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2016 Implications of Population Growth Rate Projections and Pollen Limitation for the Conservation of a Threatened Dioecious Plant Natali Rubi Ramirez-Bullon
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COLLEGE OF ARTS AND SCIENCES
IMPLICATIONS OF POPULATION GROWTH RATE PROJECTIONS AND POLLEN
LIMITATION FOR THE CONSERVATION OF A THREATENED DIOECIOUS PLANT
By
NATALI RAMIREZ-BULLON
A Thesis submitted to the Department of Biological Science in partial fulfillment of the requirements for the degree of Master of Science
2016 Natali Ramirez-Bullon defended this thesis on November 2, 2016. The members of the supervisory committee were:
Alice Winn Professor Directing Thesis
Joseph Travis Committee Member
Nora Underwood Committee Member
The Graduate School has verified and approved the above-named committee members, and certifies that the thesis has been approved in accordance with university requirements.
ii
This thesis is dedicated to my dear mom Rocio Ana Matilde BullΓ³n Arana de RamΓrez, who at a very young age taught me to examine my surroundings, stimulated my love for encyclopedias, and inspired me to change the world by educating people.
iii ACKNOWLEDGMENTS
I would like to first thank my advisor Dr. Alice Winn for giving me the opportunity to join her lab, dedicating her time and patience to my uncountable questions and interruptions. She went beyond the call of duty spending many hours giving me feedback to improve my scientific writing and communications skills. For that, I will always be grateful particularly because as an English as a second language student I was uncomfortable speaking in front of a big group of scientist. She built my expertise in population ecology by teaching me how to set up a demographic study, analyze demographic data, and how to conduct a pollen limitation experiment.
Second, I would like to acknowledge the members of my committee not only for their expertise in developing my research ideas but also for being a great source of encouragement in my academic life. A conversation with Dr. Joseph Travis always provided me with a refreshing boost in my scientific curiosity that has cultivated my biological intuition. I am grateful to Dr. Nora Underwood for her insightful suggestions while developing my research proposals.
For Dr. Vivian Negron-Ortiz, I have special thanks for not only sharing her data with me, but also for giving me the opportunity to work with endangered and threatened plants in the first year that I moved to the USA. Her mentorship motivated me to continue to focus on plant conservation issues.
The Garden Club of America - Catherine H. Fellowship, The Florida Native Plant Society, and the Department of Biological Science provided me with the funds necessary to complete my research.
The St. Joseph Buffer Preserve staff supported my research and provided accommodation during my fieldwork. Florida Fish and Wildlife Conservation Commission biologistsβ Jerry Pitts and Billy Sermons helped with research permits and provided field assistance retagging plants at Box-R Wildlife Management Area. Jim Moyers, former wildlife biologist for the St. Joe Company, helped me obtain access to the population in Panama City, Florida.
Finally, I would like to acknowledge all the people that helped me in the field. Anthony Miller assisted me in almost every field day from 2013 to 2015. My friends, Katelyn Pearson, Brendan Scherer, Eve Culbreth, Jason Cassara, and Terence Reading helped me collecting data in 2016. I am very grateful to Dr. Thomas Miller for his assistance setting up my demographic plot in Gulf County and letting me use his lab video camera. Carla Vanderbilt trained me in how to use the video software.
iv TABLE OF CONTENTS
List of Tables ...... viii
List of figures ...... ix
Abstract ...... xi
Chapter 1 Introduction ...... 1
Chapter 2 Demographic analysis of three populations of a threatened dioecious perennial plant . 2
Introduction ...... 2
Methods...... 4
Species description...... 4
Study area...... 6
Data sources ...... 7
Do male and female adult plants differ in their vital rates? ...... 9
Euphorbia telephioides demographic model construction and estimation of vital rates ...... 10
Deterministic projection and elasticity ...... 14
Results ...... 15
Do male and female adult plants differ in their vital rates? ...... 15
What are the projected population growth rates of each population and which stage of the life cycle is lambda most sensitive to? ...... 15
Discussion ...... 17
Chapter 3 Comparison of deterministic and stochastic projections of the status of three populations of a threatened dioecious perennial plant ...... 21
Introduction ...... 21
Methods...... 23
Species description...... 23
Study area...... 24 v Prior demographic projection ...... 24
Alternative demographic projections construction ...... 25
Results ...... 28
Do projections based on data excluding non-flowering plants produce greater estimates of lambda than projections from a combination of all data available? ...... 28
How much lower are stochastic projections than deterministic projections that combine all data? ...... 28
Discussion ...... 31
Chapter 4 Pollen limitation and its consequences for demography in a threatened dioecious perennial plant ...... 34
Introduction ...... 34
Methods...... 36
Species description...... 36
Study area...... 38
Pollen supplementation experiments ...... 38
Effects of flowering initiation on pollen limitation ...... 39
Effects of local pollen limitation ...... 40
Simulating the consequences of increased levels of pollen limitation for population growth ...... 41
Results ...... 41
Effects of local pollen limitation ...... 45
Simulating the consequences of increased levels of pollen limitation on population growth ...... 46
Discussion ...... 48
Chapter 5 Conclusion ...... 52
Appendix A Supplementary Information ...... 53
vi References ...... 58
Biographical Sketch ...... 64
vii LIST OF TABLES
Table 1: Fire frequency records for each population ...... 6
Table 2: Data source description for all three populations ...... 8
Table 3: Number of viable seeds planted and germination percentages in 2011 and 2012 for each population ...... 9
Table 4: Growth rate (Lambda) estimates and 95% confidence intervals (CI) for each population using all data ...... 17
Table 5: Description of demographic projections within each site...... 26
Table 6: Comparisons of female and male stem growth in centimeters from 2011 to 2016 at each population ...... 53
Table 7: Comparisons of the average number of flowers produced in female and male plants from 2011 to 2016 at each population. There were not enough samples to conduct the comparisons in Bay and Franklin counties for 2015. I used the log transformation to comply with the t-test assumptions when pertinent...... 53
Table 8: All deterministic transition matrices for three populations of E. telephioides...... 54
Table 9: Transition matrices for Bay County...... 55
Table 10: Transition matrices for Gulf County...... 55
Table 11: Transition matrices for Franklin County ...... 56
Table 12: Adults only transition matrices for three populations of E. telephioides constructed using data from mature plants collected during 2011 to 2016...... 57
viii LIST OF FIGURES
Figure 1: Euphorbia telephioides cyathium in male and female plants. Stamen (A), glandular bracts (B), involucre (C), and pistil (D)...... 5
Figure 2: Map of Euphorbia telephioides populations. Red dots indicate the location of each study site...... 7
Figure 3: Euphorbia telephioides stage structured life cycle. Nodes represent stages. Each possible contribution to population growth is identified by a letter and two numbers that correspond to the columns and rows in the transition matrix shown below. The second digit corresponds to each stage at time t in consecutive order starting with (1) Seedling, (2) Non- Flowering, (3) Dormant and (4) Flowering, the first digit correspondπ΄π΄ to the fate at time t+1. For example: The probability of dormant individuals to become flowering at time t+1 is represented by 43...... 11
Figureππ 4: Number of individuals that flowered from one to seven times between 2010 and 2016 in three populations of E. telephioides. Color indicates data from each gender black for female and gray for male plants...... 16
Figure 5: Elasticity of Lambda to changes in each matrix element for each population using all data in a deterministic projection. Population growth rate, Lambda, was proportionally most sensitive to variation in the stasis of non-flowering plants (a22) in all three populations...... 18
Figure 6: Population growth rates (Lambda) represented as open dots and bootstrapped 95% confidence intervals for each projection of Ξ» in all three populations. Adults only projection excludes data from randomly marked non-flowering individuals...... 29
Figure 7: Observed differences in lambda estimates of all data projection minus adults only projection. Adults only projection excludes data from randomly marked non-flowering individuals. Circles represent observed differences in lambda and whiskers represent 95% confidence intervals of lambda differences by chance...... 30
Figure 8: Observed differences in lambda estimates of all data deterministic projection minus all data stochastic projection. Circles represent observed differences in lambda and whiskers represent 95% confidence intervals of lambda differences by chance...... 30
Figure 9: Euphorbia telephioides female plants and seed. Pollinator (A), mature fruits with three locules (B), fruits after seed dispersal (C) and (D) mature viable seeds...... 37
Figure 10: Distribution of mean number of fruits per flower and mean viable seeds per fruit produced for control (open pollination) and pollen supplemented plants in Franklin County in May 2015. Boxes represent the interquartile distribution, the bold lines in boxes represent the medians, and whiskers show the maximum and minimum values...... 42 ix Figure 11:Distributions of Julian date of flowering initiation for male (gray bars) and female (black bars) plants in Franklin County...... 43
Figure 12: Distribution of number of mean number of fruits and mean viable seed produced per fruit for control (open pollination) and pollen supplemented plants in Gulf County in May 2015. Boxes represent the interquartile distribution, the bold lines in boxes represent the medians, whiskers show the maximum and minimum values, and open points denote data points outside 1.5 times the lower interquartile range...... 44
Figure 13: Distributions of Julian date of flowering initiation for male (gray bars) and female (black bars) plants in Gulf County...... 45
Figure 14: Projected population growth rates and bootstrapped 95% confidence intervals for population with zero to 80% simulated pollen limitation in Franklin County...... 47
Figure 15: Projected population growth rates and bootstrapped 95% confidence intervals for population with zero to 80% simulated pollen limitation in Gulf County...... 47
Figure 16: Projected population growth rates and bootstrapped 95% confidence intervals for population with zero to 80% simulated pollen limitation in Bay County...... 48
x ABSTRACT
The effective conservation of threatened and endangered plants requires an understanding of population dynamics and the evaluation of factors that could reduce population growth. I constructed and analyzed a stage structured demographic model for Euphorbia telephioides, a threatened dioecious perennial herb, to determine the current status of three populations, compare projections of population growth using different methods, and determine the effects of pollen limitation in the population dynamics of this species. Dioecious plants are prone to pollen limitation due to their inability to self-pollinate. Studies indicate that pollen limitation reduces seed set in plants due to insufficient quantity or quality of pollen, which can reduce population growth rate due to the decrease in fecundity. I combined experimental tests for pollen limitation with construction and analysis of structured demographic models, to examine how increased levels of pollen limitation would affect population growth rates.
Determining the current status of populations, and simulating the consequences of possible threats, such as pollen limitation, provides a quantitative basis for conservation actions. I compared deterministic and stochastic projections of a stage structured demographic model to examine how environmental variation affects population growth rates, and I examined the effects of parameterizing the model excluding demographic measures of randomly marked individuals in the population growth rates (Lambda). The majority of estimated lambdas and their 95% confidence intervals indicate that these three populations are projected to decline. Lambda estimated excluding randomly marked individuals overestimated population growth because adult plants had 100% survival. I did not find evidence of significant pollen limitation of fruit or seed production, and simulations of increased levels of pollen limitation reduce Lambda at a modest rate between 0.17% to 1.91%. The main advantage of constructing a structured demographic model is that these models allow us to integrate data on different stages of a complex life cycle. In the case of E. telephioides elasticity analysis indicates that increasing stasis of non-flowering plants could lead to increasing population growth rates
xi CHAPTER 1 INTRODUCTION
Every threatened and endangered plant requires a recovery plan by law, however this document does not often include quantitative guidelines to assess species recovery. Structured demographic models could help quantify progress toward conservation goals because they can determine if a population is growing, declining or stable by linking the fates of individuals with the species life cycle. Furthermore, once these demographic models are parameterized we can conduct prospective perturbation analysis, such as elasticity analysis, to inform managers what would happen if specific vital rates are changed and how that might affect population growth rates. However, the construction and analysis of these models is not trivial because they require an understanding of the species life cycle, the evaluation of model assumptions, and the collection of demographic information from marked individuals.
If at risk species populations are projected to decline, the next step is to evaluate possible factors contributing this decline. Pollen limitation, the insufficient quantity or quality of pollen for reproduction, is common in flowering plants and could contribute to lower population growth rates because of reduced seed set expected in pollen limited plants.
This study aims to contribute to the conservation of Euphorbia telephioides, a threatened dioecious plant endemic to coastal Northwest Florida by examining the demography of three protected populations and conducting experimental tests of pollen limitation. First, I constructed a structured demographic model to determine population growth rates (lambda) assuming vital rates remain constant. Second, I incorporated variation in the vital rates using a stochastic projection and compared those estimates with deterministic lambda. Last, I combined information from pollen limitation tests with the structured demographic model to simulate how increased levels of pollen limitation could contribute to the decline of these protected populations.
1 CHAPTER 2 DEMOGRAPHIC ANALYSIS OF THREE POPULATIONS OF A THREATENED DIOECIOUS PERENNIAL PLANT
Introduction
Conserving plant species requires not only land preservation but an understanding of the dynamics of plant populations. In the United States more than half of all federally listed species are plants and they receive less than five percent of total funding for conservation (NegrΓ³n-Ortiz 2014b). Moreover, most of those limited funds are used to acquire land, but land preservation would not necessarily ensure the persistence of endangered and threatened plants. For example, a long term study of orchids of the Catoctin Mountains, Maryland, revealed rapid decline of 90.5% of the species of orchids present even in protected land (Knapp and Wiegand 2014). In consequence, among the most important challenges in plant conservation are to determine if protected populations are growing, stable, or declining and to identify the factors that influence changes in population size. Demographic modeling is a vital tool in such efforts (Schemske et al. 1994, Caswell 2001).
Demographic models allow the estimation of population growth rates, the assessment of extinction probabilities, and the simulations of possible threats and their consequences to population growth rates. Stage - structured demographic models integrate vital rates in the context of the life cycle, making them especially advantageous when the life cycle can be described by size classes or developmental stages (Caswell 2001). In long-lived plants, stage - structured demographic models are particularly valuable because they permit the study of species with a complex life cycle because they can incorporate life history information like plant dormancy, seed dormancy, periodic recruitment, and clonal growth (Menges 2000). Furthermore, these models allow us to conduct other simulations such as perturbation analysis. Perturbation analysis, also known as sensitivity analysis can help determine what stages in the life cycle or which vital rates contribute the most to population growth (Schemske et al. 1994, Caswell 2001).
2
Constructing stage - structured demographic models requires the collection of demographic data from marked individuals and deciding the number of stages that best represent the life cycle of the target species. Ideally demographic parameters should be estimated from census of marked individuals, from birth until death (Bierzychudek 1982). However, for endangered or threatened long-lived species, this information is not always available, and recovery plans for these species do not require the collection of data necessary to parameterize these models (Schaffer et al. 2002). Fortunately, in a few cases there is demographic data available from serendipitous observations or experiments that could allow the construction of structured demographic models. For example, the construction of a structured demographic model for the loggerhead sea turtle, Caretta caretta, using vital rate estimates collected at different locations and in different years, resulted in a model supporting the implementation of novel management practices that protected the juveniles, which were identified as the stage that contributes the most to population growth (Crouse et al. 1987). Combining different sources of data to construct structured demographic models for long-lived species with complex life cycles could allow us to answer more detailed questions such as which stages are more important for population growth (Caswell 2001), as well as to determine which management practices are more cost effective (Shea et al. 2010, Kerr et al. 2016).
Beyond the difficulties in constructing and analyzing demographic models for any plant population, some taxa present extra challenges. Most flowering plants present both genders in the same plant so there is no need to structure their demography by gender. But approximately 6% of flowering plant species are dioecious (Renner and Ricklefs 1995), meaning that pistillate (female) and staminate (male) flowers are produced on different plants. Populations of dioecious plant species require special consideration for demographic modeling because of the lower expected growth, survival, and flowering frequency in female plants compared to male plants (Geber et al. 1999). These differences in female and male plants are expected due to the higher cost of reproduction in females (Harper 1977, Geber et al. 1999, Obeso 2002). These differences in reproductive cost have been shown to result in slower growth, lower rates of survival, and less frequent flowering for females (Geber et al. 1999). Consequently, efforts should be made to estimate vital rates for both genders to detect significant differences in growth, survival and
3 flowering frequency. If differences are detected, then a model that incorporates genders separately will provide a better estimate of population growth than a model than assumes equal vital rates for the two genders. Dioecious plant taxa are more likely to be threatened than non- dioecious sister groups (Vamosi and Vamosi 2005), but perhaps because they are uncommon, dioecious plants are rarely modeled.
I combined multiple sources of existing information with newly collected data to construct and analyze demographic models for three populations of Euphorbia telephioides, a threatened perennial dioecious plant, with the objectives to determine 1) if male and female plants differ in their vital rates, 2) the projected population growth rates of each population, and 3) which stage of the life cycle is more important for conservation.
Methods
Species description
Euphorbia telephioides Chapman (Euphorbiaceae), is an herbaceous perennial dioecious plant endemic to coastal Bay, Gulf, and Franklin counties in the Florida Panhandle (Bridges and Orzell 2002). This species prefers sandy ridges in Flatwoods or scrubby pineland, and can be locally abundant in disturbed sandy road embankments (Bridges and Orzell 2002). It is also sometimes found in wetlands with seepage slope species such as wiregrass, toothache grass, plumed beaksedge, flattened pipewort, and woolly huckleberry. Euphorbia telephioides populations have been reported in 40 sites (U.S. Fish and Wildlife Service 2007, Trapnell et al. 2012). Current sites are disjunct, but allozyme analysis for 17 populations of E. telephioides supports very high species-wide and population level genetic diversity relative to similar taxa, along with low population differentiation, which suggests that this species was previously more continuously distributed and became fragmented recently (Trapnell et al. 2012). These results are consistent with the recent development of the coastal habitat where this species occurs (Figure 2).
4 Individuals are 20-40 cm tall, with leaves that are slightly succulent, alternate and obovate to oblanceolate. Established individuals have a large tuberous root, presumably adapted to recurrent fire and prolonged dormancy (Trapnell et al. 2012).This species is expected to have a long length of life based on field observations of the small size of 5 year old seedlings that are (not greater than 2 cm in height) relative to reproductive adults (personal observation). Plants can go dormant for a year and re-appear after burning or mowing (U.S. Fish and Wildlife Service 2007). The inflorescence is a widely branched cyme displaying several cyathia. A cyathium (Figure 1) is developmentally intermediate between a flower and an inflorescence, and typically comprises several apetalous staminate flowers surrounding a single pistillate flower. In E. telephioides the cyathium is surrounded by five approximately circular purple glandular bracts (Bridges and Orzell 2002).
Figure 1: Euphorbia telephioides cyathium in male and female plants. Stamen (A), glandular bracts (B), involucre (C), and pistil (D).
Euphorbia telephioides is functionally dioecious with individuals bearing either pistillate or staminate cyathia (Figure 1), although recent information suggest this species as subdioecious because a few individuals present female and male flowers within the same cyathium on the same plant (personal observation). This plant flowers intermittently from March to October.
5 Most plants go dormant after flowering and from December to February, reappearing in spring. Euphorbia telephioides fruits have three locules, which contain a maximum of one seed each. This species has explosive seed dispersal and does not have a persistent seed bank (NegrΓ³n-Ortiz 2014a).
Study area
Euphorbia telephioides is endemic to habitats prone to periodic fire from lightning (Bridges and Orzell 2002) and the most vigorous populations occur in protected areas that are actively managed (Trapnell et al. 2012). I chose three sites because data on germination of seeds sown in the field (Table 3), survival and reproduction of flowering individuals over five years was available for those populations. Those protected sites were previously selected to collect reproductive information and in-situ germination percentage because they are managed with frequent prescribed fire (Table 1). I collected additional demographic information from the same sites (Figure 2). In Bay County, data was collected at the Breakfast Point Mitigation Bank, this population is in a pine plantation. The second population is located at the St. Joseph Bay Buffer Preserve in Gulf County, this population is in wet prairie habitat. The third population is located in mesic flatwoods at Box-R Wildlife Management Area in Franklin County.
Table 1: Fire frequency records for each population
Sites Managed by: Dates of prescribed fire Time since last fire Bay St. Joe Company 08/23/2011 5 years Gulf Florida department of 05/27/2003 03/18/2009 03/04/2014 2 years environmental protection Franklin Florida Fish and Wildlife 02/25/2009 03/31/2010 04/11/2014 2 years Conservation Commission
6
Figure 2: Map of Euphorbia telephioides populations. Red dots indicate the location of each study site.
Data sources
I obtained access to data collected by Dr. Negron-Ortiz, the federal botanist in charge of the recovery of endangered and threatened plants occurring in Northwest Florida, at each population from a reproductive study conducted from 2010 to 2015 and in-situ germination experiments conducted in 2011 and 2012 (Table 2). I also generated additional demographic data by marking 200 individuals in 2014 at each population and recording their demographic fates over one year (Table 2).
7 Table 2: Data source description for all three populations
Data source Number of Period of Variables measured name marked data individuals collection Reproductive 50 at each 2010-2016 Number of flowers, number of fruits, study population flowering frequency and stem height. Number of expected viable seeds per fruit was estimated for 2011 and 2012. In-situ 32 seedlings total 2011-2012 Germination percentage, and survival of germination (17 in Bay and 15 seedlings. study in Franklin) Demographic 317 in Bay, 317 in 2014-2016 Number of flowers, number of fruits, study Gulf, and 263 in number of expected viable seeds, Franklin. flowering frequency, stem height, survival of individuals, and recruitment
The reproductive study dataset consisted of measurements of reproductive output (number of flowers and number of fruits) and size (stem height) from 50 haphazardly chosen marked adult individuals of E. telephioides at each population. Data was collected once a month from August 2010 to May 2015. Stem height was measured in centimeters from the base of the stem to the base of the terminal leaf for non-flowering stems or the base of the first cyathium for flowering plants. Also in 2011 to 2012 only, the number of fruits and total number of viable seeds produced by some of these individuals and other unmarked plants in the area were also recorded.
The in-situ germination dataset included germination percentage for seeds collected from the individuals described above and sown in the field at each population from Summer 2011 to Fall 2012 (Table 3). Viable seeds were planted back into the site where they were collected in groups of three to nine and buried two centimeters deep in the soil inside bridal veil bags marked 8 with a numbered flag. Seed germination occurred within four to ten months of planting viable seeds. Seventeen and fifteen seedlings that emerged in Bay and Franklin County respectively were monitored once a month for two years post-germination, which allowed the measurement of first year survival and growth for seedlings. Seedlings at Gulf County were destroyed by accident and were not included in the analysis.
Table 3: Number of viable seeds planted and germination percentages in 2011 and 2012 for each population
2011 2012 Population Viable seeds planted Germination (%) Viable seeds planted Germination (%) Bay 8 75 75 16 Gulf 16 6.25 26 0 Franklin 27 48.15 36 13.89
Because the previously collected data included adult individuals or seedlings but not juvenile plants, it does not represent the full life cycle and does not constitute a random sample of the population. Therefore, I marked and measured all individuals up to 200 within a defined area at each population in 2014 (demographic study dataset) to obtain data from a random representative sample of plants. In 2015, I remeasured all marked individuals, and counted and marked new individuals that appeared within the defined areas. I assumed that the new individuals marked in 2015 came from plants that were dormant in the previous year. In addition, I remeasured the adult individuals marked in 2010 at each population in 2014, 2015, and 2016.
Do male and female adult plants differ in their vital rates?
I used a subset of the data from the reproductive study excluding subdioecious individuals to compare vital rates of male and female plants of E. telephioides within each study
9 population (Bay County n = 31, Franklin County n = 41, and Gulf County n = 44). To determine if adult male and female plants differ in their growth, I quantified the change in stem height for each individual as the difference in the maximum stem height recorded in each of two consecutive years for each pair of years for which data were available. I used a t-test to compare mean changes in stem heightfor male and female plants within each population for each one-year interval. I tested the normality assumption using the Shapiro test and I used Bartlettβs test to identify variance homogeneity.
To compare flowering frequencies in male and female plants, I calculated the number of years each adult plant flowered in the reproductive data set from 2010 to 2016. Flowering frequencies were recorded for 27 female and 4 male plants in Bay County, 26 female and 15 male plants in Franklin County, and 32 female and 12 male plants in Gulf County. Flowering frequencies were assigned as one to seven: one for plants that flowered once, two for presenting flowers in two of the seven years, and consecutively until seven if they flowered at every census. To compare flowering frequencies in male and female plants I used a Chi-square contingency test for each population.
To determine if adult male and female plants differ in the number of flowers produced. I compared the average number of flowers produced by male and female plants within each population and year using a t-test. The Shapiro test was used to test for normality and a Bartlett test was used to detect variance homogeneity.
All plants marked in 2010 were still alive in 2016. Consequently, I did not compare survival of adult males and females.
Euphorbia telephioides demographic model construction and estimation of vital rates
I constructed a model to integrate stage-specific vital rates to estimate population growth at each population. I assigned individuals to four stages: seedling, non-flowering, dormant, and flowering. I chose those stages because they are biologically different and easy to identify and expected to have different demography. The seedling stage represents individuals in their first 10 year of life; seedlings have two cotyledons that are not easily differentiated from the leaves of small non-flowering plants. The non-flowering stage includes non-flowering individuals independent of whether they have flowered in the past. The dormant stage represents vegetative individuals that were dormant (no stem present) during one year and observed in the next census. Flowering individuals were assigned to the flowering stage. I assumed individuals were dead if no stem was observed in two consecutive censuses. These stages are represented as the nodes in the life cycle diagram in Figure 3, where each arrow represents a demographic contribution of one stage to another over a one-year projection interval known as demographic transition. Stages were not structured by gender because adult male and female adult individuals did not differ in stem growth, flowering frequency, or survival (see Results).
Figure 3: Euphorbia telephioides stage structured life cycle. Nodes represent stages. Each possible contribution to population growth is identified by a letter and two numbers that correspond to the columns and rows in the transition matrix shown below. The second digit corresponds to each stage at time t in consecutive order starting with (1) Seedling, (2) Non- Flowering, (3) Dormant and (4) Flowering, the first digit correspondπ΄π΄ to the fate at time t+1. For example: The probability of dormant individuals to become flowering at time t+1 is represented by .
ππ43
The following equation is the mathematical formula for one iteration of the stage structured model, also known as matrix model:
11
( ) =
ππ π‘π‘+1 π΄π΄πππ‘π‘ The vector ( ) describes the abundance of individuals at each stage at time , and the matrix is a matrixππ thatπ‘π‘ comprises transition probabilities, the contributions of one stageπ‘π‘ to the Euphorbia telephioides next, duringπ΄π΄ a one year projection interval for . Matrix entries correspond to the transitions in Figure 3 0 0 0
= ππ14 21 22 23 24 ππ0 ππ ππ ππ π΄π΄ οΏ½ οΏ½ ππ31 ππ32 ππ33 ππ34
ππ42 ππ43 ππ44 The projection of the matrix A to asymptote to estimate lambda assuming the elements remain constant is known as a deterministic projection, and it is used to forecast the state of a population at a later time assuming no change in the values of the elements of A.
I constructed a stage-structured matrix consisting of probabilities of all possible transitions during a one-year interval for each of the three populations of Euphorbia telephioides. Matrix entries correspond to the transitions in Figure 3, and the data used to parametrize each element come from a combination of measures of plants from the three data sources available (Table 2).
I combined measures of seedlings stage and fate from sown seeds in 2011 and 2012 at Bay and Franklin counties, due to the limited number of individuals at this stage per year and site. I used the same seedling vital rates ( and ) for all three populationsβ projections. This decision combined temporal and spatial variationππ21 ππ of31 seedling vital rates. I assumed that a germinated seed could only remain a seedling during its first year of life.
Other vital rates were calculated using the multiple measures of stage and fate for each marked plant in different years as independent measures of transition probabilities (see Table 2). For example, fifty marked adult individuals from the reproductive study resulted in 250 measures of stage and fate in one population. Including data collected in different years allowed the
12 incorporation of some variation of vital rates. I will refer to the combination of measures from the reproductive study, in-situ germination study, and the demographic study as using all data.
Demographic parameters regarding the non-flowering stage were calculated using all data to estimate the probability that non-flowering individuals survive and remain at the same stage ( ), the probability of non-flowering individuals to survive and become dormant from t to t+1
(ππ22 ), and the probability of a non-flowering plant to survive and become flowering from t to t+1ππ32 ( ). ππ42 Demographic parameters regarding the dormant stage were calculated using all data, to estimate, the probability that individuals that are dormant in year t emerge into the non-flowering stage t+1 ( ), the probability that dormant individuals survive and remain dormant ( ), and the probabilityππ23 that a plant survives dormancy and flowers from t to t+1 ( ). I assumedππ33 that new plants observed in the delimited areas of the demographic study wereππ 43new recruits that came from dormant individuals not marked in the previous year.
Demographic parameters regarding the flowering stage were estimated using all data, to estimate the probability of individuals to survive the flowering stage and become non-flowering from t to t+1 ( ), the probability of flowering individuals to survive and become dormant from
to + 1 ( ππ),24 and the probability of a flowering plant to survive and flower from t to t+1 π‘π‘( π‘π‘). ππ34 ππ44 I used anonymous assignment when estimating fecundity because I was unable to identify the parents of seedlings. Fecundity ( ), the average number of new seedlings per reproductive
adult, was calculated as the estimatedππ 14total number of viable seeds produced by all females in a population at time ( ) divided by the total number of flowering plants at time
( π‘π‘ πππππ‘π‘πππππππ‘π‘ππππ) within ππππππππππeach population,π‘π‘ multiplied by the probability of seedling π‘π‘survivalππ ππππππππππππππππππ to the nextπππππππππ‘π‘ππ censusπ‘π‘ ( ). ππππππππππππ ππππππππππππππππ πππππππ π πππ π ππππ
13 Fruit set, seed set, and germination probability estimates were not available for every year transition at each site, therefore I used the average of all the available information within each population for the missing parameter. For example, germination percentage was only available for 2011 and 2012 in Franklin County; hence, I used the arithmetic mean of those germination estimates in the calculation of fecundity in Franklin County for years without germination data (2013 to 2015).
= Γ Γ
πππππ‘π‘πππππππ‘π‘ππππ πππππππππππ‘π‘ ππ ππππππππππππ πππππππππππππππ‘π‘ πππππππππ‘π‘ πππππ‘π‘ ππππππππ πππππ‘π‘
= Γ Γ π‘π‘ 14 πππππ‘π‘πππππππ‘π‘ππππ ππππππππππ π‘π‘ ππ πππππππππππππππ‘π‘ππππππ πππππππππππππππππππ‘π‘ππ ππππππππππππ ππππππππππππππππ πππππππ π πππ π ππππ ππ ππππππππππππππππππ πππππππππ‘π‘πππ‘π‘ Deterministic projection and elasticity
I estimated asymptotic growth rate (Ξ») from projection, and calculated the 95% confidence intervals for the projected population growth rate to determine the uncertainty of my estimates using bootstrapping for each of the three focal populations. The bootstrapping consisted of 10000 projections calculated by resampling individual records with replacement from the stage and fate of marked individuals recorded from 2010 to 2016.
I conducted an elasticity analysis to determine the sensitivity of lambda to proportional variation in each element of the transition matrix. Greater elasticities would indicate vital rates whose changes produce the greatest proportional changes in lambda.
All analyses were conducted using the free software R. (Core Team 2015). Statistical analyses were conducted using the package βstatsβ. Model construction and demographic analysis were conducted using the βpopbioβ package R 2.4.2 (Stubben et al. 2016) and the life cycle diagram for E. telephioides was created using the package βdiagramβ (Soetaert 2014).
14 Results
Do male and female adult plants differ in their vital rates?
Male and female plants did not differ in survival, stem growth, or flowering frequencies, however male plants produced more flowers than female plants. There was no difference in the survival of male and female flowering plants at any population. Every plant marked in 2010 was still alive in 2016. I did not find evidence of significant differences in stem growth in male and female plants, with one exception of eighteen comparisons (Table 6). In one year at Franklin
County, female plants had a greater average stem growth than male plants (ts = 2.25, d.f = 35, P = 0.03). Most reproductive plants flowered more than four times from 2010 to 2016 at each population (Figure 4). Flowering frequency was independent of gender in Gulf County (Ο2= 3.33, d.f. = 6, P = 0.77, Figure 4) and Franklin County (Ο2= 9.30, d.f. = 6, P = 0.16, Figure 4). In Bay County, male plants flower significantly more often than females (Ο2= 16.91, d.f. = 6, P = 0.01, Figure 4), but frequencies for males were based on only four individuals. Female plants produced on average three to ten flowers per plant, and male plants produced on average seven to 37 flowers per plant (Table 7).Male plants produced significantly greater average number of flowers than female plants in seven out of eighteen comparisons (Table 7).
What are the projected population growth rates of each population and which stage of the life cycle is lambda most sensitive to?
All three populations are projected to decline, and elasticity analyses indicate that proportional changes in stasis of non-flowering plants would produce greater changes in the population growth rates compared to changes in other transitions. Estimated population growth rates (Ξ») ranged from 0.962 to 0.994 (Table 4) suggesting that all three populations are projected to decline, and 95% confidence intervals do not include one, but upper confidence intervals for Gulf County are very close to one suggesting that population could be close to stability. Elasticities indicate that in all three populations, lambda was proportionally most sensitive to changes in the stasis of non-flowering plants (Figure 5). 15
Figure 4: Number of individuals that flowered from one to seven times between 2010 and 2016 in three populations of E. telephioides. Color indicates data from each gender black for female and gray for male plants.
16 Table 4: Growth rate (Lambda) estimates and 95% confidence intervals (CI) for each population using all data
Site Lower Lambda Upper limit limit of of 95% 95% CI CI Bay 0.9702 0.9843 0.9978 Gulf 0.9865 0.9937 0.9999 Franklin 0.9410 0.9620 0.9825
Discussion
I found no differences in the vital rates of male and female Euphorbia telephioides, and consequently constructed a one-sex stage structured model to estimate population growth rates. Model projections indicated that under current conditions these three populations are projected to decline, although the Gulf County population might be close to stability (Table 4). According to elasticity analysis (Figure 5), management should target increasing the survival or preventing dormancy of the non-flowering stage to increase population growth because lambda is proportionally most sensitive to the stasis of non-flowering plants.
Although several studies in dioecious plants have illustrated that male plants can have greater survival and flowering frequency than female plants due to the greater cost of reproduction in female plants (Geber et al. 1999), I did not find evidence of differences in the vital rates of male and female plants of Euphorbia telephioides. Survival was 100% in all populations, flowering frequency was independent of gender, and male and female plants had on average the same the same stem growth. In other species, female plants allocate more biomass to reproduction than male plants because of fruit production (Obeso 2002), but in the case of E. telephioides, fruits are small (diameter = 0.7 cm), fruit set is low (mean = 0.53, range: 0 β 1), and male plants produce up to six more flowers on average than female plants, which could equalize 17 the cost of reproduction for the two genders. A similar pattern was observed for Silene latifolia, in which male plants produced more flowers than female plants and there was not a significant difference in the cost of reproduction (Delph and Meagher 1995).
Figure 5: Elasticity of Lambda to changes in each matrix element for each population using all data in a deterministic projection. Population growth rate, Lambda, was proportionally most sensitive to variation in the stasis of non-flowering plants (a22) in all three populations.
18 The three populations of Euphorbia telephioides studied are currently projected to decline (Table 4) even though all are in protected sites. These predictions do not account for environmental variation. They assumed a constant environment and might have resulted in a best case scenario because more than half of the measures of fate and stage used to calculate lambda come from individuals marked after fire (Table 1), and in fire adapted plants, short time since fire increases fecundity, plant growth and projected population growth rates. For example, in a ten year study of Solidago odora, a fire adapted perennial herb, a greater proportion of stems flowering were observed in the first two years after fire (Menges and Root 2004). Also, populations of Dicerandra frutescens, a fire adapted Florida mint, had greater population growth rates within three and four years since fire compared to populations burned more than five years ago (Menges et al. 2006). Therefore, the deterministic projections for E. telephioides might have resulted in overestimates of population growth rate because they did not account for variation in the vital rates.
Treating measures of stage and fate of the same individuals from multiple years as independent could lead to underestimating environmental variation if vital rates are positively correlated because a composite of multiple year data does not account for vital rates correlations among years. If vital rates have strong positive correlations, combining information from multiple years can reduce the variation expected in good and bad years. This would overestimate lambda because increase in variation in vital rates is linked to decrease in stochastic growth rates (Fieberg and Ellner 2001). However, if vital rates are negatively correlated, it could increase stochastic growth rates because it would reduce vital rate variation (Wisdom et al. 2000). Nevertheless, vital rates correlations are rarely incorporated in estimates of lambda. The most common approach to account for these correlations is to conserve the vital rates within a year, alternating whole matrices to simulate environmental variation in a stochastic projection (Crone et al. 2011).
A common approach to incorporate multiple year data in a deterministic projection without combining repeated measures of stage and fate is to construct a mean matrix, an element-wise average projection matrix, from the matrices constructed for each year transition. I compared deterministic projection of lambda using a mean matrix (e.g. For Bay county, I
19 estimated the mean matrix from the five matrices on Table 9) and the deterministic projection combining all the data (Table 8) available using a randomization test (Caswell 2001). Population growth rates from the composite repeated measures were greater than lambda from the mean matrix at all populations; this difference was significant only in Gulf County. The advantage of combining the repeated measures to construct the projection matrix is that a greater number of samples used to parameterized each vital rate could have increased the accuracy of these estimates by reducing sampling error. Decreasing sampling error on the estimates of each vital rate could provide better assessments in perturbation analysis such as elasticities because these analyses rely on the accuracy of each element of the matrix.
Lambda was most sensitive to proportional changes of vital rates that involve transition from the non-flowering stage at each population (Figure 5). These findings are in accordance with a comparative demographic study of 102 perennial plant species which indicated that in iteroparous herbs, growth and survival transitions have greater contributions to population growth than fecundity (Franco and Silvertown 2004). Also, the contribution of non-flowering plants to population growth is in accordance with other studies in long-lived plants (Pfister 1998, Rojas-Sandoval and MelΓ©ndez-Ackerman 2013). These results suggest that determining the factors that increase non-flowering survival, reduce non-flowering dormancy and how fire frequency affect those vital rates could help identify management practices that would increase population growth rate in those populations. In addition, increasing the accuracy of demographic parameters regarding the non-flowering stage would increase the reliability of estimates of lambda.
Although combining multiple years of data in a deterministic projection is not ideal, it is essential to quantify growth rates in this model, which show that these populations are projected to decline. In consequence, land preservation is n ot enough and management actions appear to be required to ensure the recovery of this species. One advantage of constructing stage structured models is that they permit the use of elasticity analysis which suggest where management should be targeted. For E. telephioides, these analyses suggest that we should determine which factors would increase non-flowering survival, reduce non-flowering dormancy and how these vital rate are affected by greater fire frequency.
20 CHAPTER 3 COMPARISON OF DETERMINISTIC AND STOCHASTIC PROJECTIONS OF THE STATUS OF THREE POPULATIONS OF A THREATENED DIOECIOUS PERENNIAL PLANT
Introduction
Applied plant ecologist have increased the number of structured demographic models, constructing simpler models parameterized with limited sets of data to answer conservation questions, in contrast to academic assessments that focus on the development of more complex models to increase accuracy of forecasting population dynamics (Crone et al. 2011). This contrast highlights the need to evaluate the consequences of different methods to calculate population growth rates using limited datasets. Stage- structured demographic models, constructed using a matrix of transition probabilities among life history stages, are used to project equilibrium population growth rates (Bierzychudek 1999). These projections can be deterministic, assuming vital rates remain constant over time, or stochastic assuming vital rates vary due to environmental variation. Assuming vital rates are constant is common, although it is an unrealistic scenario because it is known that environmental variation causes variation in the vital rates, and ignoring this variation will lead to overestimates of population growth rates.
The examination of the assumptions underlying estimates of population growth rates is especially necessary when studying a threatened species because limited data will often only allow a deterministic projection, but overestimation of population growth could give a false signal of recovery. Models that assume a constant environment will overestimate population growth because population growth is a multiplicative process and the arithmetic mean of the population growth will be higher than its geometric mean in a variable environment (Lewontin and Cohen 1969). Temporal environmental variation can be stochastic or periodic, and it could affect different life cycle stages differently. In the case of endangered and threatened species, the effect of environmental variation should be incorporated in the predictions of population growth, 21 because populations that experience greater fluctuations in population size will have greater extinction probabilities and models that assume a constant environment will overestimate population growth rates (Ovaskainen and Meerson 2010).
One method to incorporate variation in vital rates in estimation of population growth rates is to calculate population growth using a stochastic projection; however, this requires the collection of demographic data for multiple years. In contrast, deterministic projections circumvent this intensive and expensive data collection by assuming vital rates are constant. Stochastic projections can incorporate variation in the vital rates if there is demographic information to construct more than one matrix. When there is not enough information for a credible stochastic analysis, other approaches can be used to incorporate information on year-to- year variation in vital rates. When there is insufficient data for a stochastic analysis, it would be useful to compare estimated population growth rates using a variety of methods to incorporate environmental variation. Stochastic projections will always be lower than deterministic projections, so estimating the magnitude of how much a deterministic projection overestimates lambda is important to make management decisions.
Besides the need to address temporal variation in lambda estimates in natural populations, another possible limitation of structured demographic models is that they require demographic information from individuals at each life cycle stage in order to generate accurate vital rates (Bierzychudek 1999). Recovery plans tend to allocate projects to collect data from reproductive adults in the populations so it is necessary to evaluate the consequences of parameterizing a structured model using samples of individuals that do not represent all life stages (Schaffer et al. 2002). For example, managers often prioritize collecting reproductive data because successful reproduction is required to maintain populations of at risk species. However, data from reproductive individuals limits the ability to fully parameterize a structured model. In the absence of data on survival of non-reproductive plants, the model would assume that these individuals have the same vital rates as adults, which is unlikely. For example, in the long-lived slow growing tree Taxus floridana, survival probabilities increase with increasing stem size (Kwit et al. 2004). If most of the individuals used to parameterize a demographic model are
22 larger, it can overestimate survival, leading to greater values of lambda than a projection that includes the lower survival probabilities of younger individuals.
I previously conducted deterministic projections of population growth for three populations of the threatened perennial plant, Euphorbia telephioides, based on composite stage and fate data of marked individuals measured from 2010 to 2016. Those deterministic projections included year-to-year environmental variation by combining demographic information collected in multiple years. Here I contrasted estimates of lambda using a deterministic and stochastic projection using the same data. My objectives were to determine 1) how much does a projection that excludes data for small non-flowering plants over-estimate lambda compared to a projection constructed from vital rates for individuals at all life stages, and 2) how different are stochastic projections from deterministic projections that incorporate environmental variation as multiple annual measures of stage and fate for the same plants as independent data.
Methods
Species description
Euphorbia telephioides is a long-lived dioecious coastal herb adapted to fire prone habitats (Bridges and Orzell 2002). This threatened plant is endemic to Northwest Florida and occurs in recently fragmented habitat (Trapnell et al. 2012), with some protected populations managed with frequent prescribed fire (e.g Table 1). Euphorbia telephioides is a slow growing, probably long-lived herb, and some individuals experience prolonged dormancy of up to a year. There is no evidence of seed bank, because seeds do no persist in the soil for more than one year (personal observation). This speciesβ complex life cycle precludes the determination of age in the field and previous analysis found no differences in the vital rates of male and female plants.
23 Study area
Euphorbia telephioides occurs in Bay, Gulf and Franklin County, I chose to study three populations, one located at each County (Figure 2) because there was data available from a reproductive study and an in-situ germination experiment to estimate demographic transitions (Table 2). I established demographic plots at each location in 2014 to complement the existing datasets (see details in Chapter 2 - data sources). All three populations are protected and are managed with prescribed fire (Table 1).
Prior demographic projection
I constructed a deterministic projection for each population combining measures of stage and fate from three data sources. Two of the datasets available were collected by Dr. Negron- Ortiz, the federal botanist at the U.S. Fish and Wildlife Service β Panama City Field office, from 2010 to 2016. She marked 50 flowering individuals in 2010 at each population for a reproductive study. This data set consisted of annual measures of survival of individuals, number of flower, number of fruits, number of expected and viable seeds per fruit estimated only for 2011 and 2012. Her second data set come from an in-situ germination study conducted in 2011 and 2012, information recorded included, percentage of germination of viable seeds sown in the soil, and survival of emerged seedlings (Table 3). To fully parameterize a demographic model for each population of this species I marked a random sample of 200 individuals in each population in 2014. I will refer to this set of data as the demographic study data set. The demographic dataset contain measures of number of flowers, number of fruits, number of expected viable seeds, survival of individuals, and recruitment measured from 2014 to 2016.
I assigned individuals to four stages (seedlings, non-flowering, flowering, dormant, and flowering) represented as the nodes in the life cycle diagram in Figure 3, because those stages are biologically different and expected to have different vital rates. I estimated the demographic contributions of one stage to another over a one-year projection from the composite of the three datasets available represented by the arrows in Figure 3. For fecundity, I used anonymous
24 assignment because it was impossible to identify seedling parentage. Fecundity was estimated as the average number of new seedlings per reproductive adult from the total number of viable seeds produced by all females in a population divided by the total number of flowering plants within each population, and multiplied by the probability of seedling survival to the next census.
I calculated lambda by deterministic projection combining all the measures of stage and fate from 2010 to 2016 for each population assuming those measures were independent, this allowed me to incorporate environmental variation in a deterministic projection. Lambda was calculated for each population using the βpopbioβ package R 2.4.2 (Stubben et al. 2016).
Alternative demographic projections construction
To examine the consequences of not adding demographic information from non- flowering individuals and not implementing a stochastic projection to estimate lambda, I compared my original analysis with two other projections of population growth rate for each population (Table 5). I used all data available from an in-situ germination study, reproductive study, and a demographic study (Table 2). I estimated two additional projections, comparing three projections total. Two projections used a composite of all data available but with different assumptions such as vital rates are constant (All deterministic) or vital rates vary (All stochastic). The other projection was parameterized with data from the reproductive study and the in situ germination study but excluded data on non-reproductive individuals to examine the consequences of assessing a species using commonly collected data not intended to calculate population growth rates (Adults only). For each projection, I assigned individuals to four discrete stages: seedling, non-flowering, dormant, and flowering (Figure 3).
I constructed stage-structured matrices for each projection consisting of probabilities of all possible transition, the demographic contribution of one stage to the next, represented by the arrows in the life cycle diagram in Figure 3. Below is the equation for one iteration of the matrix model, where ( ) represents a vector with the abundance of individuals, and matrix comprises transition probabilities during a one year projection for Euphorbia telephioides: ππ π‘π‘ π΄π΄
25 ( ) =
ππ π‘π‘+1 π΄π΄πππ‘π‘ 0 0 0
= ππ14 21 22 23 24 ππ0 ππ ππ ππ π΄π΄ οΏ½ οΏ½ ππ31 ππ32 ππ33 ππ34
ππ42 ππ43 ππ44
Table 5: Description of demographic projections within each site.
Projection Data used to parameterized it name All Deterministic projection from combination of measures of stage and fate of deterministic 50 adult individuals from the reproductive study from 2011 to 2016 treated as independent measures, measures of stage and fate from a random sample of individuals marked in 2014 and re-censused in 2015 and 2016, and seedling stage and fate from the in-situ germination study. Adults only Deterministic projection using repeated measures of stage and fate from 50 adult individuals from the reproductive study from 2011 to 2016 and seedling stage and fate from the in-situ germination study. All Stochastic projection from five projection matrices with equal probability Stochastic constructed using all data available for each year transition from 2011 to 2016.
For the All deterministic projection and Adults only projection (Table 5), I constructed one matrix per population (Table 8 and Table 12 respectively). For the stochastic projection, I constructed one matrix per year transition resulting in five matrices per population (Table 9, 10 and 11). The data used to parametrize each element of the matrix differs for each demographic projection and population except for the parameters regarding the seedling stage. I used the same demographic parameters for the seedling stage ( and ) for all three populations and for every projection. Those estimates were generated 21by combining31 seedling data from Bay and ππ ππ 26 Franklin counties germinated in different years (Table 3). I assumed seedlings can only remain in that stage for one year. To determine fecundity ( ), I used anonymous assignment and the same formulas and criteria as described in chapterππ14 2.
To determine if using repeated measures of adult individuals of a long lived plant would result in a greater estimates of Ξ» than a projection of the combination of all data available, I constructed a stage structured matrix using the reproductive study data (Table 2), consisting of the repeated measures of 50 adult individuals from 2011 to 2016 for the adults only deterministic projection.
To compare deterministic lambda with estimates of lambda that incorporate information on annual variation in the vital rates of Euphorbia telephioides I constructed and analyzed a stochastic projection for each population by sampling one of five projection matrices (Table 9, 10 and 11) for each projection interval with equal probabilities. This method assumes that the environmental conditions reflected in these five matrices are equally likely to occur in any sequence. I calculated stochastic growth rate by simulation after 50000 projection intervals and applied an exponential transformation to compare it with deterministic lambda. I calculated the 95% confidence intervals for the stochastic projected population growth rate.
To determine if Ξ» from one projection is significantly different from another, I used a randomization test procedure, which compared the observed difference between Ξ» for two projections with the differences expected by chance (Caswell 2001). The expected distribution was calculated by combining the datasets, but maintaining their sample size and stage sampling records randomly without replacement, and calculating the difference in Ξ» for each of 1000 pairs of samples. I concluded an estimate of Ξ» was significantly different from another if the observed difference between them exceeded the upper 95% confidence limit of the distribution of differences expected by chance.
Projection matrices constructions and demographic analysis were conducted using the βpopbioβ package R 2.4.2 (Stubben et al. 2016) written for the free software package R (Core Team 2015).
27 Results
Of the nine estimates of lambda, all but two indicate these populations are projected to decline (Figure 6). For all three populations the deterministic projection with the largest estimate was the Adults only projection, which excluded data for non-flowering plants (Figure 6).
Do projections based on data excluding non-flowering plants produce greater estimates of lambda than projections from a combination of all data available?
The Ξ» from a deterministic projection excluding randomly marked non-flowering plants was greater than Ξ» from a deterministic projection including data from all life stages in Bay County (2.78%), and Franklin County (8.06%), these differences were statistically significant at both populations (Figure 7). In Franklin County, not including data from non-flowering plants could lead to a false signal of recovery because excluding non-flowering plants produced Ξ» estimates greater than one. For the Gulf County population, projections excluding randomly marked plants generated Ξ» values 0.12% greater than Ξ» values generated from projections including data from all life stages.
How much lower are stochastic projections than deterministic projections that combine all data?
As expected, the Ξ» from a deterministic projection using all data was consistently greater than Ξ» from a stochastic projection using all data, and all were less than one. The magnitude of the difference in Franklin was (0.36%), Bay (1.5%), and Gulf (3.1%). In Gulf County only, the deterministic Ξ» was significantly greater than the stochastic Ξ» (Figure 8).
28
Figure 6: Population growth rates (Lambda) represented as open dots and bootstrapped 95% confidence intervals for each projection of Ξ» in all three populations. Adults only projection excludes data from randomly marked non-flowering individuals.
29
Figure 7: Observed differences in lambda estimates of all data projection minus adults only projection. Adults only projection excludes data from randomly marked non-flowering individuals. Circles represent observed differences in lambda and whiskers represent 95% confidence intervals of lambda differences by chance.
Figure 8: Observed differences in lambda estimates of all data deterministic projection minus all data stochastic projection. Circles represent observed differences in lambda and whiskers represent 95% confidence intervals of lambda differences by chance.
30 Discussion
All three populations are projected to decline based on deterministic and stochastic projections using a combination of all data available (Figure 6).Using samples of mature individuals "only" meaning non-flowering plants were excluded to parameterize the demographic model (Adults only projection) produced greater estimates of lambda in all populations compared to the other two projections (Figure 6). Combining all data in a deterministic projection was not significantly different from a stochastic projection in Bay and Franklin counties (Figure 8). However, for Gulf County stochastic lambda (Ξ» = 0.9629) was significantly lower than deterministic lambda (Ξ» = 0.9937). Excluding demographic information from individuals at one stage can lead to inaccurate estimates of population growth rates, such as determining that the population has lower expected decline because of the exclusion of smaller non-flowering plants would overestimate survival probabilities. Incorporating environmental variation in vital rates by combining demographic information for multiple years appeared to produce similar estimates of population growth rate as a stochastic projection.
I aimed to determine the consequences of only using serendipitously available information to calculate population growth for an at risk species. The longest data set available for this species only included information from adult individuals, which normally are prioritized in conservation projects because contribute most obviously to population growth. In addition, mature individuals are often easier to identify and detect than immature individuals. The advantage of this particular dataset (Reproductive study) is that it comes from marked individuals, which made possible the use of a structured model. I expected that population growth rates based on adult plants only would result in greater estimates of lambda than projections using all data because established adults had 100% survival from 2011 to 2016 but in randomly marked plants most individuals were non-flowering and survival was less than 100% for these individuals. Projections that excluded data from randomly marked individuals were greater than deterministic projection including all data available in all three populations (Figure 6) and significantly larger in Bay and Franklin counties (Figure 7). These results accentuate the need to incorporate data for all life stages because overestimating lambda might fail to identify a population at risk. The collection of sufficient data to parameterize a demographic model should 31 be included in recovery plans (Schaffer et al. 2002), because the continuous monitoring of mature individuals only is likely to lead to significant overestimation of lambda (Figure 7).
Stochastic projections are preferred to answer conservation questions because deterministic projections assume that all vital rates remain approximately constant through time, which is not realistic considering environmental variation can affect vital rates (TorΓ€ng et al. 2010, Schafer et al. 2010). Stochastic projections were lower than deterministic projections as expected. In Bay County and Franklin County the stochastic projections were modestly lower from 1.5% and 0.36 % respectively, and the deterministic projections using all the data were not significantly different (Figure 8), possibly because combining data from different years in a deterministic projection captured variation in the same way as the stochastic projection. Another study comparing demographic information of 50 perennial plants, compared another method of incorporating annual variation determined that an average matrix of vital rates, mean matrix lambda, was a good predictor of stochastic lambda, particularly for species with small matrix dimensions (Buckley et al. 2010). In Gulf County, Ξ» from deterministic projections were significantly greater than stochastic projections, and close to one, which could have led to the conclusion that this population is close to stability (Figure 6 and Figure 8).
Most projections indicated that these populations are declining, although some long-lived species could appear to be declining but remain stable due to transient events, population growth produced by deviance from stable stage structure (Mcdonald et al. 2016). For example, saguaro cactus populations were projected to decline, and mortality rates remained constant, but due to episodes of mass recruitment this species persisted after 85 years (Pierson and Turner 1998). It has been suggested that non-stationary environmental variation, such as changes caused by alteration of land use, could lead to dominance by transient dynamics, and therefore the evaluation of how variance in population structure affects transition probabilities would be more accurate than estimating asymptotic lambda (Koons et al. 2016).
Despite the limitation on the accuracy of forecasting the future size of a population, deterministic projections allow some evaluation of current status of a population, and identify which information is needed to improve the accuracy of estimates of lambda, which is essential
32 to conservation management. From these projection comparisons, I can conclude that parameterizing a projection with data from adults only could lead to overestimates of lambda. I suggest that increasing measures from non-flowering or immature individuals, would improve the estimates of lambda for Euphorbia telephioides because previous elasticity analysis showed that lambda is most sensitive to transitions from that stage (Figure 5). Combining measures of multiple years of adults and randomly marked plants as independent measures is not ideal, but it allowed the comparisons of different approaches and its consequences for estimating population growth rates.
It has been suggested that comparing different projections using long term data from studies designed to parameterize demographic models could allow the understanding the utility and limitations of these estimates for the conservation of endangered and threatened plants (Schaffer et al. 2002). Long term demographic studies would have sufficient data to disentangle environmental variation which is the main driver of stochasticity in plant populations (Crone et al. 2011). For example, in a study comparing different methods to estimate stochastic population growth rate using different number of matrices, it was determine that having only three matrices available to estimate vital rates correlation lead to distorted estimates of lambda (Ramula and LehtilΓ€ 2005). Measuring changes in the demography of threatened species over a long period would help to determine if projections of lambda using a subsample of a few years did predict the population growth observed in the field. From these comparisons, we can conclude that it is necessary to include demographic information from individuals at each stage, because a sample of adult individuals only can lead to overestimates of lambda.
33 CHAPTER 4 POLLEN LIMITATION AND ITS CONSEQUENCES FOR DEMOGRAPHY IN A THREATENED DIOECIOUS PERENNIAL PLANT
Introduction
The effective conservation of vulnerable plants requires an understanding of population dynamics and the evaluation of factors that could reduce population growth. Pollen limitation, which refers to the receipt of insufficient quality or quantity of pollen for reproduction (Ashman et al. 2004, Knight et al. 2005), has been found to be common in flowering plants (Burd 1994) and could have demographic consequences. Nevertheless, only a few studies have quantified the effects of pollen limitation on population growth rates and these have reported different results (Ramula et al. 2007, Price et al. 2008, Lundgren et al. 2015). For example, in a pollen limited herbaceous perennial, the addition of pollen significantly increased the projected population growth rates when compared to the projected population growth rates of the control plants (Law et al. 2010). However, in another pollen limited perennial plant, the projected population growth rate based on pollen supplemented plants did not exceed the rate of population growth projected for control plants (EhrlΓ©n and Eriksson 1995). Nevertheless, estimating pollen limitation in threatened and endangered plants is important because the expected lower number of seed produced in pollen-limited plants would decrease fecundity and consequently the population growth rate.
Some features have been identified as increasing the likelihood of pollen limitation such as self-incompatibility, the use of biotic vectors for pollination, inconspicuous flowers, and habitat fragmentation (Knight et al. 2005). Dioecious species, where pistillate (female) and staminate (male) flowers are produced on different plants, are prone to pollen limitation because besides being incapable of selfing, female plants might not flower as often as male plants due to the expected greater cost of reproduction in female plants (Geber et al. 1999, Obeso 2002), 34 greater number of male flowers could increase pollinator preference to male plants reducing male to female visits (Charlesworth 1993). Distance between male and female plants might also affect pollen limitation due to pollinator behavior (de Jong et al. 2005). Female plants of Silene latifolia had lower seed production when planted at more than four meters distance from compatible pollen source (Anderson et al. 2015). A study that quantified fruit and seed set and its relation to the number of male plants in Lobelia cardinalis, a short-lived perennial, found an increased average seed set in plants surrounded by a greater density of male plants (Bartkowska and Johnston 2014).
In most dioecious plants, male plants flower earlier than female plants (Forrest 2014), which could result in increased probabilities of pollen limitation if there are fewer male flowers available when female plants are receptive or if pollinators learn to prefer male plants. An empirical study showed that fruit set was not dependent of the timing of flowering initiation in female plants but it was dependent on the date in the middle of the start and the end of flowering, resulting in greater fruit set when male and female plants presented their maximum number of inflorescences (Abe 2001). Further, flowering timing might influence how many species of pollinators a plant relies on, for example synchronous mass flowering might attract a diverse community of generalist pollinators that donβt travel as much from plant to plant (Ghazoul 2005).
Plants occurring in fragmented habitats are at a greater risk of pollen limitation when compared to plants distributed in continuous landscape because habitat fragmentation reduces population size (Knight et al. 2005, Aguilar et al. 2006, Dauber et al. 2010). In small populations stochasticity can overcome other processes expected to regulate population dynamics in larger populations (Lande 1988), which could result in increased likelihood of pollen limitation in dioecious plants if stochasticity led to female biased sex ratio (Bartkowska and Johnston 2014). Also, smaller populations of nectariferous plants are less attractive to pollinators and receive less pollen for reproduction than larger populations (Γ gren 1996). Further, habitat fragmentation might change the composition of biotic vectors for pollination, and increase the distance pollinators need to travel from plant to plant (Knight et al. 2005). Pollinator composition is important because plants pollinated by specialist pollinators have greater probabilities of
35 receiving enough pollen for reproduction than plants that rely on generalist pollinators (Ghazoul 2005).
I tested for pollen limitation in three populations of the threatened dioecious perennial plant Euphorbia telephioides and evaluated the consequences of pollen limitation for the projected growth rates of these populations. The evaluation of pollen limitation in this species is particularly important because is threatened, it is likely to be pollen limited because is dioecious, relies on biotic vectors for pollination, bears a small number of inconspicuous flowers, and occurs in recently fragmented habitats. Particularly, I examined 1) Is seed or fruit set pollen limited at each population?, 2) Does the magnitude of pollen limitation increase if male and female plants differ in the date of flower initiation?, 3) Is fruit or seed set greater in female plants surrounded by more male plants?, and 4) What are the consequences of pollen limitation for the population growth rate?
Methods
Species description
Euphorbia telephioides is a dioecious herbaceous perennial federally listed as threatened. This species is endemic to coastal Bay, Franklin, and Gulf counties occurring in xeric, scrubby pine flatwoods (Bridges and Orzell 2002). A genetic study of 17 populations suggested the distribution of this species was continuous in the past but has become recently fragmented based on the low genetic differentiation among populations and the high overall levels of genetic variation (Trapnell et al. 2012). Euphorbia telephioides populations are predominantly threatened by coastal development, timbering and fire suppression (U.S. Fish and Wildlife Service 2009), all of which could contribute to reduced population size and habitat fragmentation.
Reproductive plants produce branched inflorescences where specialized inflorescences called cyathia (Figure 9, A) are arranged as a compound cyme. Cyathia in Euphorbia
36 telephioides are 1 to 2mm in diameter, have a purple involucre or flower envelope with five attached glands that produce nectar (Bridges and Orzell 2002). The female cyathium consists of one flower with three fused carpels producing one ovule per locule. This female cyathium remains receptive for approximately seven days (personal observation). The male cyathium is formed by multiple male flowers, each consisting of a stamen and a pedicel, arranged in a cyme inside the involucre. Each male cyathium disperses pollen for approximately 15 days (personal observation). After fertilization, female plants produce fruits that can produce a maximum of three seeds (Figure 9, B). Mature fruits have explosive dispersal (Figure 9, C), and viable seeds can be easily identified due to their dark seed coat and ability to maintain their shape after a gentle pinch (Figure 9, D).
A B
C
D
Figure 9: Euphorbia telephioides female plants and seed. Pollinator (A), mature fruits with three locules (B), fruits after seed dispersal (C) and (D) mature viable seeds.
37 Study area
I conducted a test for pollen limitation in two protected populations of E. telephioides in coastal Franklin and Gulf County. The Franklin population is located at Box-R Wildlife Management Area in Franklin County, and is managed by the Florida Fish and Wildlife Conservation Commission (FWC). The second population, located at the St. Joseph Bay Buffer Preserve in Gulf County, is managed by the Department of Environmental Protection (DEP). I intended to test for pollen limitation at an additional population in Bay County at Breakfast Point Mitigation Bank, but only two female plants flowered in the population in spring 2015.
Stage-structured demographic models parameterized with field data predict that all three populations are projected to decline, with Lambda ranging from 0.929 to 0.988 (Chapter 2). Bootstrapped 95% confidence intervals for population growth did not include one in any of the three populations.
Pollen supplementation experiments
To test for pollen limitation of seed and fruit production, I compared the fruit and seed set of plants for which I hand pollinated all open flowers with a group of unmanipulated control plants. A total of 38 female plants in Franklin County, and 51 in Gulf County were marked with pink flags and an aluminum tag. Marked plants were assigned at random to either control or pollen supplementation treatments and were checked for open flowers at least once a week from the last week of March to Mid-July of 2015.
All the open cyathia of a supplemented plant were hand pollinated once with two different pollen donors from the same population. Anthers were collected haphazardly from available pollen donors within each population. The total number of cyathia, open cyathia, and number of fruits was recorded each week for each female marked plant. Female cyathia were considered open if the style was elongated and the stigma was visible.
38 Mature fruits were enclosed in bridal veil bags to prevent seed dispersal prior to determination of seed number per fruit. I scored the total number of viable seeds of every fruit collected per treatment and viable seeds were dispersed in situ immediately after counting.
To determine if there is pollen limitation of fruit set, I compared the fruit set of pollen supplemented plants and unmanipulated control plants using the Wilcoxon rank test. I used the non-parametric test because fruit set, did not fit any known distribution from the exponential family even after transformation.
I also used the Wilcoxon rank test to compare the average number of viable seeds produced per fruit for each treatment, to determine if there is pollen limitation at the level of seeds per fruit. Each fruit was treated as an independent unit, for this analysis because of the small sample size of fruits from which seeds were counted (18 fruits for Franklin County, and 43 fruits for Gulf County).
Effects of flowering initiation on pollen limitation
To determine if the time of flowering initiation affects pollen limitation, I recorded the date when the first flower was observed for each female marked plant using the Julian calendar. I also marked 57 male plants in Franklin County and 69 male plants in Gulf County to determine if female and male plants differ in the date of flowering initiation. For each male plant, I recorded the Julian date of flower initiation, the number of cyathia open, and the total number of cyathia present each week from the last week of March to mid-July. Male cyathia were considered open if at least one anther was observed. I tested whether male and female plants had the same average date of flowering initiation using a generalized linear model (GLM) with a gamma distribution.
39 Effects of local pollen limitation
In addition to the pollen supplementation experiments I evaluated whether the number of nearby male plants and total number of open male cyathia influences fruit and seed set of female control plants at two spatial scales: within one and five meter radius circles centered on each female control plant. The spatial scale was chosen arbitrarily because there was no information on which species pollinates E. telephioides. To determine if control plants produced more fruit per flower when surrounded by more male plants or more male open cyathia, I recorded how many male plants occurred within one and five meters radius of each control female plant and how many male open cyathia were observed every week from March to mid-July at each spatial scale. I used a beta regression to determine if fruit set was dependent on the number of male plants or number of total open male cyathia around the female control plants at each spatial scale. Fruit set was calculated for a total of 20 female plants in Franklin, and 22 female plants in Gulf. I increased fruit set values of zero to 0.001 and reduced fruit sets of 1 to 0.999 to run the beta regression.
In an effort to identify pollinators for E. telephioides I set video cameras at 50 cm from focal female plants with open cyathia at each site starting at 11 AM. I recorded video for three hours in Franklin County, 3.5 hours in Gulf County, and two hours in Bay County. I used the Vegas Movie Studio HD 11.0 software to examine the video recordings.
All analyses were conducted using R version 3.2.1 (Core Team 2015). To help determine the distributions of dependent variables, I used the R-package fitdistrplus and function descdist (Marie et al. 2015). The function descdist plots the data distribution as points in a plot where other known distributions are plotted using the estimations of skewness and Pearsonβs kurtosis values to determine the type of distribution consistent with these values (Marie et al. 2015). I used the package betareg to carry out beta regressions (Cribari-Neto and Zeileis 2009). The stats package for R was also used, to test for normality (shapiro.test) and for homogeneity of variance (Bartlett.test).
40 Simulating the consequences of increased levels of pollen limitation for population growth
I used a deterministic stage-structured demographic model parameterized with data from the same populations in which I tested for pollen limitation (described in chapter 2) to simulate the effect of pollen limitation on projected population growth rate. To determine the consequences of different levels of pollen limitation, I calculated population growth rates using the deterministic projection combining all available data (βAll data deterministic projectionβ) after reducing the fertility in the models by 20, 40, 60, and 80% for each population to simulate the effects of pollen limitation on seed production. I calculated 95% confidence intervals for the growth rate from each simulation by resampling 10000 times with replacement for the same number of plants that were used to estimate the demographic parameters. I calculated the percentage of decline of Lambda at 80% of pollen limitation to describe how much strong pollen limitation could affect population growth.
The model construction and demographic analysis were conducted using the βpopbioβ package R 2.4.2 (Stubben and Milligan, 2007) written for the free software package R (Core Team 2015).
Results
Of the 38 female plants marked in Franklin County, one plant went missing, another was eliminated because the flowers were consumed by herbivores, and two were excluded because after producing female cyathia, they also produced some male cyathia. These hermaphroditic plants were eliminated from the analysis because it is not known if their female cyathia are less fertile than cyathia in female plants. Consequently, 20 plants comprised the control treatment and 14 plants remained in the pollen supplementation treatment. The number of cyathia produced per female plant in Franklin ranged from 1 to 16 with a mean of 4.5 for the control and 6.21 for the pollen-supplemented plants. The average fruit set in the pollen-supplemented plants was 0.62 fruits per plant. For control plants, the average fruit set per plant was 0.53. The numbers of fruits
41 produced per flower for control (open pollination) and pollen supplemented plants in Franklin were not statistically different (Wilcoxon rank test, W = 117.5; P = 0.43, Figure 10).
Figure 10: Distribution of mean number of fruits per flower and mean viable seeds per fruit produced for control (open pollination) and pollen supplemented plants in Franklin County in May 2015. Boxes represent the interquartile distribution, the bold lines in boxes represent the medians, and whiskers show the maximum and minimum values.
Approximately 50 mature fruits were bagged in Franklin but only 18 fruits were included in the analysis of number of viable seeds per fruit because the majority of bags did not hold seeds after fruit dispersal due to human error, weather conditions, or herbivores. Five fruits of four plants in the control treatment were compared to 13 fruits of eight plants in the pollen- supplemented treatment to evaluate if viable seed production per fruit was pollen limited. The average number of viable seeds per fruit was 1.6 for the control treatment and 1.82 for the pollen-supplemented fruits. There is no evidence for pollen limitation in the number of viable seeds per fruit produced in Franklin (Wilcoxon rank test, W = 28; P = 0.67, Figure 10).
42 In Franklin County, the median date of flowering initiation is seven days earlier for male plants than for female plants (GLM, t = 3.44, df = 90; P < 0.001, Figure 11).
Figure 11:Distributions of Julian date of flowering initiation for male (gray bars) and female (black bars) plants in Franklin County
In Gulf County, 51 female plants were marked, but three plants were consumed by herbivores leaving 25 plants in the control and 23 plants in the pollen supplemented treatment. Female plants produced one to 22 cyathia per plant. Control plants produced on average 5.2 cyathia and pollen-supplemented plants had 4 cyathia on average. The average fruit set in both the control plants and pollen-supplemented plants was 0.82. There is no evidence of pollen limitation in the fruit set of female plants at the Gulf population (Wilcoxon rank test, W = 284; P = 0.94, Figure 12).
43
Figure 12: Distribution of number of mean number of fruits and mean viable seed produced per fruit for control (open pollination) and pollen supplemented plants in Gulf County in May 2015. Boxes represent the interquartile distribution, the bold lines in boxes represent the medians, whiskers show the maximum and minimum values, and open points denote data points outside 1.5 times the lower interquartile range.
A hundred fruits were bagged in Gulf County, but losses due to human error, herbivores and weather conditions reduced the sample size to 43. I compared the average number of viable seeds per fruit treating each fruits as an independent unit for 27 fruits of eleven control plants and16 fruits of seven plants in the pollen supplementation treatment. The mean and the median viable seed per fruit were both 2.0 for the two treatments (Figure 12). There is no evidence for pollen limitation in the number of viable seeds per fruit produced in Gulf (Wilcoxon rank test, W = 205; P = 0.78).
In Gulf County the median date of flowering initiation was the same for both genders. However, male plants initiated flowering significantly earlier than female plants (GLM, t = 4.05, df = 117, P < 0.001, Figure 13).
44
Figure 13: Distributions of Julian date of flowering initiation for male (gray bars) and female (black bars) plants in Gulf County.
Effects of local pollen limitation
In Franklin County, a range of 0 to 3 male plants, with 0 to 15 open male cyathia were recorded within one meter of 20 female control plants. Fruit set was independent of the number of male plants (Beta regression z value = 0.67, df = 3, R2 = 0.03, P = 0.51) and the number of male open cyathia (Beta regression z value = 0.06, df = 3, R2 = 0.006, P = 0.74) within a one- meter radius centered at each female control plant. The number of male plants present within five meters ranged from 1 to 15 and the number of male open cyathia varied from 4 to 69. At a five- meter radius, fruit set was also independent of the number of male plants (Beta regression z value = 0.64, df = 3, R2 = 0.02, P = 0.52) and the number of male open cyathia (Beta regression z value = 0.57, df = 3, R2 = 0.02, P = 0.57).
45 In Gulf County, there were 0 to 5 male plants within one meter of 22 control females, with 0 to 132 open male cyathia. Fruit set increased with the number of male plants present (Beta regression z value = 1.97, df = 3, R2 = 0.298, P = 0.049), but did not depend on the number of male open cyathia (Beta regression z value = 1.29, df = 3, R2 = 0.145, P = 0.197). At five meters, there were 1 to 17 male plants with 11 to 274 open cyathia. Fruit set was independent of the number of male plants (Beta regression z value = 1.4, df = 3, R2 = 0.12, P = 0.16) and total number of open male cyathia (Beta regression z value = -0.38, df = 3, R2 = 0.01, P = 0.70) within a five-meter radius.
Video recording in Franklin County did not detect any visitors to cyathia. In Gulf County, a female plant with three open cyathia and a developing fruit was visited. A bee (Figure 9) was recorded visiting this focal plant five times at 15 to 30 minutes intervals, visiting each open female cyathium. Each visit lasted approximately 3 to 5 minutes. The bee could not be identified from the video recording, however, another bee was collected at the same location the following week and identified as Colletes sp. At Bay County, two small flies were observed visiting a plant but they did not contact the stigmas.
Simulating the consequences of increased levels of pollen limitation on population growth
All three populations are projected to decline under current conditions according to a deterministic projection using all data available from 2010 to 2016, assuming vital rates remain constant and there is no pollen limitation (Chapter 2). After simulating increased levels of pollen limitation by reducing seed set, population growth rate decreased 1.91% in Franklin County (Figure 14), and 0.17% in Gulf County (Figure 15) at the highest level of pollen limitation simulated (80% reduction in seed set). In Bay County, population growth rate declined 1.11% at 80% reduction of seed set (Figure 16). The confidence intervals for each projection at increased levels of pollen limitation include the estimate for lambda without pollen limitation.
46
Figure 14: Projected population growth rates and bootstrapped 95% confidence intervals for population with zero to 80% simulated pollen limitation in Franklin County.
Figure 15: Projected population growth rates and bootstrapped 95% confidence intervals for population with zero to 80% simulated pollen limitation in Gulf County.
47
Figure 16: Projected population growth rates and bootstrapped 95% confidence intervals for population with zero to 80% simulated pollen limitation in Bay County.
Discussion
Pollen supplementation experiments in Franklin and Gulf County indicated that fruit and seed production were not pollen limited in 2015; there was not a significant difference in the mean number of fruits per flower or viable seeds per fruit in control and pollen supplemented plants (Figure 10 and Figure 12). These results are unexpected considering that E. telephioides, is dioecious, relies on biotic vectors for pollination, occurs in recently fragmented habitats, and produces inconspicuous cyathia, all of which make it prone to pollen limitation (Knight et al. 2005). Although I did not detect significant pollen limitation in this one flowering season, simulating pollen limitation by reducing fecundity estimates by 80% at each population decreased Lambda by 1.91% in Franklin County, 0.17% in Gulf County and 1.11% in Bay County. These simulations suggest that, if it did occur pollen limitation would speed the rate of decline of these populations but at a modest rate. These small effects are consistent with the low elasticity values observed for fecundity in demographic projections (Chapter 2; Figure 5).
48 I did not find evidence of pollen limitation of number of fruits or viable seeds in E. telephioides despite many features that made them prone to pollen limitation. The lack of evidence of insufficient quantity or quality of pollen could reflect variation among years, if 2015 was particularly good for pollinators. Also, E. telephioides has features that could counter the risk of pollen limitation such as, long duration for pollen receptivity in female cyathia (Abe 2001, Ghazoul 2005), synchrony of flowering timing in male and female plants (Abe 2001), and nectar production (Larson and Barrett 2000). I observed that female and male plants produce nectar at midday (Figure 9), and female cyathia remain receptive approximately seven days, which can allow for multiple pollinator visits, increasing their chances for fertilization.
To determine if seed set was pollen limited, I assumed that seed set of fruits were independent of each other which inflated the degrees of freedom in the comparisons of seed set for supplemented and control treatments. Although this could have made it more likely to detect pollen limitation, I did not find any evidence for it. It is possible that seed production could be resource limited instead of pollen limited. In resource limited plants the production of seeds is not dependent on quantity of pollen received (Zimmerman and Pyke 1988). For example, in an empirical study, increasing resource availability such as light by pruning vegetation near focal plants of Geranium maculatum, a perennial herb, increased fruit set significantly compared to the previous two years fruit set (Mccall and Primack 1987).
The population in which male plants flowered significantly earlier than female plants exhibited greater increase in fruit set after pollen addition. Pollen supplemented plants in Franklin County did have a greater median number of fruit per flower and viable seed per fruit than control plants (Figure 10), although these differences were not statistically significant. This trend could be explained by the difference in the flowering initiation date, where female plants that flower later might co-flower with fewer male plants (Figure 11), which could explain why the addition of pollen increased fruit and seed production slightly. In Gulf County, the median flowering initiation was the same for male and female plants (Figure 13), and there were no differences in fruit and set in pollen supplemented plants and control plants for this population. In addition, Gulf County had greater fruit and seed set than Franklin County, which suggest that flowering timing is important for reproduction, and agrees with an empirical study that found
49 that fruit set was greater when the overlap in male and female flowering timing was larger (Abe 2001).
In Franklin County, fruit set of focal female plants did not depend on the number of male plants or cyathia present within a one meter or five meter radius, however in Gulf County at one meter, the fruit set increased with the number of male plants present (Beta regression z value = 1.97, df = 3, R2 = 0.298, P = 0.049), which suggest there might be pollen limitation at Gulf county at this smaller scale. There were more male plants and open cyathia in Gulf County compared to Franklin County at both spatial scales. The lower quantity of male plants around female plants at both scales might explain why Franklin County had lower fruit and seed set when compared to Gulf County. These results are similar to an empirical study in four insect- pollinated dioecious species that found increased average seed set in pollen supplemented plants located furthest from male plants (de Jong et al. 2005).
Viable seed production in control plants ranged from zero to three, with a median value below the maximum of three for both populations, which suggest there might be a reason other than pollen limitation why plants are not producing the maximum of number of seeds, such as herbivory, resource limitation (Snow and Whigham 1989, Ackerman and Montalvo 1990, Calvo 1990), or biparental inbreeding depression. For example, herbivory caused greater decline in the fecundity of a long-lived herb than did pollen limitation (Knight 2004). Resource limitation in fruit and seed set is common in flowering plants and can have greater effects than pollen limitation in some species (Wesselingh 2007). Small populations of self-incompatible plants can experience lower seed set due to biparental inbreeding depression (Ellstrand and Elam 1993).
In Bay County, I could not test for pollen limitation because only two female plants flowered compared to more than 20 male plants. This skewed sex ratio supports the importance of simulating effects of pollen limitation in small populations because just by chance sex ratio could also be strongly female biased, which would promote pollen limitation. There is evidence of sex ratio variation in dioecious plants that could led to increased levels of pollen limitation when male plants are rare (Field et al. 2013).
50 Simulating an increase in the levels of pollen limitation decreased the projected rate of population growth in all populations of E. telephioides as expected, but by a small proportion. Franklin County had a greater percentage of decline (Figure 14; Figure 15 and Figure 16). In Gulf County, increasing pollen limitation to 80% reduced population growth rate by 0.17%. These small changes in population growth rate at each site could be explained by their already low fecundity and the expected low elasticity in fecundity for long-lived perennial plants (Franco and Silvertown 2004). Also, if fruit and seed production are resource limited rather than pollen limited, population growth rate would not be affected by varying degrees of pollen limitation. For example, a study in a herbaceous perennial legume did not find a difference in the population growth rates parameterized from pollen supplemented plants and control plants, because the increased seed set in pollen supplemented plants reduced its growth and flowering frequency in the subsequent year, which would suggested that Lambda was not pollen limited but resource limited (EhrlΓ©n and Eriksson 1995).
Despite finding at best modest evidence of pollen limitation in these populations, I recommend the continuous evaluation of pollen limitation in these populations because they are projected to decline even without accounting for stochastic fluctuations. In small populations, stochasticity can overcome other process that determine sex ratio which can result in female biased populations, which would be at an increased risk of pollen limitation. Besides the reevaluation of pollen limitation in these populations, I proposed to examine the possibility of resource limitation and biparental inbreeding to account for the lower than maximum number of seeds produced.
51 CHAPTER 5 CONCLUSION
Three protected populations of Euphorbia telephioides are projected to decline (Table 4). Incorporating variation in the vital rates produced lower estimates of lambda than projections that assumed vital rates were constant (Figure 6). Parameterizing a demographic model using measures of fate and stage from seedlings and mature individuals, which is often the only information available, produced greater estimates of lambda than projections that also incorporated data from immature individuals (Figure 6). The incorporation of measures of stage and fate from individuals at each stage of the life cycle is necessary because overestimating lambda could lead to erroneously conclude that those populations would persist without management actions.
I did not find evidence of pollen limitation in two populations (Figure 10 and Figure 12), however in Gulf County there is evidence of pollen limitation at a small scale (1m), fruit set increased when greater number of male plants were present. Increasing pollen limitation by reducing seed set at 80% reduced population growth rates but at a modest rate from 0.17% to 1.91%. These findings are not surprising considering the low elasticity values for fecundity in this species (Figure 5). Pollen limitation does not appear to contribute to the decline in these populations, other factors should be examined such as how prescribed fire affects vital rate variation, and particularly how fire frequency affect the stasis of non-flowering plants because that vital rate had the greatest elasticity values in all three populations (Figure 5). In addition, determining if resource limitation can cause lower production of viable seeds would be important for the persistence of this species.
The continuous survey of marked individuals of Euphorbia telephioides would improve the accuracy in the estimates of lambda for these populations, as well as could allow for further evaluation of quantitative methods to assess the recovery of at risk species.
52 APPENDIX A SUPPLEMENTARY INFORMATION
Table 6: Comparisons of female and male stem growth in centimeters from 2011 to 2016 at each population
Female Male Degrees t-test average average T - of P - Population Year (cm) (cm) value freedom value Bay 2010 to 2011 -2.24 -0.3 -0.62 29 0.54 Bay 2011 to 2012 -3.08 -5.65 0.85 27 0.4 Bay 2012 to 2013 3.47 6.1 -0.85 27 0.4 Bay 2013 to 2014 -2.69 -4.17 0.72 25 0.48 Bay 2014 to 2015 3 2.49 0.37 45 0.71 Bay 2015 to 2016 -1.32 0.25 -0.35 20 0.73 Gulf 2010 to 2011 -2.36 -0.68 -0.11 14 0.91 Gulf 2011 to 2012 -2.9 -1.98 -0.54 33 0.6 Gulf 2012 to 2013 -0.24 -0.49 0.15 37 0.88 Gulf 2013 to 2014 -4.33 -5.06 0.38 34 0.71 Gulf 2014 to 2015 4.57 5.01 -0.3 42 0.77 Gulf 2015 to 2016 -0.61 -1.34 0.31 31 0.76 Franklin 2010 to 2011 -4.3 2.79 -0.43 38 0.67 Franklin 2011 to 2012 0.8 -0.52 0.77 34 0.44 Franklin 2012 to 2013 -0.46 -3.46 2.25 35 0.03 Franklin 2013 to 2014 -4.98 -4.05 -0.72 26 0.47 Franklin 2014 to 2015 5.68 2.02 1.93 28 0.06 Franklin 2015 to 2016 -1.02 -1.86 0.39 16 0.71
Table 7: Comparisons of the average number of flowers produced in female and male plants from 2011 to 2016 at each population. There were not enough samples to conduct the comparisons in Bay and Franklin counties for 2015. I used the log transformation to comply with the t-test assumptions when pertinent.
Degrees Female Male of t-test P - Population Year average average T value freedom value Bay 2010 3.88 11.33 -1.82 18 0.09 53 Table 7 - continued
Degrees Female Male of t-test P - Population Year average average T value freedom value Bay 2010 3.88 11.33 -1.82 18 0.09 Bay 2011 5.2 12 -1.75 22 0.09 Bay 2012 9.4 37 -2.8 27 0.0093 Bay 2013 3.68 25 -5.54 24 1.07E-05 Bay 2014 10.52 27.25 -1.022 23 0.32 Gulf 2010 5.86 11.9 -1.42 30 0.16 Gulf 2011 5.43 35.5 -2.93 29 0.0065 Gulf 2012 5.95 9.33 -1.12 29 0.27 Gulf 2013 5.67 15.2 -0.75 29 0.46 Gulf 2014 9.74 16.58 -0.43 33 0.67 Gulf 2015 5.13 13.25 -2.02 10 0.07 Gulf 2016 4.25 10 -1.14 10 0.07 Franklin 2010 5.22 11.77 -1.93 29 0.06 Franklin 2011 5.78 14 -3.12 30 0.003961 Franklin 2012 4.33 17.61 -6.25 35 3.62E-07 Franklin 2013 3.17 8.36 -2.11 21 0.04677 Franklin 2014 4.73 12 -2.32 26 0.03 Franklin 2016 3.29 6.67 -2.27 11 0.04
Table 8: All deterministic transition matrices for three populations of E. telephioides.
0 0 0 0.18 0 0 0 0.03 0.53 0.87 0.32 0.53 0.93 0.39 0.71 0.86 0.03 0.19 0.02 0.12 0.03 0.08 0.03 0.03 π΅π΅ππππ οΏ½ 0 0.07 0.11 0.55οΏ½ πΊπΊππππππ οΏ½ 0 0.05 0.04 0.58οΏ½ 0 0 0 0.33 0.53 0.85 0.44 0.61 0.03 0.24 0.03 0.11 πΉπΉπππππππΉπΉππππππ οΏ½ 0 0.07 0.12 0.41οΏ½
54 Table 9: Transition matrices for Bay County.
0 0 0 0.41 0.53 0.75 0.1 2011 2012 0.7 0.03 0.06 0 0.05 π΅π΅ππππ π‘π‘ππ οΏ½ 0 0.16 0.25 0.85οΏ½ 0 0 0 0.21 0.53 1 0.38 2012 2013 0.82 0.03 0.04 0 0.12 π΅π΅ππππ π‘π‘ππ οΏ½ 0 0.04 0 0.5 οΏ½ 0 0 0 0.42 0.53 0.25 0.53 2013 2014 0.83 0.03 0.09 0.25 0.13 π΅π΅ππππ π‘π‘ππ οΏ½ 0 0 0.05 0.3 οΏ½ 0 0 0 0.01 0.53 0.89 0.19 2014 2015 0.74 0.03 0.08 0.02 0.1 π΅π΅ππππ π‘π‘ππ οΏ½ 0 0.08 0.09 0.67οΏ½ 0 0 0 0.05 0.53 0.87 0.38 2015 2016 0.63 0.03 0.34 0 0.17 π΅π΅ππππ π‘π‘ππ οΏ½ 0 0.03 0.1 0.45οΏ½
Table 10: Transition matrices for Gulf County.
0 0 0 0.06 0.53 0.85 0.28 2011 2012 0.78 0.03 0.12 0 0.06 πΊπΊππππππ π‘π‘ππ οΏ½ 0 0.02 0.14 0.67οΏ½ 0 0 0 0 0.53 0.83 0.29 2012 2013 0.72 0.03 0.04 0.17 0 πΊπΊππππππ π‘π‘ππ οΏ½ 0 0.17 0 0.71οΏ½ 0 0 0 0.02 0.53 1 0.44 2013 2014 0.7 0.03 0.1 0 0.05 πΊπΊππππππ π‘π‘ππ οΏ½ 0 0.12 0 0.5 οΏ½
55 Table10 β continued
0 0 0 0.02 0.53 0.95 0.31 2014 2015 0.88 0.03 0.05 0.02 0.03 πΊπΊππππππ π‘π‘ππ οΏ½ 0 0.05 0.03 0.66οΏ½ 0 0 0 0.05 0.53 0.86 0.55 2015 2016 0.89 0.03 0.1 0.07 0 πΊπΊππππππ π‘π‘ππ οΏ½ 0 0.01 0.07 0.45οΏ½
Table 11: Transition matrices for Franklin County
0 0 0 0.86 0.53 0.67 0.28 2011 2012 0.68 0.03 0.1 0 0.03 πΉπΉπππππππΉπΉππππππ π‘π‘ππ οΏ½ 0 0.12 0.33 0.69οΏ½ 0 0 0 0.19 0.53 1 0.54 2012 2013 0.63 0.03 0.09 0 0 πΉπΉπππππππΉπΉππππππ π‘π‘ππ οΏ½ 0 0.18 0 0.46οΏ½ 0 0 0 0.29 0.53 1 0.5 2013 2014 0.75 0.03 0.16 0 0.3 πΉπΉπππππππΉπΉππππππ π‘π‘ππ οΏ½ 0 0.02 0 0.2 οΏ½ 0 0 0 0.09 0.53 0.91 0.5 2014 2015 0.64 0.03 0.17 0 0.23 πΉπΉπππππππΉπΉππππππ π‘π‘ππ οΏ½ 0 0.03 0.09 0.23οΏ½ 0 0 0 0.03 0.53 0.83 0.41 2015 2016 0.57 0.03 0.37 0.05 0.24 πΉπΉπππππππΉπΉππππππ π‘π‘ππ οΏ½ 0 0.06 0.13 0.35οΏ½
56 Table 12: Adults only transition matrices for three populations of E. telephioides constructed using data from mature plants collected during 2011 to 2016.
0 0 0 0.25 0 0 0 0.07 0.53 0.56 0.29 0.53 0.7 0.37 0.78 0.73 0.03 0.08 0.12 0.12 0.03 0.08 0.22 0.04 π΅π΅ππππ οΏ½ 0 0.11 0.28 0.59οΏ½ πΊπΊππππππ οΏ½ 0 0.17 0.09 0.59οΏ½ 0 0 0 0.42 0.53 0.54 0.44 0.61 0.03 0.19 0.17 0.12 πΉπΉπππππππΉπΉππππππ οΏ½ 0 0.17 0.29 0.44οΏ½
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63 BIOGRAPHICAL SKETCH
Natali Ramirez-Bullon was born on August 31, 1984 in Lima, Peru. She graduated with a B.S. in Biological Science from Universidad Nacional Agraria La Molina (UNALM) in 2007. During her undergraduate studies, she joined the research team of the Octavio Velarde NuΓ±ez Botanical Garden at UNALM, which resulted in the opportunity to conduct her undergraduate thesis in collaboration with the Royal Botanic Gardens KEW. She investigated methods of germination and the phenology of seven species of cactus. After graduation, she worked for conservation non-profit organizations, environmental consulting companies, and the federal government as a field plant biologist. In 2013 she joined the Winn Lab at Florida State University to increase her quantitative and analytical skills to become an expert in plant population ecology.
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