massachusetts. US.-\.

Caswell. H. and T.N. Kaye. 2001. Stochastic demography and conser\ ation of an endangered perennial plant {Lomaiium bradshawii) in a dynamic fire regime. .A.d\ ances in Ecological Research 32:1-51.

Chaloupka. .M. 2002. Stochastic simulation modelling of southern Great Barrier Reef green turtle population dynamics. Ecological Modelling 148:79-109.

Cole. F.R.. A.C. .Medeiros. L.L. Loope. and W.W. Zuehlke. 1992. Effects of the .\rgentine ant on arthropod fauna of Hawaiian high-ele\ ation shrubland. Ecolog\- 73: 1313-1322.

Crone. E.E. 2001. Is surv ivorship a better fimess surrogate than fecundity? Evolution 55:2611-2614.

Crooks. K..R.. M..A.. Sanjayan. and D.F. Doak. 1998. New insights on cheetah conserv ation through demographic modeling. Conservation Biology 12:889-895.

Crouse. D.T.. L.B. Crowder. and H. Caswell. 1987. A stage based population model for loggerhead sea turtles and implications for conservation. Ecology 68:1412-1423.

Crowder. L.B.. D.T. Crouse. S.S. Heppell. and T.H. Martin. 1994. Predicting the impact of turtle e.xcluder devices on loggerhead sea turtle populations. Ecological Applications 4:437-445. de Kroon. H.. A. Plaiser. J. van Groenendael. and H. Caswell. 1986. Elasticity; The relati\ e contribution of demographic parameters to population growth rate. Ecology 67:1427-1431. de Kjoon. H., J. \ an Groenendael. and J. Ehrien. 2000. Elasticities: a re\iew of methods and model limitations. Ecology 81:607-61 S.

Doak. D.. P. K.arei\ a. and B. KJepetka. 1994. Modeling population viabilit\' for the desert tortoise in the western Mojave desert. Ecological .Applications 4:446-460.

Fieberg. J. and S.P. Ellner. 2001. Stochastic matrix models for conser\ation and management: a comparative review of methods. Ecology Letters 4: 244-266.

Gross. K.. J.R. Lockwood 111. C.C. Frost, and W.F. Morris. 1998. .Modeling controlled burning and trampling reduction for conservation of Hudsonia moniana. Conser\ ation Biology 12:1291-1301.

Harding. E.K... D.F. Doak. and J.D. .\lbertson. 2001. Evaluating the effectiveness of predator control: the non-nati\e red fox as a case study. Conser\ation Biolog\' 15:1114-

1122.

Heppell. S.S.. L.B. Crowder. and D.T. Crouse. 1996. .Models to evaluate headstarting as a management tool for long-lived turtles. Ecological .-Applications 6:556-565.

Horvitz. C.C. and D.W. Schemske. 1995. Spatiotemporal variation in demographic transitions of a tropical understory herb: projection of a matrix analysis. Ecological .Monographs 65: 155-192. 254

Legendre. S. and J. Clobert. 1995. L'LM. a software for conserv ation and e\ olutionar\ biologists. Journal of Applied Statistics 22:817-832.

Loope. L.L. and C.F. Crivellone. 1986. Status of the Haleakala silversword: past and present. Cooperative National Park Resource Studies Unit. University of Hawaii. Honolulu. Tech. Rep. 58.

-Menges. E.S. 2000jz. Applications of population viability analyses in plant conserv ation. Ecological Bulletins 48:73-84.

Menges. E.S. 20006. Population viability analyses in plants: challenges and opportunities. Trends in Ecology and Evolution 15:51-56.

Mills. L.S.. D.F. Doak. and M.J. Wisdom. 1999. Reliability of conservation actions based on elasticity analysis of matri.x models. Conser\ation Biology 13:815-829.

Nakaoka. .M. 1997. Demography of the marine bi\ alve "^'oldia notabilis in fluctuating en\ ironments: an analysis using a stochastic matri.x model. Oikos 79:59-68.

Powell. E-A.. 1992. Life history, reproductive biology, and conserx ation of the Mauna Kea silversword. Argyroxiphiiim sandwicense DC (Asteraceae). an endangered plant of Hawaii. Ph.D. dissertation. University of Hawaii at .Manoa. Honolulu. Hawaii.

Ratsirarson. J. J..A.. Silander. Jr.. and A.F. Richard. 1996. Conservation and management of a threatened Madagascar palm species. Neodypsis decaryi. Jumelle. Conser\'ation Biology 10:40-52.

Reed. J..VI.. L.S. .Mills. J.B. Dunning. Jr.. E.S. Menges. K.S. McKelvey. R. Fr\e. S.R. Beissinger. M.C. .Anstett. and P..Miller. 2002. Emerging issues in population \ iability analysis. Consenation Biology 16:7-19.

Robichau.\. R.H.. E..'\. Friar, and D.W. Mount. 1997. Molecular genetic consequences of a population bottleneck associated with reintroduction of the Mauna Kea siK ersword (Argyroxiphium sandwicense ssp. sandwicense [.A.steraceae]). Conserv ation Biology 11:1140-1146.

Rubin. E.S.. W.M. Boyce. and E.P. Caswell-Chen. 2002. Modeling demographic processes in an endangered population of bighorn sheep. Journal of Wildlife .Management 66:796-810.

Schemske. D.W., B.C. Husband. M.H. Ruckelshaus. C. Goodwillie. I.M. Parker, and J.G. Bishop. 1994. Ev aluating approaches to the conserv ation of rare and endangered plants. Ecology 75:584-606.

SiK ertovvn. J.. M. Franco. I. Pisanty. and A. Mendoze. 1993. Comparative demography: relativ e importance of life cycle components to the finite rate of increase in woody and herbaceous perennials. Journal of Ecology 81:465-476.

L'.S. Fish and Wildlife Service. 1986. Determination of endangered status for Argyroxiphium sandwicense ssp. sandwicense ('.A.hinahina or Mauna Kea silversword). Federal Register 51:9814-9820.

U.S. Fish and Wildlife Service. 1992. Determination of endangered or threatened status for 15 plants from the Island of Maui. HI. Federal Register 57:20772-20787.

L'.S. Fish and Wildlife Service. 1994. Recovery plan for the Mauna Kea silversword (Argy roxiphium sandwicense ssp. sandwicense). Portland. Oregon. 256

Table 1. A\ erage and range of demographic vital rates for the Haleakala silversword.

19S2 - 2001. Deterministic models were based on the average vital rates; stochastic models were based on a beta distribution defined by the mean and standard deviation of each \ ital rate. The last column presents the elasticity associated with each transition.

Average SD Range Elasticity

Growth seedling 0.690 0.315 0.148 - 1.000 0.020 juvenile 0.093 0.070 0.008-0.291 0.027 small 0.042 0.027 0.008-0.081 0.026

Survival juvenile 0.800 0.087 0.669-0.956 0.131 small 0.888 0.056 0.764-0.947 0.396 large 0.895 0.085 0.689-0.977 0.347

Regression small 0.027 0.040 0.000-0.106 0.007 large 0.025 0.043 0.000-0.167 0.007

Flowering smair 0.003 0.005 0.000-0.017 0.000 larae 0.068 0.078 0.000-0.068 0.020 257

Table 2. Sih ersword transition matrix. Transitions marked with an asterisk are present in the Mauna Kea sih ersword life cycle only. The probabilities of all transitions to the seed and seedling stage classes were estimated as the product of the following variables:

ByB„= achene production by small and large reproductive plants, respectively: F = percent seed set: G.G„ = germination rate of newly-produced and one year old or older seeds: SSc, = sur\ i\ al rate of seeds and newly-germinated seedlings.

Seed Seedling Juvenile Small Large Sm. rep. Lg. rep.

Seed (l-Cr;).S FBS(\-G)S FBF,(\-G)S

Seedling FB^GSg FBfiGSc

Juvenile

Small p * P 35

Large P44

Sm. rep.

Lg. rep. Table 3. Results of density-independent, stochastic simulations for the Haleakala and

Mauna K.ea sih erswords. including mean population growth rate, growth rate of the mean population, probability of extinction, and time to extinction (if applicable).

Simulations were based on a beta distribution defined by the mean and standard deviation of each \ ital rate (1982 - 2001). Results are from 500 replicates of a 100-year population projection. Simulations began with 50.000 plants plus 20.000 seeds (Haleakala) or 5.000 plants plus 1.000 seeds (Mauna Kea); plants were initially distributed among the different stage classes according to the stable stage distribution. The average matrix simulated baseline conditions, with no change to average vital rates; the low matrix simulated the effects of browsing, with sur\'ival and growth rates of all vegetative stage classes decreased b\ 25" o; the high matrix simulated the benefits of outplanting. with sur\ i\ al and grov\th rates of all vegetative stage classes increased by 25'' o. 259

trans matnx mean /. /. of mean pop. T to extinction " 0 seed set (mean = SE)

HALEA1CA.LA Low 50% 0.782 0.791 l.O 46.3 = 0.2 40% 0.774 0.782 l.O 44.3 = 0.1 30% 0.764 0.772 1.0 42.3 = 0.1 20% 0.752 0.759 1.0 39.8 0.1 10% 0.735 0.740 1.0 36.7 = 0.1 .•\\erage 50""% 1.030 1.037 0 \ .-K 40% 1.020 1.026 0 N .A 30% 1.009 1.014 0 N .A 20% 0.994 0.998 0 N .A 10% 0.973 0.977 0 N A High "50% I.I 15 1.119 0 N A 40% 1.102 1.106 0 N .A 30% 1.086 1.089 0 N .A 20% 1.065 1.068 0 N .A 10% 1.035 1.038 0 N .A

MALNA KEA Low 50% 0.802 0.805 1.0 44.6 = 0.1 40"., 0.794 0.797 1.0 42.5 = 0.1 30% 0.784 0.787 1.0 40.2 = 0.1 20",, 0.772 0.774 1.0 37.3 = 0.1 10 "o 0.755 0.757 1.0 33.5 = 0.1 .A\erage 50^" 0 1.045 1.052 0 \ A 40 "o 1.035 1.042 0 N .A 30°,, 1.024 1.030 0 N .A 20% 1.009 1.015 0 N A 10 "o 0.989 0.994 0 N .A High ''50"o 1.123 1.125 0 N .A 40"o 1.110 1.112 0 N A 30"o 1.094 1.096 0 N/A 20 "o 1.074 1.076 0 N A 10% 1.045 1.047 0 N .A 260

Table 4. Results of density-dependent, stochastic simulations for the Haleakala and

Mauna K.ea sih erswords. including mean population growth rate, growth rate of the mean population, probability of extinction, and time to extinction (if applicable).

Simulations were based on a beta distribution defined by the mean and standard deviation of each \ ital rate (1982 - 2001). Results are trom 500 replicates of a 100-year population projection. Simulations began with 50.000 plants plus 20.000 seeds (Haleakala) or 5.000 plants plus 1.000 seeds (Mauna K.ea); plants were initially distributed among the different stage classes according to the stable stage distribution. The average matrix simulated baseline conditions, with no change to a\ erage vital rates: the low matrix simulated the effects of browsing, with survival and growth rates of all vegetative stage classes decreased b\' 25° o; the high matrix simulated the benefits of outplanting. with surv ival and grov\th rates of all vegetative stage classes increased by 25° o. 261

trans matrix mean k K of mean pop. P..extinction T to extinction poll, efficiency (mean ± SE)

H.ALE.AK_-\L.\ Low 100% 0.702 0.705 32.8 = 0.1 75° 0 0.700 0.702 31.9 = 0.1 50" 0 0.698 0.701 31.5 = 0.1 25% 0.697 0.700 31.1 =0.1 .•\\erage 100% 0.999 1.015 0 N A 15°o 0.964 0.987 0 N A 50% 0.948 0.958 0 N A 25% 0.938 0.940 0 N A High ^100% 1.077 1.080 0 N'A 75% 1.068 1.072 0 N A 50% 1.053 1.061 0 N A 25% 1.019 1.035 0 N A

-VIALXA KEA Lou 100% 0.716 0.719 26.0 = 0.1 75% 0.715 0.719 25.8 = 0.1 50% 0.715 0.719 25.7 = 0.1 25% 0.715 0.718 25.7 = 0.! .•\\cTage 100% 0.964 0.980 0 N A 75% 0.954 0.958 0 N A 50% 0.951 0.954 0 N A 25% 0.949 0.951 0 N/A Higti ^100% 1.096 1.103 0 N/A 75°o 1.062 1.079 0 N/A 50% 1.024 1.052 0 N/A 25" 0 0.991 1.003 0 N,A 262

FIGL RE LEGENDS

FIGURE 1. Silversword lite cycle graph, with arrows depicting all possible transitions

among seven stage classes. Dashed arrows indicate transitions that are in the Mauna Kea

sih ersword life cycle only: all other transitions are present in the life cycles of the

Haleakala and Mauna Kea sih erswords.

FIGL'RE 2. Density-dependent seed set in the Haleakala silversword. and the predicted

effects of reduced pollination efficiency on silversword seed set. In both graphs, the solid

line indicates the obser\ ed relationship between tlowering plant abundance and

sih ersword seed set. and the dotted lines indicate the predicted relationships between

tlowering plant abundance and seed set if pollination efficiency declines to 75° o. SCo.or

25° o of its current le\el. In (A), the y-axis is the non-transformed level of seed set (y =

F): in (B). y == -In (1 - F Fma.x)- where F - percent seed set and Fmux = the ma.\imum seed

set obserx ed. or 0.40. The slopes of the transformed lines were used in density-

dependent stochastic simulations, in order to assess the effect of reduced pollination efficiency on /..

FIGURE 3. Elasticities of ten life history transitions in the silversword life cycle, across a range of demographic \ ital rates. Elasticities are based on three transition matrices

{low. a\erage. high) representing a range of transition probabilities. The average matri.x is comprised of the average vital rates observ ed in the field trom 1982 - 2001; the low 263 matrix is comprised of the average vital rates minus one SD; the high matrix is comprised of the average \ ital rates plus one SD.

FIGURE 4. Relative effects on k of proportional changes in silversword vital rates. In the perturbation analyses, each vital rate is altered one at a time by the stated amount.

Vital rates were increased by (A) 10% and (B) 20%. and decreased by (C) 10°o and (D)

20° o of their original value. The dotted line indicates the baseline k of 0.985. the sil\ ersword population growth rate in the absence of any perturbations; the heavy dashed line indicates a /. of 1.0. a stable population growth rate.

FIGURE 5. Haleakala silversword seed set in Argentine ant-infested and non-ant- infested areas. Bars represent the mean percent seed set (for each plant) ± 1 SE. In the open treatment, capitula were open-pollinated; in the augment treatment, capitula were open-pollinated and received supplemental outcross pollen. Differences in seed set were highly significant among the three pollination treatments: ANOVA. F2.13 = 13.274.

P = 0.0007. Italicized letters above bars indicate significant differences between treatments (Tukey test, alpha < 0.05). Sample sizes above bars indicate the number of plants in each treatment; for each plant, three capitula were sampled and analyzed.

FIGURE 6. Silversword population growth rate {k), as a function of percent seed set (F).

Values of A are based on a deterministic model using average demographic vital rates 264 observ ed in the field trom 1982 - 2001. The dotted line indicates a /. of 1.0. a stable population growth rate.

FIGURE 7. Impact of browsing on sih ersword population growth rate (/.). across a range of seed set levels. The solid line indicates /. for a deterministic model based on a\ erage sih ersword vital rates; the dashed lines indicate k for the same model when sur\i\al and growth rates of all vegetati\e stage classes are reduced by 25''-o (light). 50° o

(medium), and (heavy), in order to simulate different levels of browsing intensity.

The dotted line indicates a k of 1.0. a stable population growth rate.

FIGURE 8. Relati\ e effects on silversword population growth rate (}.) of increased germination and seedling sur\i\al rates, due to greenhouse rearing (light dashed line), increased survival and growth rates of all vegetative stage classes, due to outplanting

(light solid lines) and increased germination and survival and growth rates of all

\ egetative stage classes, due to greenhouse rearing and outplanting combined (heavy dotted lines), across a range of seed set levels. The dark solid line indicates /. for a deterministic model based on average silversword vital rates, and the dark dashed line indicates a /. of 1.0. a stable population growth rate. Adult survival and growth rates were increased by I0°o (squares) and 20% (triangles); germination and seedling sur\ival rates w ere increased trom 5°o (simulating field conditions) to 50% (simulating greenhouse conditions). 265

FIGURE 9. Effects of polycarpy on silversword population grov\ih rate (/.). across a range of seed set le\ els. The dark solid line indicates X for a deterministic model based on a\ erage silversword vital rates; the dashed lines indicate different probabilities ot small and large reproductiv e individuals returning to the small and large adult stage classes after tlowering (ie.. incidence of polycarpy). The light dotted line indicates a /. ot

1.0. a stable population growth rate.

FIGURE 10. Stable stage distribution for the silversword population across a range of

\ ital rates and seed set levels. The average transition matrix is based on av erage demographic vital rates observed from 1982 - 2001. In the low transition matrix. sur\ i\ al and growth rates of all vegetative stage classes are reduced by 50 percent, to simulate medium levels of browsing; in the high transition matrix, survival and growth rates of all v egetative stage classes are increased by 20 percent to simulate the benefits associated with outplanting. Within each U-eatment (low. average, high), percent seed set ranges from 10 to 50 percent, as depicted in the legend.

FIGURE 11. Projected population size over a 100-year period for the (A) Haleakala silversword and (B) Mauna Kea silversword. based on density-independent, stochastic simulations. Simulations were based on a beta distribution defined by the mean and standard dev iation of each vital rate; markers show the mean (SE) population size predicted by 500 replicates of the 100-year simulation. In both graphs, lines represent different lev els of seed set. ranging from 10 to 40%. as depicted in the legend. The 266

Vlauna K.ea simulation incorporates a probability of polycarpy of 0.50. In (A), all

simulations began with an initial population size of 50.000 plants plus 20.000 seeds; in

(B). all simulations began with an initial population size of 5.000 plants plus 1.000 seeds.

In both graphs, the initial population size u as distributed among the different stage

classes according to the stable stage distribution. Individuals in the seed stage class are

not included in this figure.

FIGURE 12. Mean population grovsih rate (/.) of five hundred 100-year density-

independent stochastic simulations based on average vital rates (solid line), reduced

sur\i\al and growth rates of all vegetatixe stage classes due to browsing (diamonds),

increased sur\ i\ al and growth rates of all \ egetati\ e stage classes due to outplanting

(squares), and increased germination and seedling survixal rates due to greenhouse

rearing (triangles). Estimates of/, are shown across a range of seed set levels, trom 10 to

50" 0. The dashed line indicates a /. of 1.0. a stable population growth rate.

FIGURE 13. Projected .Mauna Kea silversword population size over a 100-year period,

based on a density-independent stochastic simulation, when polycarpy is included (dotted

line) and e.xcluded (solid line) trom the model. In the polycarpic simulation. P:<5 and P4^ equaled 0.5. Markers show the mean (SE) population size predicted by 500 replicates of

the 100-year simulation. The simulation was based on average vital rates and 20" o seed set. The initial population was comprised of 5.000 plants distributed among the different 267

vegetative stage classes according to the stable stage distribution, plus 1.000 seeds.

Indiv iduals in the seed stage class are not included in this figure.

FIGL'RE 14. Projected population size over a 100-year period for the (.\) Haleakala silv ersword and (B) Mauna Kea silversword. based on density-dependent, stochastic simulations using average demographic vital rates and different levels of pollination efficiency. In both graphs, the solid line indicates projected population size when

pollination efficiency is at the current level, as determined in the Haleakala silversword

population; dotted lines indicate projected population size when pollination efficiency is

reduced to 75° o. 50° o. and 25° o of its current level. Markers show the mean (SE)

population size predicted by 500 replicates of the 100-year simulation. In (.-X). all simulations began with an initial population size of 50.000 plants plus 20.000 seeds; in

(B). all simulations began with an initial population size of 5.000 plants plus 1.000 seeds.

In both graphs, the initial population size was distributed among the different stage classes according to the stable stage distribution. Individuals in the seed stage class are not included in this figure. The .Mauna Kea simulation incorporates a probability of pol>carpy (P;5. P4t,) of 0.50.

FIGL'RE 15. Stable stage class distribution for the (A) Haleakala silversword and (B)

Mauna Kea silversword. at different levels of pollination efficiency. Bars represent the proportion of individuals in each of the seven stage classes when pollinator efficiency is

100"o. 75° o. 50° 0. and 25° o of its current level. seed

sdlg

JUV

sm sm rep

Igrep

FIGURE I 269

45

100%

75%

50%

0 500 1000 1500 2000 3000

# of flowering plants

4 • 100%

3

75%

50% 0.5 5% 0 0 500 1000 1500 2000 2500 3000 # of flowering plants

FIGURE 2 270

Minimum o.s

O.fi

0.4

A\erage ii.>.

U O.h

^ 0.4

X:':"- 0.2

II rs ^3. 8

Maximum o.s

0.6

Ir. 0.4

0.: Ml a-'. pi] 1 *• ^

sdlg ju\- sm juv- sm sm Ig sm Ig Growth Sur\T\'al Regression Fbwerine

FIGURE 3 1.04 10%

1.02 •

0.98

C 0.96 vv--' lirvU.# 0.94 «r»m

0.92 sdlg ju\- sm ju\' sm Ig sm Ig sm Ig

Growth Sur\i\al Resression Flowerins

[.04 B 20%

1.02

0.98 zii

0.96

0.94

0.92 sdlg ju\' sm juv sm Ig sm ig sm Ig

Growth Survi\al Resression Flowerins

FIGURE 4 Ill

1.04 -10%

1.02

0.98 ZJj

O 0.96 I 0.94 m

0.92 sdlg juv sm juv sm Ig sm Ig sm Ig

Growth SuTNival Resression Flowerina

1.04 • D - 20 %

jj 1.02 •

H 0.98

C 0.96

0.94

0.92 sdlg ju\- sm ju\ sm Ig sm Ig sm Ig

Growth Sur\i\al Regression Flowering

FIGURE 4 (cont'd) Opea No ants Opea .Ants

T reatment

FIGURE 5 274

I.o:

1.01

0.99

0.98

0.97

0.96

0.95

0.94 0 10 20 30 40 50

Percent seed set

FIGURE 6 * No browsing —*— Light —•— Medium —•— Heav.}. 1.2

• •• •))( X...

0.8 ^ —4 * * A

0.6 ^ » • • 0.4 • • • 0.2

10 20 30 40 50

Percent seed set

FIGURE 7 276

!.6

1.5

1.4 —baseline • - 1 0° 0 1.3 A -20''o - -• germination 1.2 A - - -germ -10° o A A A • - -A- - -germ -20° o 1.1 A • • • •

0.9 20 30 40 50

Percent seed set

FIGURE 8 277

- - P = 0.75 --m--P = 0.50 -- P = 0.25 x P = 0.00

1.06

1.04

-£ 1.02

0.98

0.96 10 20 30 40 50

Percent seed set

FIGURE 9 • 10 0 20 0 30 >40 150

Low

riTM riT^

Average

mn [Irfc Qi«. _

High

sdlg juv sm Ig smrep Ig rep Stage class

FIGURE 10 ft of plants // of plants

S s

O o o c H o g O mp a s o

4^ O

I J •cJ 280

baseline survixal • • "A" aermmatran

o.ei 10 20 30 40 50 Percent seed set

FIGURE 12 —•— monocarpic polycarpic

14.000

12.000

10.000

8.000

6.000

4.000

2.000

0 0 10 20 30 40 50 60 70 80 90

Time (years)

FIGURE 13 iOO% • 75° 0 A SC'O • 25° 0 300.000 A

200.000

150.000

100.000

0 0 20 30 40 50 60 70 80 90 100

9.000

8.000

".UUU

6.0(X)

5.000

4.000

3.000

2.000

1.000

70 80 90 100

Time (years)

FIGURE 14 loxi (UN sm sni rep rep sccil sdli; fu> sni k sm rep iu rep

Stagt cla$s Stagv cias^ FIGURE 15