Habitat Quality, Competition and Recruitment Processes in Two Marine Gobies

Home , Elacatinus evelynae, Recruitment (biology)

HABITAT QUALITY, COMPETITION AND RECRUITMENT PROCESSES IN TWO MARINE GOBIES

JACQUELINE A. WILSON

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2004

Jacqueline A. Wilson

This work is dedicated to my father, Robert J. Wilson, and my husband, Brian R. Farber. Their love, support and encouragement kept me going and allowed me to finish.

ACKNOWLEDGMENTS

I would like to thank my advisor, C. Osenberg, for his insights, knowledge, contribution to my intellectual development, and endless guidance and editing of my dissertation. I must also acknowledge that the experimental design, analysis, and interpretation of this work were influenced by discussions with B. Bolker as well as the

St. Mary/Osenberg/Bolker labs. I am also grateful for logistical help at the University of

Florida from D. Julian, and for the work done in collaboration with L. Vigliola. I would like to thank entire dissertation committee, C. Osenberg, B. Bolker, R. Holt, C. St. Mary, and W. Lindberg (and L. McEdward, who was involved in the initial development of this work), for their knowledge, guidance, and helpful comments on my dissertation. I am also grateful to R. Warner for the use of his lab and field equipment in St. Croix. I would like to thank B. Farber for his assistance in the field and endless support throughout this project. I am particularly thankful to S. Savene, M. Kellogg and T. Adam for their tremendous help in the field. I am also grateful to my family and friends who made this work possible and for the support that I received in St. Croix from the Bidelspachers and members of the R. Warner, K. Clifton and J. Godwin labs. This work was supported by funding from an EPA STAR Fellowship, and grants from the PADI Foundation, Project

AWARE and Sigma Xi.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... iv

LIST OF TABLES...... viii

LIST OF FIGURES ...... x

ABSTRACT...... xii

CHAPTER

1 GENERAL INTRODUCTION ...... 1

Proposed Work ...... 9 Future Work...... 11

2 ASSESSMENT OF HABITAT QUALITY: DETERMINING PROCESSES THAT DRIVE SPATIAL VARIATION IN SURVIVAL AND SETTLEMENT OF TWO SPECIES OF MARINE GOBIES ...... 18

Introduction...... 18 Methods ...... 21 Experimental Procedures...... 21 Study species ...... 21 Experimental design...... 22 Experimental set-up 1: 2000 ...... 23 Experimental set-up 2: 2001 ...... 24 Experimental set-up 3, 4 & 5: 2002 ...... 25 Settlement surveys...... 26 Analyses ...... 27 Survival ...... 27 Covariation among settlement level and habitat quality ...... 28 Attributes of quality ...... 29 Results...... 31 Survival...... 31 Covariation Among Habitat Quality and Settlement...... 32 Attributes of Quality...... 32 Discussion...... 33

v 3 SETTLEMENT DYNAMICS AND COMPETITIVE ABILITY OF TWO SPECIES OF GOBIES, ELACATINUS EVELYNAE AND E. PROCHILOS...... 51

Introduction...... 51 Methods ...... 54 Study System...... 54 Settlement Patterns ...... 55 Experimental Design ...... 56 Analyses ...... 58 Competitive Ability...... 59 Results...... 60 Settlement Patterns ...... 60 Competitive Ability...... 62 Discussion...... 64

4 AGE CLASS COMPETITIVE INTERACTIONS IN A MARINE GOBY, ELACATINUS PROCHILOS ...... 83

Introduction...... 83 Methods ...... 85 Experimental Design ...... 85 Experimental Set-Up ...... 87 Analyses ...... 87 Results...... 88 Discussion...... 90

5 AGE AND GROWTH OF TWO SPECIES OF MARINE GOBIES BASED ON OTOLITH ANALYSES ...... 100

Introduction...... 100 Methods ...... 105 Study System...... 105 Sampling...... 106 Otolith Analysis...... 107 Validation of Daily Increments ...... 108 Settlement Marks...... 109 Application of Back-Calculation Models...... 111 Comparison of Back-Calculation Models ...... 111 Results...... 113 Validation of Daily Increments ...... 113 Settlement Marks...... 113 Back-Calculation Models ...... 114 Discussion...... 117

6 SUMMARY, IMPLICATIONS, AND CONCLUSIONS...... 138

Summary and Overview of Experimental Work ...... 138

vi Implications: Speculation About Mechanisms of Coexistence ...... 141 The Storage Effect: Linking Theory with Empirical Aspects of Fish Settlement....144 Empirical Evidence of the Temporal Storage Effect...... 148 Buffered Population Growth ...... 148 Covariance Between the Environment and the Strength of Competition...... 149 Differential Responses to the Environment...... 151 Quantifying the Temporal Storage Effect...... 151 Implications of the Storage Effect ...... 152 Future Directions ...... 155

APPENDIX

A APPROXIMATING AN ADDITIVE MODEL OF MORTALITY FROM THE LOG ADDITIVE MODEL (OR HAZARD) USED IN THE SURVIVAL ANALYSIS...... 162

B ESTIMATING VARIANCE ON HAZARD (MORTALITY) (TAKEN FROM COLLETT 1994) ...... 165

C ESTIMATING THE VARIANCE OF THE STRENGTH OF DENSITY INDEPENDENCE AND THE STRENGH OF DENSITY DEPENDENCE ESTIMATED FROM A LOG ADDITIVE MODEL...... 167

LIST OF REFERENCES...... 169

BIOGRAPHICAL SKETCH ...... 187

vii

LIST OF TABLES

Table page

2-1. Summary of coral heads used in survival experiments ...... 41

2-2. Coral heads surveyed for settlement during a settlement pulse in July of 2000 and June of 2001...... 42

2-3. Results from survival analysis to determine effect of habitat quality...... 43

2-4. Loadings of the six variables (log transformed) on the first two discriminant functions (DF) for the canonical discriminant function analyses...... 44

2-5. Estimates from the log additive model of the strength of density independence and the strength of density dependence...... 45

3-1. Experimental design for the competitive ability experiment...... 69

3-2. Correlation between settlement of E. evelynae and E. prochilos...... 70

3-3. Analysis of variance of the natural log of settlement for the two species on three patch reefs over 13 settlement events...... 71

3-4. Average settlement of E. evelynae and E. prochilos over four years to different species of coral to three separate patch reefs...... 72

3-5. Results from survival analysis to determine effect of density...... 73

3-6. Results from survival analysis to determine competitive effects and competitive responses...... 74

4-1. Experimental set-up for age class experiment...... 95

4-2. Coefficients and results from the survival analysis to test for the responses and effects of different age classes...... 96

4-3. Results from survival analysis on per capita effects on the instantaneous mortality rate of each age class on itself and on one another...... 97

5-1. Five back-calculation models investigated in this study...... 122

viii 5-2. Index of accuracy, Ia, of back-calculation for 5 different back-calculation growth models...... 123

5-3. Results from the LME model to compare the deviation of the observed, standard length measurements from the predicted back-calculated estimates...... 124

6-1. Refined model of the Analysis of Variance of Table 3-3 in Chapter 3...... 158

6-2. Contribution of the temporal storage effect towards stable coexistence...... 159

LIST OF FIGURES

Figure page

1-1. Graphical representation of the relationship between adult density and initial settler density according to three different scenarios...... 13

1-2. Graphical representation of the relationship between instantaneous mortality and settler density and the relationship between adult density and initial settler density...... 14

1-3. Graphical representation of the relationship between adult density and initial settler density in habitats that differ in quality where there is a correlation between settlement level and habitat quality...... 15

1-4. Phylogenetic relationship of the American seven-spined gobies...... 16

2-1. Graphical representation of survival of settlers at time t to time t+1 over habitats of different quality...... 46

2-2. The main effects of a) quality, b) density, and c) experiment on the survival of gobies as estimated with survival analysis...... 47

2-3. The relationship between the original number of fishes present on coral heads and the total number of settlers to those coral heads...... 49

2-4. Relationship between the mean scores for each habitat quality on the first two discriminant functions...... 50

3-1. Mean longevity of targets (the average number of days targets remained alive on coral heads) for the two species on coral heads of different quality...... 75

3-2. Variation in settlement over time...... 76

3-3. Average preference of settlers of each goby species for different coral species on three patch reefs in Tague Bay over four years...... 77

3-4. Survival of targets according to the main effects in the survival analysis...... 79

3-5. Survival of targets according to the main effects, species and age class, in the survival analysis...... 81

x 4-1. Mean longevity of “targets” for each age class assemblage versus the number of fish on each coral head in each treatment...... 98

4-2. Survival of targets (older fish or settlers) according to the main effects in the survival analysis according to the following survival model on day 1...... 99

5-1. Relationship between otolith size and fish length and back-calculation of size at age...... 125

5-2. Deviation of the observed number of increments from the expected number of increments...... 126

5-3. Transition-centered profiles for the two species of gobies...... 127

5-4. Relationship between relative somatic growth versus relative otolith growth rates...... 128

5-5. Proportionality coefficient c estimated at the individual level...... 129

5-6. Length versus otolith size relationship for each species...... 130

5-7. Deviation of the back-calculated size at age from the measured standard fish length...... 131

5-8. Relationship between the back-calculated size at age for the different back- calculation models versus the observed standard length measurements for E. evelynae...... 133

5-9. Relationship between the back-calculated size at age for the different back- calculation models versus the observed standard length measurements for E. prochilos...... 134

5-10. Relationship between otolith radius versus observed standard length for the four different food treatments for E. evelynae...... 135

5-11. Relationship between otolith radius versus observed standard length for the four different food treatments for E. prochilos...... 136

5-12. Depiction of how underestimating true age can overestimate back-calculated size at age...... 100

6-1. The average number of adults on coral heads for the two goby species just prior to settlement over 13 months during 4 years...... 160

6-2. The relationship between the mean strength of competition and the environmental response for 13 different settlement events...... 161

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

HABITAT QUALITY, COMPETITION, AND RECRUITMENT PROCESSES IN TWO MARINE GOBIES

Jacqueline A. Wilson

May 2004

Chair: Craig. W. Osenberg Major Department: Zoology

Much research on the population dynamics of reef fishes has focused on the high degree of spatial and temporal variation in settlement (or the planktonic supply of new individuals to the reef habitat). However, post-settlement processes, such as the strength of density independent and/or density dependent processes, have assumed to be more homogenous over space and time. My research, which quantified processes which shape the distribution and abundance of two marine gobies, Elacatinus evelynae and E. prochilos, in St. Croix, U.S.V.I., quantified the strength of post-settlement processes and determined whether or not they were uniform over space. I found that the strength of density independence varied among corals and drove variation in habitat quality. In addition, settlement was greater to sites of higher quality (i.e., sites receiving the most settlers also yielded weaker density independent mortality). This positive covariance between settlement and habitat quality can mask the underlying effect of density dependence in observational studies. Indeed, density had much stronger effects in this

xii system than inferred from spatial correlations between density and survival (Wilson and

Osenberg 2002). Density had significantly negative effects on survival of both species; however, the negative effects of increased density were more offset by increased quality for E. evelynae than for E. prochilos.

In addition, experimental manipulations demonstrated that E. evelynae and E. prochilos had similar competitive effects and responses to one another’s densities, and otolith analyses also revealed that both species experienced similar allometric growth patterns (as predicted from a Modified Fry growth model). Finally, this work also explored age-structured interactions for E. prochilos; however, there were no differences in the competitive effects within and between age classes of younger and older fish.

Given these species’ ecological and morphological similarities, I investigated plausible mechanisms responsible for their co-existence. I used settlement data and estimates of the strength of competition for the two species to evaluate how differences in species’ responses to environmental variation may be driving stable coexistence of these two gobies. My work suggested that the temporal storage effect may be contributing to stable coexistence of these two species in this system.

xiii

CHAPTER 1 GENERAL INTRODUCTION

Understanding processes that shape marine systems has been a source of controversy for decades. In fact, determining processes that shape populations has been a major topic of debate in ecology, in general (Sinclair 1989, Sinclair and Pech 1996,

Hanski 1990). Some ecologists have argued that populations persist in nature due to density dependent processes that regulate population size (Nicholson 1933, Lack 1966).

Others have argued that negative feedback on population growth is not significant enough to explain the distribution and abundance of different species; rather populations are mainly shaped by stochastic extinction and re-colonization events (Andrewartha and

Birch 1954, Reddingius 1971). However, such extremes rarely reveal the mechanism(s) regulating animal populations (Dennis and Taper 1994), and they do not help us understand and compare different systems within a common framework. More general approaches have emerged that incorporate elements of both sides of this debate. For example, many authors have suggested that density dependence is not as prevalent as predicted by standard ecological theory and that density dependent regulation may only occur when densities are very high (Strong 1986, Dennis and Taper 1994). In addition, the importance of density dependent and density independent processes may depend on the system and temporal and spatial scale under consideration (Hanski 1990). The question should not be not whether density dependence exists; rather, it should focus on the important ecological implications as well as evolutionary relevance of density dependence when it does exist. For example, density dependent processes can provide

1 2 selection pressures that can shape events from social organization to habitat selection

(Sinclair and Pech 1996). However, because population dynamics are influenced by the strength of density dependent and density independent processes, it is important to consider both when investigating population dynamics.

Much of the theory of population dynamics, and especially models that examine the role of density dependence, has been developed for closed populations. Yet, many ecological studies are done on sufficiently small spatial scales that the study population is open to migration. For instance, most marine organisms have open populations, characterized by a bipartite life cycle (i.e., a dispersive, pelagic larval stage followed by a relatively site-attached, adult phase) (Sale 1980, Thresher 1984, McEdward 1995) where local reproductive output is unrelated to subsequent larval settlement from the plankton

(Talbot et al. 1978, Sale and Douglas 1984). Settlement (the transition from a larva to a benthic juvenile) and post-settlement processes can have strong simultaneous influences on the dynamics of marine organisms, such as reef fishes, and may interact (Warner and

Hughes 1988, Caley et al. 1996, Schmitt and Holbrook 1996, Steele 1997a, Wilson and

Osenberg 2002, Shima and Osenberg 2003). As a result, there is a need to estimate

(rather than detect) processes (Osenberg et al. 2002) and to quantify their relative importance to discern how settlement and post-settlement processes combine to shape the distribution and abundance of reef fish populations (Victor 1986, Jones 1987, 1988,

Shulman and Ogden 1987, Booth 1992, Caley et al. 1996, Schmitt and Holbrook 1996,

1999, Steele 1997a, 1997b, Schmitt et al. 1999). Processes that affect larvae prior to settlement must also be addressed (Sponaugle and Cowen 1996a, b, McCormick and

Molony 1995, Vigliola 1999, Searcy and Sponaugle 2000, Sponaugle et al. 2003).

However, this integration is not simple; pre-settlement, settlement, and post- settlement processes can all affect population dynamics and these processes potentially interact. For example, pre-settlement factors (such as supply of larvae, mortality in the plankton, and condition and competency of larvae) (Gaines et al. 1985, Houde 1987,

Roughgarden et al. 1988, Dufour and Galzin 1993) can affect settlement intensity and the condition of settlers, and therefore, the strength of post-settlement density dependence and independence (Doherty 1981, 1991, 2002, Sale et al. 1984, McCormick and Molony

1992, Doherty and Fowler 1994, Forrester 1995, Caley 1995, Steele 1997b, Booth and

Hixon 1999, Searcy and Sponaugle 2001, Bergenius et al. 2002, Vigliola and Meekan

2002). Other studies have attempted to integrate settlement and post-settlement processes into a common framework (e.g., see Schmitt et al. 1999, Wilson and Osenberg 2002,

Shima and Osenberg 2003).

Schmitt et al. (1999) developed one such approach to model how the supply of recruits or “colonists” and density independent and density dependent mortality influenced subsequent juvenile densities of a marine fish. They used a Beverton-Holt settlement function, in which the number of juveniles increases to an asymptote as the initial settlement intensity increases. The Beverton-Holt function describes the results of many empirical studies (Steele 1997b, Doherty 2002, Wilson and Osenberg 2002, Shima and Osenberg 2003). Schmitt et al. used the inverse of the asymptote as an estimate of the strength of density dependence; however, in their integrated formulation, this estimate of density dependence is confounded with density independent processes and study duration. Therefore Osenberg et al. (2002) formulated an instantaneous version of the

Beverton-Holt model to compare the strength of density dependence in a meta-analysis.

They assumed that instantaneous mortality rate (µ) of a single-aged cohort was a linear

function of the cohort's initial density (N) (see Bolker et al. 2002, Osenberg et al. 2002,

Shima and Osenberg 2003)

µ = α + βN (1-1)

where α is the density independent mortality rate and β is the per capita effect of one

settler (or particular age class in question) on the instantaneous mortality rate of other

settlers. If only the beginning and ending density of the cohort is known, an integrated

form of Eq. 1-1 can be used to estimate α and β (Bolker et al. 2002, Osenberg et al. 2002,

Shima and Osenberg 2003)

e−αt N N = 0 (1-2) t β (1 − e−αt )N 1 + 0 α

where Nt is the number of individuals after some time t, and N0 is the initial number of individuals.

Schmitt et al. (1999) and Osenberg et al. (2002) lay a conceptual foundation for future work. However, their work (along with most previous studies) is limited in at least two ways. First, the cohort approach focuses on a single age class (i.e., settlers) and ignores age class interactions. These interactions are important for many reef fishes

(Jones 1987, Wilson 1998, Schmitt and Holbrook 1999, Bolker et al. 2002), and work in other systems has shown that we can not interpret population dynamics by focusing our attention on a single stage (i.e., larvae, recruits or juveniles) in the life history of a focal organism (Nisbet and Bence 1989, Osenberg et al. 1992, 1994, Mittelbach and Osenberg

1993, Claessen et al. 2002). The presence of population stage structure (the co- occurrence of distinct, multiple life history stages within a single population) can lead to

5 very different population dynamics than those found in unstructured populations

(Mittelbach et al. 1988, Nisbet and Bence 1989, Briggs 1993, Briggs and Godfray 1995,

Olson et al. 1995). For instance, asymmetric interactions among different age classes can lead to oscillatory population dynamics (DeRoos et al. 1992, Persson et al. 2000).

Therefore, in order to extrapolate longer term dynamics (i.e., multiple generations) over larger spatial and temporal scales, we must recognize that different age classes or stages interact with one another and, if appropriate, explore reef fish dynamics using a stage structured approach (e.g., Bolker et al. 2002).

Secondly, much research has focused on the high degree of spatial and temporal variation in the distribution and abundance of marine fishes (Luckhurst and Luckhurst

1977, Doherty 1983, Williams 1983, McFarland et al. 1985, Robertson et al. 1988, 1993,

Robertson 1990, Sponaugle and Cowen 1994, 1997). Variation in larval supply is thought to be the major factor driving variation in the distribution, size and age structure, and dynamics of these open populations (Caswell 1978, Doherty 1983, 1991, Victor

1983, 1986, Doherty and Williams 1988, Carr 1994) where density dependence is thought to homogenize this variation. However, the strength of density dependent and density independent processes may also vary in space or time, and might therefore promote rather than diminish variation in abundance (e.g., Caselle 1999, Shima 1999,

Wilson and Osenberg 2002, Shima and Osenberg 2003). For example, Wilson and

Osenberg (2002) suggested that intrinsic qualities of coral heads varied spatially. They hypothesized that this spatial variation in quality allowed high quality coral heads to receive higher levels of settlement without incurring higher levels of mortality despite negative effects of density on post-settlement survival: i.e., negative effects of high

6 density were completely offset by the effects of higher habitat quality. They argued that variation in the intrinsic quality of a coral head could be determined by microhabitat characteristics such as predator density, refugia from predators (Behrents 1987, Hixon and Beets 1989, 1993), or food resources (Nemeth 1996).

The purpose of my dissertation research was to take an integrative approach to better understand what processes drives the distribution and abundance of two species of reef fishes. In particular, I aimed to quantify to what extent density independent mortality and density dependent mortality affected these populations simultaneously.

Typically, strictly density independent mortality would result in a linear relationship between input (i.e. settlers) and subsequent adults (Figure 1-1a). Therefore, variation in the distribution and abundance would mirror variation in larval supply and subsequent settlement. However, if density dependence is the primary determinant of reef fish population size and structure, then a curvilinear relationship between input and output would be expected, which would dampen the variation seen in initial settlement (Figure

1-1b). Obviously, these systems are not that simple, and multiple processes act in concert

(Warner and Hughes 1988, Caley et al. 1996, Schmitt and Holbrook 1996, Steele 1997a).

Density independent mortality and density dependent mortality act simultaneously to shape the distribution and abundance of reef fishes. In particular, when settlement levels are low, density independent processes are important, since density may not be high enough to invoke density dependent mortality. Nevertheless, at high settlement and subsequent high post-settlement densities, variation can be dampened by both density independent and density dependent mortality (Figure 1-1c).

However, current research (e.g. Wilson and Osenberg 2002, Shima and Osenberg

2003) has indicated that the strength of density independence and/or density dependence

may vary in space, complicating scenarios such as the one depicted in Figure 1-1c. This

variation can be depicted in two ways within the framework of the instantaneous

Beverton-Holt model in Eq. 1-1 (Figure 1-2a, b). If the strength of density independence

(α) varies among coral heads, then the relationship of mortality over the density of

settlers would result in parallel, straight lines with the same slope but with different

intercepts (Figure 1-2a). This can be translated to a recruitment function (i.e., Eq. 1-2)

which results in a suite of curved lines (each line represents habitats of different quality)

that vary in their initial slope and asymptote (Figure 1-2b). Alternatively, if the strength

of density dependence (β) varies in space but the strength of density independence does not, then the relationship of mortality over the density of settlers would result in a series of straight lines with different slopes but a common intercept (Figure 1-1c). In terms of a recruitment function, this results in, again, a suite of curves, with different asymptotes, but the same initial slopes (Figure 1-1d). However, it is important to note that the strength of density independence and density dependence may vary simultaneously, which would result in nonparallel, straight lines between mortality and the density of settlers (the lines in Figure 1-2a could cross).

Additionally, the factor(s) that influences settlement and post-settlement survival may be correlated. Work by Wilson and Osenberg (2002) and Osenberg and Shima

(2003) suggested that variation in habitat quality and settlement intensity can covary (see

Figure 1-3). Such covariation among different processes (i.e., correlation between settlement and post-settlement survival) may mask the effect of density and alter our

8 understanding of factors which drive dynamics of marine systems (Chesson 1998,

Osenberg et al. 2002). This is particularly important because approximately half of all studies of density dependence in reef fishes are observational. Thus, the demonstration of covariation among settlement and post-settlement process (i.e., “cryptic density dependence” – see Shima and Osenberg 2003) has the potential to explain some of the ongoing controversy about the relative importance of density dependence and density independence in marine fishes.

By considering variation and covariance in parameters that govern the dynamics of different life stages, we can conceptually link and provide a cohesive framework to evaluate processes that occur during different phases of the life history of organisms (also see Chesson 1998, Hixon 1998, Schmitt et al. 1999, Doherty 2002, Osenberg et al. 2002).

Such “stage-structure” can also exist during the post-settlement phase of reef fishes.

Many reef fishes settle monthly throughout the year (Robertson 1992), so multiple cohorts generally occur together. If multiple life history stages co-occur in these populations, then it is most appropriate for us to take a stage-structured approach to understand the dynamics of these systems and evaluate how differences in habitat quality will influence these dynamics.

Finally, coral reef fish communities are diverse systems, often comprised of 10 to

100s of species within a locale (Goldman and Talbot 1976, Smith and Tyler 1972, Talbot et al. 1978). The factors that maintain this high diversity have long intrigued biologists, but mechanisms that maintain this diversity are not well understood (but see Sale 1977,

Chesson and Warner 1981, Warner and Chesson 1985, Chesson 2003, Mora et al. 2003,

Munday 2004). Thus, research should be conducted to try to better understand processes

that might maintain diversity in these systems. A likely candidate, based on theoretical

studies, is spatial and temporal variation in settlement (Doherty and Williams 1988,

Chesson and Warner 1981, Warner and Chesson 1985, Chesson 2003, Munday 2004).

Importantly, this mechanism of coexistence which focuses on variation in settlement of

different species and the strength of post-settlement competition both within and among

species ties back directly to standard settlement/post-settlement population-level studies

of processes which determine the distribution and abundance of different species.

Proposed Work

The overall objective of this work was to better understand processes affecting the

variability in the distribution and abundance of two reef fishes, Elacatinus evelynae and

E. prochilos. These species are within the tribe, Gobiosomatini (further subdivided into

the Gobiosoma and the Microgobius groups: Figure 1-4), which is comprised of the

naked seven-spined gobies; these species are highly diverse in both their morphology and

ecology (Rüber et al. 2003). The two species used in this study, Elacatinus evelynae and

E. prochilos, fall within the Gobiosoma group and, more specifically, within the

Elacatinus clade (Figure 1-4), comprised of cleaning gobies.

Elacatinus has at least 20 described species in the tropical western Atlantic Ocean

(Böhlke and Robins 1968, Sazima et al. 1997) and is the largest genus of fishes found on

coral reefs in this region (Taylor and Van Tassell 2002). Colin (1975) and Robins et al.

(1991) originally placed cleaning gobies within one genus, Gobiosoma; however, due to

the recent re-classification by Rüber et al. (2003), I will refer to these two species of

cleaning gobies as Elacatinus evelynae and E. prochilos throughout the rest of this work.

Elacatinus evelynae and E. prochilos are morphologically and ecologically similar (Colin 1975), occupying live coral substrate in Tague Bay of St. Croix, U.S.V.I.

In addition, these species have similar settlement patterns, often occupying the same coral heads located on patch reefs in St. Croix. Given past work (i.e., Wilson 1998, Wilson and Osenberg 2002), one major objective of my dissertation work was to identify if variation in the strength of density independence and/or density dependence drives variation in the distribution and abundance of these species (i.e., through habitat quality,

Figure 1-2). If such variation was documented, I also wanted to determine if settlement and variation in post-settlement processes were correlated to definitively test if such a correlation could drive “cryptic density dependence” (see Wilson and Osenberg 2002 and

Shima and Osenberg 2003): the under-estimation of the strength of density dependence in observational studies. Finally, because multiple age classes of both species often co- occur on coral heads, I also quantified the strength of competitive interactions arising within and between age classes.

In all of these studies, I concentrated on post-settlement survival. I was unable to quantify growth rates due to high mortality rates. However, because growth studies can add valuable insights about post-settlement processes in future studies, I conducted a study to test if otoliths (i.e., small ear-bones located in the semi-circular canals) could be used to assess growth rates. Otoliths have been used for gleaning information on growth and sizes at previous, unobserved life history stages (such as reconstructing size at settlement estimates from juvenile or adult fish; see Francis 1990, Vigliola et al. 2000,

Bergenius et al. 2002). Thus, I determined the validity of using otoliths for obtaining estimates of age and also evaluated if different growth models varied in their ability to describe growth trajectories. While these techniques were not central to work conducted in my dissertation, verification of the appropriateness of these techniques for these

11 species will be critical for future work investigating possible variation in larval quality

(estimated via variation in back-calculated size at settlement) as well as estimating adult longevity, age at reproduction and dispersal abilities of these species (estimated via age at settlement).

The final, albeit speculative, goal of this work was to evaluate different mechanisms that might facilitate coexistence of these two species. In particular, the role of settlement variation and the storage effect (sensu Chesson 2003) were evaluated. The storage effect is comprised of three elements: species specific responses to the environment (in terms of species differences in per capita reproductive rates resulting from environmental variation), a long lived-life history stage, and covariance between the strength of competition and the environmental response of a given species. The storage effect works when a relatively persistent stage (e.g., a long-lived adult) buffers the effects of variable recruitment. These buffering effects prevent catastrophic population decline when poor recruitment events occur. As a consequence, good settlement events are not canceled out by population declines during periods of poor settlement (Chesson and

Warner 1981, Warner and Chesson 1985, Chesson 1994). This helps a species recover from low density. It also acts to stabilize a species’ presence in the system by allowing a species at low density to experience higher per capita growth rates compared to more abundant species that are more limited by intraspecific competition.

Future Work

In the future I plan to develop a population dynamics model that will provide a conceptual framework to quantify how age class interactions, interspecific interactions, and variation in habitat quality affect adult densities of these two species. Estimates of these processes, based on the empirical studies, will be used to develop and parameterize

12 the model. Thus, my dissertation research provides the conceptual and empirical basis for this work – it was designed to quantify the strength of density dependence and density independence, estimate the spatial variation in these processes, and quantify differential age class and competitive interactions between the two species. In fact, variation in the larval input and competitive abilities of these species are an important component of the maintenance of diversity in these systems (Doherty and Williams 1988, Chesson and

Warner 1981, Warner and Chesson 1985, Chesson 2003). In future studies, I also will use my empirical data to more rigorously evaluate the storage effect and determine its role in promoting coexistence of E. evelynae and E. prochilos.

a) slope=1

slope<1 +1) t ( s Adult

Settlers (t )

b) slope=1 +1) t ( Adults

Settlers (t)

c) slope=1 slope<1 +1) t ( Adults

Settlers (t )

Figure 1-1. Graphical representation of the relationship between adult density and initial settler density according to three different scenarios. a) only density independent mortality, b) only density dependent mortality, c) density independent and density dependent mortality. Closed circles represent different levels of settlement through time.

b) a) weakest density independence weakest density independence

) ) µ µ

( ( y y t t i i l l a a rt rt strongest density independence Mo Mo strongest density independence

Denstiy of Settlers Denstiy of Settlers

c) d)

weakest density dependence

weakest density dependence 14 ) ) µ µ

( ( strongest density dependence y y

alit alit

Mort Mort

strongest density dependence

Density of Settlers Density of Settlers

Figure 1-2. Graphical representation of the relationship between instantaneous mortality and settler density according to Eq. 1-1, and the relationship between adult density and initial settler density according to Eq. 1-2. a) variation in the strength of density independence, or α, in the continuous-time form of the Beverton-Holt model in Eq. 1-1, b) variation in the strength of density independence, or α, in the integrated form of the Beverton-Holt model in Eq. 1-2, c) variation in the strength of density dependence, or β, in the continuous-time form of the Beverton-Holt model in Eq. 1-1, and d) variation in the strength of density dependence, or β, in the integrated form of the Beverton-Holt model in Eq. 1-2.

high habitat quality +1) t

Adults ( low habitat quality

Settlers (t)

Figure 1-3. Graphical representation of the relationship between adult density and initial settler density in habitats that differ in quality where there is a correlation between settlement level and habitat quality (see Wilson and Osenberg 2002, Shima and Osenberg 2003). Closed circles represent different levels of settlement on coral heads of different quality during one settlement event. Note: variation in habitat quality could be driven by variation in the strength of density independent and/or density dependent mortality; neither is specified in this representation.

Figure 1-4. Phylogenetic relationship of the American seven-spined gobies based on a Bayesian phylogenetic analysis of mitochondrial 12S rRNA, rRNA-Val, and 16S rRNA. Figure and figure legend taken from Rüber et al. 2003 (Figure 2).

CHAPTER 2 ASSESSMENT OF HABITAT QUALITY: DETERMINING PROCESSES THAT DRIVE SPATIAL VARIATION IN SURVIVAL AND SETTLEMENT OF TWO SPECIES OF MARINE GOBIES

Introduction

Processes that affect population dynamics can exhibit considerable spatial and temporal variability. For example, competition and/or predation can vary among different habitats, driving variation in densities of different species as well as relative densities of individual species (Osenberg et al. 1994, Olson et al. 1995, Hemphill 1991,

Nanami and Nishihira 2001, Wethey 2002, Martin and Joron 2003). Other processes, such as dispersal, can also be spatially variable where variable dispersal into or out of a given area can have important demographic and population dynamic consequences

(Armsworth 2002, Lowe 2003, Kreuzer and Huntly 2003). Considerable research has focused on dispersal in marine systems, or settlement (or the planktonic supply of new individuals to the reef habitat), which is notoriously unpredictable over space and time

(Luckhurst and Luckhurst 1977, Doherty 1983, Williams 1983, McFarland et al. 1985,

Robertson et al. 1988, 1993, Robertson 1990, Sponaugle and Cowen 1994, 1997).

Conversely, post-settlement processes, such as compensatory density dependent mortality, are thought to decrease spatial variability (Jones 1987, Bertness et al. 1992,

Forrester 1995, Hixon and Carr 1997). Consequently, unlike settlement, the strength of density dependence is often assumed to be homogenous in space and time (e.g. Schmitt et al. 1999, but see Wilson and Osenberg 2002, Shima and Osenberg 2003). Indeed, many studies implicitly assume that results from a single study of competition can be applied to

18 19 many sites, in part because it is difficult to quantify spatial or temporal variation in the strength of competition or density dependence. Yet few ecologists would ever assume that a single estimate of settlement would apply generally. If post-settlement processes vary in space and time, then this variation can have important implications on the abundance and distribution of fishes, especially if the strength of these processes covaries with settlement intensity (Chesson 1998, Shima 1999, Wilson and Osenberg 2002,

Holbrook and Schmitt 2003, Shima and Osenberg 2003). This is particularly important in marine systems where historical debate has argued for fish populations being structured either by the input of larvae or by post-settlement process re-shaping initial settlement patterns (Caley et al 1996, Schmitt et al. 1999). This debate has been driven by studies that failed to demonstrate density dependent settlement and/or post-settlement mortality (see review by Doherty 1991, Osenberg et al. 2002). However, if the strength of density dependence and/or density independence varies over space and time, it can affect patterns initially thought to be due to variation in larval supply alone. In addition, covariation among different processes (i.e., correlation between settlement and post- settlement survival) may mask the effect of density and alter our understanding of factors which drive dynamics of marine systems (Chesson 1998, Osenberg et al. 2002, Shima and Osenberg 2003).

For instance, Wilson and Osenberg (2002) found that post-settlement survival was constant across a natural gradient in settler density, but survival declined win increasing density in a manipulative experiment. Wilson and Osenberg (2002) hypothesized that this mismatch between their observational and experimental results arose because 1) survival declined with density, but 2) habitat quality varied spatially, and 3) larvae settled

20 at higher rates to higher quality sites. As a result, fishes that settled at high densities survived as well as fish that settled at low densities – the high habitat quality compensated for the negative effects of high density. Thus, a positive association between settlement and quality could mask the underlying effects of density on survival

(Figure 2-1a). Because approximately half of all studies of density dependence in reef fishes are observational, Wilson and Osenberg's (2002) hypothesis has the potential to explain some of the ongoing controversy about the relative importance of density dependence and density independence in marine fishes.

Experimental work in this system (Wilson and Osenberg 2002) as well as work in other systems indicated that effects of density on survival can be well described by a

Beverton-Holt relationship (e.g., Figure 2-1; see Steele 1997b, Schmitt et al. 1999,

Osenberg et al. 2002, Shima and Osenberg 2003). Variation in quality (i.e., per capita survival at a common density) can be driven by spatial variation in the strength of density dependent and/or density independent processes, both of which lead biased estimates of the strength of density dependence and density independence (Wilson and Osenberg

2002, Shima and Osenberg 2003). Because variation in the strength of density independence and/or density dependence will have important and different implications for population dynamics of reef fishes, understanding which processes drive variation in habitat quality is critical for understanding how reefs function.

Here I experimentally tested the model proposed by Wilson and Osenberg (2002).

In particular, I 1) determined if sites varied in quality, by quantifying the survival of fishes when fishes were manipulated to a common density (if coral heads varied in quality, then heads of putative high quality should yield greater survival of fishes when

placed at a common density: Figure 2-1b); 2) statistically evaluated if this variation in

habitat quality resulted from variation in the strength of density dependent or density

independent processes; and 3) explored the environmental factors that might be

responsible for the observed variation in quality. I also quantified the correlation

between settlement and quality to assess the underlying phenomenon that biases the

estimation of density dependence using observational data. This is one of the first

experimental studies to evaluate how variation in post-settlement processes may drive

variation in habitat quality and to explore patterns of covariance in demographic

parameters (i.e., settlement and post-settlement mortality) (but see Wilson and Osenberg

2002 and Shima and Osenberg 2003).

Methods

Experimental Procedures

Study species

Elacatinus evelynae and E. prochilos are small (< 34 mm standard length, SL) cleaning gobies that can remove ectoparasites from larger fishes (Colin 1975). The two species are ecologically and morphologically similar, relatively sedentary, dwell on live scleractinian corals (and occasionally on rock surfaces and the outer surface of sponges), and co-occur at depths from 0 to 50 m. Settlement of each species begins as early as the

last quarter moon, peaks around the new moon, and continues as late as the first quarter

moon (a period as long as two weeks, but only a few days). New settlers lack

pigmentation for approximately 24 hours after settling on coral heads, allowing settlers to

be easily distinguished from older fishes.

Experimental design

Five experiments were conducted over three summers (June-August 2000, June-

August 2001, May-September 2002) in Tague Bay on the northeast part of St. Croix,

U.S.V.I. (17° 45′ 40′′ N, 65° 35′ 30′′ W). Each experiment manipulated fish density across a range of coral heads hypothesized to vary in habitat quality. It was hypothesized that if there was variation in habitat quality, then higher quality sites, which received more settlers and produced more, older survivors than lower quality sites, would have higher densities of resident fishes. Therefore, the number of resident fishes was used as a surrogate of putative habitat quality. The general design allowed me to evaluate the effects of density (e.g., by comparing survival at low and high density) and habitat quality (by comparing survival across different putative quality classes at a common density) (Figure 2-1b). Experiments done in 2000 and 2001 were specifically designed to test for differences in survivorship of fishes at common densities on habitats of different putative quality. The three experiments conducted in 2002 were not specifically designed to cross density and quality, but a subset of the studies allowed me to examine the results in light of this framework. In each experiment, I used fishes that were of a similar size, although the size of fishes used varied among experiments (see Table 2-1).

Before beginning an experiment, coral heads were surveyed and the resident

Elacatinus were counted and placed into size/age classes (settler: < 16 mm,

corresponding to fishes that settled within the previous two weeks; juvenile: > 16 mm but

< 22 mm, or approximately two - four weeks post-settlement; and adult: > 22 mm, or

more than one month post-settlement). Based on previous work (Wilson and Osenberg

2002, Shima and Osenberg 2003), I hypothesized that sites with higher densities of fishes

were of highest quality (thus ameliorating the negative effects associated with higher

density). Thus, experimental sites were placed in putative habitat quality classes based

on the initial number of resident Elacatinus. I predicted that fishes placed on putatively

high quality sites would survive better than fishes placed at the same density but on

putatively low quality sites.

Following assignment of coral heads to putative quality classes and prior to the

start of any experimental manipulation, I removed all resident E. evelynae and E. prochilos. Details for each experiment are given below, but in general, all experiments

used a “target/neighbor” design (Goldberg and Werner 1983, Olson et al. 1995), in which

neighbor density was crossed with putative habitat quality. Due to low replication and

limited statistical power for any single experiment, I analyzed the data from the five

experiments in a single analysis to help increase power. Targets and neighbors typically

consisted of a random mixture of the two species based on their natural abundances in the

study areas (which averaged ~ 44% E. prochilos). Because the two species are

approximately equivalent in their competitive effects and responses, slight differences in

relative abundances likely had little effect on the results (see Chapter 3). Targets and

neighbors in all experiments were tagged using different colors of acrylic paint, and I

monitored the survival of targets over time.

Experimental set-up 1: 2000

In 2000 the experiment was conducted on 24 Diploria strigosa coral heads on six

patch reefs. Diploria strigosa was the most abundant coral species on the patch reefs,

and therefore, the most amenable species for locating the most coral heads that were

similar in size but varied in fish density. Each reef functioned as a block with one

replicate of each of the four treatments per patch reef (six replicates per treatment).

Preliminary analysis, however, showed the effect of patch reef was not significant

(F5,15 =1.63, P = 0.21), so the patch reef term was dropped from subsequent analyses.

Fishes used to stock experimental coral heads were collected by hand from D. strigosa coral heads in an adjacent bay (Boiler Bay) using quinaldine and small aquarium

nets and brought back to the lab to be measured and tagged. Tagged fishes were then

stocked the following morning to coral heads of different putative quality at one of two

densities (see Table 2-1). Experimental fish density (fishes/cm2; see Table 2-1) was

fixed, but there was some variation in coral head size (see Table 2-1). This resulted in a

different number of fishes per coral. In addition, experimental density was crossed with

“high” and “low” putative habitat quality. Putative habitat quality was based on the

initial number of resident Elacatinus on experimental sites; “low” putative quality sites

had resident densities below the median whereas “high” putative quality sites had

resident densities above the median.

Each coral head was stocked with fishes for two consecutive days, and the second

day of stocking was considered as the first day (or starting density) for monitoring

survival. Coral heads were then surveyed on days 4, 8, and 11, and any missing

individuals were replaced with fishes tagged with a different color. Surrounding areas

were searched for tagged fishes that may have moved from experimental sites. Since

only 8 tagged individuals were found away from experimental sites, I assumed the

disappearance of tagged individuals represented mortality. On day 11, any remaining

tagged fishes were removed, measured, euthanized and preserved in 95% ETOH.

Experimental set-up 2: 2001

The experiment in 2000 was repeated in 2001 on the backreef in Tague Bay using

24 Montastrea annularis coral heads (six replicates per treatment). Montastrea annularis

was the most abundant coral species on the backreef area and was the gobies' most

preferred substrate (see Wilson 1998); however, this species rarely occurs on the patch

reefs used in 2000. Fishes used to stock experimental coral heads were collected from M. annularis coral heads in Boiler Bay, immediately taken to the experimental sites in Tague

Bay, and measured and tagged underwater. As in 2000, experimental fish density

(fishes/cm2; see Table 2-1) was fixed at two levels, and crossed with “high” and “low”

putative habitat quality. Each coral head was stocked with fishes for two consecutive

days, and the second day of stocking was considered the first day for monitoring survival.

Coral heads were then surveyed on days 2, 3, 4, 8 and 12, and any missing tagged

individuals were replaced with juveniles tagged with a different color. On day 12, all

remaining tagged fishes were removed, measured, euthanized and preserved in 95%

ETOH.

Experimental set-up 3, 4 & 5: 2002

In 2002, three experiments were conducted along the backreef in Tague Bay using

the same M. annularis coral heads used in 2001. In these three experiments I used a

fixed number of fishes per coral head which resulted in a variable density (fishes/cm2)

among heads within the same treatment. However, this variation was small relative to the

variation among treatments (see Table 2-1).

Experiment 3 – In this experiment there were three density treatments (fishes per

coral head): 1) three E. prochilos, 2) three E. evelynae and three E. prochilos, 3) three E. evelynae and three E. prochilos plus five E. evelynae or 4) three E. evelynae and three E. prochilos plus five E. prochilos settlers. Therefore, density was 3, 6 or 11 fishes/coral

head (see Table 2-1). Treatments were replicated six times, and replicates were assigned

to coral heads along a gradient of putative habitat quality (quality was based on the initial

26 number of resident Elacatinus on experimental coral heads). Fishes were collected and tagged and stocked to experimental coral heads as in 2001, except fishes were monitored for survival on days 1, 2, 3, 4, 6, 8, 10 and 12. On day 12, all remaining tagged fishes were removed, measured, euthanized and preserved in 95% ETOH.

Experiment 4 - This study provided an estimate of survival of E. prochilos settlers at low density (3 fishes/coral head), which was replicated four times and assigned to coral heads along a gradient of putative habitat quality (quality was based on the initial number of resident Elacatinus on experimental coral heads). Fishes were collected, tagged, stocked to experimental coral heads, and monitored for survival as in Experiment 3.

Experiment 5 - This study consisted of one treatment of three older E. prochilos

(see Table 2-1). As in experiment 4, the treatment was replicated four times and assigned to coral heads along a gradient of putative habitat quality (quality was based on the initial number of resident Elacatinus on experimental coral heads). Fishes were collected, tagged, stocked to experimental coral heads, and monitored for survival as in Experiment

Settlement surveys

To test for a correlation in potential spatial variation in habitat quality and settlement intensity, during 2000 and 2001 settlement was monitored on a daily basis to coral heads that were used in the Experiments 1 and 2 (Table 2-2). After experimental manipulations were conducted in 2000 (i.e., after Experiment 1), settlement was monitored to 24 cleared coral heads on patch reefs for 10 days during a July settlement pulse. New settlers were removed each morning. In 2001, before any experimental manipulations began (i.e., before Experiment 2), settlement was monitored to 36 un- manipulated coral heads (i.e. no removal of fishes had occurred; see Table 2-2) on the

27 backreef for 10 days during a June settlement pulse. New settlers were recorded each morning (i.e., those lacking pigmentation); however, new settlers were not removed.

Analyses

Survival

I used survival analysis (SAS v 8.02) on the pooled data to analyze the effects of habitat quality, density and experiment on the survival of gobies. Survival analysis is concerned with the distribution of lifetimes (Crawley 2002) and is designed for longitudinal data on the occurrence of events, such as deaths (Allison 1995). Survival analysis was particularly appropriate for this study because the error distribution of survival data is not normal, and individuals in the different experiments were surveyed over different time periods with some individuals still alive at the end of the experiments

(i.e., data were interval and right-censored) (Allison 1995, Crawley 2002, Venables and

Ripley 2002). Survival analysis uses maximum likelihood estimates of the survivor function (the probability an individual survives during a given time period) and the hazard function (the probability an individual will die during a given time period or event) of a lifetime variable, T. The lifetime variable, T, is the event time for some particular individual. There are many different models for survival data, and what distinguishes one from another is the probability distribution for T. In this study, I compared two commonly used parametric models (the Weibull model and a special case of the Weibull, the exponential model).

The log-survival time model was logT = γ 0 + γ QQi + γ D Ni + γ E Ei + γ QDQi Ni + γ QEQiEi + γ DE NiEi + γ QDEQi NiEi + σε (2-1)

where γi are the estimated parameters for each covariate (such as N for density, Q for

quality and E for experiment), σ is the scale parameter (σ = 1 for the exponential

distribution (Allison 1995); in the Weibull, σ is unconstrained), and ε has a distribution that is either exponential or Weibull depending on the model being evaluated (Collett

1994). Model selection was based on whether or not the estimated scale parameter was significantly different from 1 (i.e., if the scale parameter was not significantly different from 1, then an exponential model was used). The factors “Habitat Quality” and

“Density” were used as continuous variables whereas “Experiment” was used as a categorical variable in the analyses. “Habitat Quality” was assigned based on the number of resident fishes found on coral heads when initially surveyed at the beginning of each summer and ranged from 1 to 18 fishes per head. “Density” was based on the number of fishes stocked to each experimental coral head and ranged from 2 to 11 fishes per coral head. Other work has shown that fish density (measured on per unit area), and fish number (per coral head), can both have significant effects on fish dynamics (Shima

2001). I analyzed the data on a per coral head and per unit area basis. Both measures of density gave similar results (there was a marginal effect of density [P = 0.08] when

“density” was analyzed as fishes per unit area). However, since coral heads are the most

natural unit of measurement, I will present results only for the number of fishes per coral

head.

Covariation among settlement level and habitat quality

Since settlement rates were monitored during two different years, I first used

Analysis of Covariance (ANCOVA) (PROC GLM) to determine if there was an effect of

year on settlement levels to habitats of different putative quality (i.e., quality was the

29 covariate). Similarly, since settlement occurred to natural substrate that varied in size, I also tested for a relationship between settlement and size of coral heads (PROC REG).

Because there was no significant effect of year (year: P = 0.37; year x habitat quality:

P = 0.68) or of coral size (P = 0.34), I pooled the 2000 and 2001 data (24 coral heads in

2000 and 36 coral heads in 2001; see Table 2-2) and examined the relationship between number of settlers and the initial number of residents (i.e., putative habitat quality) using a linear regression (PROC REG). The total number of settlers and initial number of resident fishes were square root transformed to normalize the data (Sokal and Rohlf

1995).

Attributes of quality

I also measured biological and physical attributes of all experimental coral heads located on the backreef used in 2001 and 2002 (a total of 42 coral heads) to determine if there were any correlates of habitat quality. Specifically, I measured the surface area (see

Wilson and Osenberg 2002 for methods), height, and depth of each experimental coral head. Small clouds of mysid shrimp (Mysidium spp.) have been observed under ledges and in crevices along the reef, and E. evelynae and E. prochilos swim and feed in these clouds (Wilson, personal observation). Therefore, I measured the distance of all shrimp clouds within 15 m of each experimental coral head, using the minimum distance as a measure of shrimp availability. At the end of each summer (i.e., after all manipulations had been completed), I also squirted quinaldine or clove oil around all edges and in all crevices of each coral head, and identified and counted the number of potential competitors (damselfishes, banded coral shrimps, and other goby species) and small predators (blennies, wrasses, crabs, puffers, serranids, and mantis shrimp). All biological variables (i.e., the number of predators, competitors and the minimum distance of shrimp

clouds to coral heads) as well as physical measurements (height, depth and surface area)

of coral heads were included in a canonical discriminant function analysis that was done

separately for each year to examine how these attributes were related to habitat quality.

Habitat quality was made into a categorical variable by dividing quality into six

categories based on the initial number of resident fishes found on coral heads (one being

the lowest and six being the highest level of “quality”). Height, surface area, depth, and

the minimum distance of shrimp clouds were log transformed, and the number of

predators and competitors were square root transformed to normalize the data (Sokal and

Rolf 1995).

Another correlate of habitat quality may be indicated by cleaning rates;

Elacatinus evelynae and E. prochilos are cleaners, removing ectoparasites from other fishes. Therefore, an a priori expectation might be that sites that have higher visitation

rates and higher cleaning levels are sites with higher food resources, and thus, of higher

quality. In 2002 I quantified cleaning rates on six putative “high” and four putative

“low” quality coral heads on three different patch reefs during three different morning

periods (between 6:00 – 7:00am). Early morning corresponded to peak cleaning behavior

of these fishes (K. Clifton, personal communication). Putative “high” and “low” quality

sites were chosen based on the average number of fishes present on coral heads during 15

settlement events and on the average number of settlers these heads received over these

settlement periods. “High” quality sites had, on average, 4.96 ± 1.57 fishes and received

5.8 ± 1.21 settlers per settlement event. “Low” quality sites had, on average, 1.40 ± 0.38

fishes and received 1.75 ± 0.57 settlers per settlement event. The number of visits (the

number of fishes attempted to be cleaned by a goby), cleaning bouts (number of fish

actually cleaned by the gobies), duration of cleaning bouts and species visited and

cleaned were recorded during a 20 minute interval at each low and high quality site.

During each 20 minute interval, one diver observed a low quality site, while another diver

observed a high quality site to control for differences in cleaning rates during a particular

time of day. Coral heads were blocked by reef; however, there was no difference in the

number of visits (F2,5 = 0.07, P = 0.94), cleaning bouts (F2,5 = 0.08, P = 0.93), or duration

of cleaning bouts (F2,5 = 0.62, P = 0.57) among the three patch reefs. Therefore, the reef

term was dropped from subsequent analyses, and t-tests were used to compare if

visitation rates or cleaning behaviors (the number and duration of cleaning bouts) differed

among habitats of different putative quality.

Results

Survival

A survivorship analysis of the full model showed no significant interactions

(Table 2-3a). Therefore, I removed all interaction terms and re-ran the model with only

the main factors included (i.e., density, habitat quality, and experiment).

The simplified model revealed demonstrable effects of all three main factors

(Table 2-3b), and included a scale parameter that was significantly less than 1 (P = 0.05,

Table 2-3b), indicating that an exponential model provided a somewhat poorer fit than the more general Weibull model. Quantitative coefficients from the survival analysis can

be transformed into a more intuitive interpretation; they can be translated into the percent

increase in the expected time to mortality for each one-unit increase in the covariate, xi,

according to the following transformation: 100%(eγi - 1) (see Allison 1995). For

example, each additional increment in quality resulted in a 3.35% decrease in the hazard

rate (Table 2-3b) whereas each additional competitor (i.e., the density term) resulted in a

5.54 % increase in the hazard rate (Table 2-3b). The estimated ratio of the expected

(mean) survival times for categorical coefficients can be estimated by simply taking eγi

(Allison 1995). Thus, survival was highest in Experiment 1, lowest in Experiment 2 and intermediate in Experiments 3, 4, and 5 (Table 2-3b, Figure 2-2c). Survival in

Experiment 2 was almost two thirds (67%) less than in Experiment 1. Survival in

Experiment 3 was approximately half (49% less) of survival in Experiment 1, whereas survival in Experiments 4 and 5 were only about 10% less than survival in Experiment 1.

However, due to the large error associated with the survival coefficients (see Table 2-3), the differences in survival among experiments were not significant. In addition, the lack of the significant interaction between habitat quality and density (Table 2-3a) suggests that while density generally reduced survival, the effect of density on survival was the same across all habitat qualities. Hence, the strength of density dependence did not vary among sites of different quality, and therefore, variation in habitat quality was driven by variation in the strength of density independent processes.

Covariation Among Habitat Quality and Settlement

There was a positive, albeit variable, relationship between habitat quality (the initial number of fishes present on coral heads) and settlement level (F1,58 = 6.20,

P = 0.01, r2=0.11; Figure 2-3). This is of particular importance because it demonstrates the phenomenon (i.e., the correlation between settlement and habitat quality) hypothesized by Wilson and Osenberg (2002) operates in this system and can mask the effect of density dependence (Figure 2-1a).

Attributes of Quality

I used a canonical discriminant function analysis to determine if habitat quality could be explained by coral head attributes. However, there was no clear pattern of the

33 scores for quality on either discriminant function in 2001 or 2002 (Figure 2-4a, b); therefore, neither analysis was able to distinguish between habitat qualities based on the measured biological and physical attributes of coral heads (2001: λ30,102 = 0.39, P = 0.61;

2002: λ30,106 = 0.47, P = 0.83). In addition, the magnitude of these correlates in relation to habitat quality changed from year to year (Figure 2-4a, b), suggesting no temporal consistency in these attributes and quality.

Gobies cleaned other fishes, and these behaviors could have influenced spatial variation in survival. Overall, gobies predominantly cleaned damselfishes, parrotfishes, squirrelfishes, cardinal fishes and surgeonfishes, but occasionally they also cleaned trumpet fish, wrasses, goatfish, and grunts. Interestingly, there were fewer cleaning events at high quality sites than at low quality sites. On average, 5.6 ± 1.54 fishes visited high quality sites, whereas 15 ± 1.54 fishes visited low quality sites (t8=-2.98, P = 0.02).

Similarly, there were fewer cleaning bouts at high quality sites (3.42 ± 1.5) than at low quality sites (8.5 ± 0.96) (t8=-2.86, P = 0.02). However, cleaning duration did not differ among sites of different quality (t8 = -0.30, P = 0.51).

Discussion

This study was designed to test the hypothesis that coral heads varied spatially in habitat quality (as inferred by survival at a fixed density), and to test if settlement covaried with variation in habitat quality, therefore possibly masking the effects of density dependence (see Wilson and Osenberg 2002). I found that some coral heads offered higher per capita survival than others at a common density of gobies (Figure 2-

2a), indicating spatial variation in quality. In addition, settlement was greater to sites of higher quality (Figure 2-3). Indeed, Wilson and Osenberg (2002) observed that fishes

that settled to sites with more gobies survived just as well as fishes that settled to low

density sites, despite deleterious effects of density on survival. These new results

demonstrate that the negative effects of density were offset by the higher quality, thus

homogenizing survival across space. Such a process could obscure the effects of density

dependence and has been termed “cryptic density dependence” by Shima and Osenberg

(2003).

In addition, this work showed differences in quality were driven by spatial

variation in density independent mortality. Density independent mortality was lower in

sites of higher quality (as inferred by the effect of quality in the survival model). The

survival analysis provides tests of the effects of certain processes and estimates of their

importance. Ideally, one should compare these estimates across systems, but two

problems arise. First, few studies provide estimates of the strengths of processes; instead

they focus on detection (see Osenberg et al. 2002). Second, previous studies of fish

survival that focus on estimation have not used survival analysis. Instead, previous

studies (which follow a cohort without replacement of lost individuals) quantify the

strength of density independence and density dependence using the Beverton-Holt model.

The Beverton-Holt model assumes that instantaneous mortality rate (µ) is a linear function of density (N) (see Bolker et al. 2002, Osenberg et al. 2002, Shima and

Osenberg 2003)

µ = α + βN (2-2)

where α is the density independent mortality rate, β is the per capita effect of

conspecifics (which is the per capita strength of density dependent mortality), and the

values of α and β are > 0. If densities decline through time and only beginning and

ending densities of fishes are known, an integrated form of Eq. 2-2 can be used to

estimate α and β (Bolker et al. 2002, Osenberg et al. 2002, Shima and Osenberg 2003).

Although this approach has been used successfully, it has some limitations relative to survival analysis.

Survival analysis was specifically designed to analyze survival data, which is not normally distributed (i.e., the error distribution follows a Weibull or gamma-model distribution), and it is usually right and interval-censored. Secondly, survival analysis estimates the trajectory of survival through time, allowing you to use a time series of survival to determine which models of survival (i.e., exponential, Weibull, etc.) best fits the available data. However, while survival analysis can determine a statistical effect and estimate the effect of a given covariate, it is difficult to directly translate the results into comparable estimates of the strength of density independent or density dependent processes as depicted in a Beverton-Holt approach.

To increase the comparability between the survival analysis and previous studies,

I re-expressed estimates from the survival analysis in a form more comparable to the

Beverton-Holt framework. Survival analysis can be used to estimate the hazard function, which is the instantaneous death rate for an individual surviving to time t (Collett 1994,

Crawley 2002), which is conceptually identical to µ in the Beverton-Holt framework. A

Taylor series approximation can be used to approximate an additive model of mortality

from the hazard function, or log-additive model, to approximate estimates of α and β in

Eq. 2-2 within each habitat quality i (see Appendix A). The additive equivalent of

mortality from the log-additive model is

' ' µi = αi + βi N. (2-3)

' ' The terms αi and βi are defined in Appendix A (Equations A-5 and A-6), the variances

' ' associated with αi and βi are defined in Appendix C (Equations C-1 and C-2). Given that there was no significant difference in survival among experiments (see Table 2-3), an

' ' average experiment effect was used to estimate of αi and βi (see Table 2-5).

' Estimates of density independence from Eq. 2-3 (αi ) showed that 1) density independent processes were almost twice as strong in the lowest quality sites than in the highest quality sites (Table 2-5), 2) in low quality sites, the strength of density independent processes could be almost two orders of magnitude stronger than the per capita strength of density dependence, and 3) in high quality sites, the strength of density independence could be almost an order of magnitude stronger than the per capita strength

' of density dependence (Table 2-5). The estimates of density dependence ( βi = 0.005 to

0.009 ± ~0.006 95% CI) from Eq. 2-3 (see Table 2-5) were approximately one-half to one-third of the strength of density dependence estimated in Wilson and Osenberg (2002)

(β= 0.051 ± 0.0291 95% CI) and Shima and Osenberg (2003) (β= 0.056 ± 0.006), suggesting that, not surprisingly, the strength of density dependence may vary over time

' as well as between systems. However, estimates of βi are from a log additive model

(i.e., survival analysis approach) whereas estimates of β are from an additive model

(Beverton-Holt approach). Thus, in the Beverton-Holt approach, the effect of density independence is added to the effect of density dependence. However, in survival analysis, the effect of density independence is multiplied by the effect of density dependence. Therefore, these two different approaches have different biological

' interpretations of the effects of density (i.e., estimates of βi are not independent from

' estimates of αi in the log additive model; see Appendix A). Therefore, while it is useful to approximate estimates from different approaches into a common currency, we must be aware of the underlying differences in those approximations when making comparisons of parameter estimates.

This study highlights the fact that processes driving variation in habitat quality may differ depending on the system being investigated. Shima and Osenberg (2003) found that variation in density dependence (β in the Beverton-Holt model) drove variation in habitat quality in their system. However, it appears that spatial variation in density independence (α) drove variation in habitat quality in the Elacatinus system.

Therefore, while cryptic density dependence may be ubiquitous among different systems, the mechanism(s) driving it may vary among systems.

Unfortunately, this study was not able to identify any clear correlates of habitat quality. Work in other systems showed significant relationships between habitat types and predator densities (Behrents 1987, Hixon and Beets 1989, Steele 1999, Holbrook and

Schmitt 2003, Shima and Osenberg 2003). This study found no spatial or temporal relationship between predators or competitors and habitat quality. One hypothesis is that potential competitors and predators do not perceive “quality” as gobies do. In addition, some of the most common potential competitors of the gobies were different species of damselfishes that can aggressively guard territories and overlap with live coral where gobies live. However, these damselfishes are found commonly over the reef in both low and high quality habitats, possibly resulting in no significant relationship between the number of potential competitors and habitat quality. In addition, while predation was

38 undoubtedly a mechanism causing post-settlement mortality of gobies, many goby predators tend to be small opportunistic, generalist predators (blennies, wrasses, puffers and small serranids), which were ubiquitous throughout the reef environment. Moreover, the most likely goby predators also lived in the algae along the edge of coral heads

(blennies, crabs, and mantis shrimp). Most predatory events that were observed occurred on the live coral/algae boundary as gobies swam off or approached the edge of a coral head (also see Holbrook and Schmitt 2002 and Webster 2003). Almost all experimental sites had at least one of these predators present in the surrounding algae, making the absence of a relationship between potential predators and habitat quality not surprising.

While there was no relationship between the number of potential competitors and predators and habitat quality, fishes on lower quality habitats exhibited more cleaning behaviors. Increased cleaning could result in increased predation risk if leaving the center of a coral head, regardless of habitat quality, results in higher mortality due to predators, especially since cleaning occurs during periods of low light (dawn and dusk) when predator-induced mortality usually occurs (Holbrook and Schmitt 2002). This would make cleaning a “risky” behavior, resulting in increased mortality risk. In addition, cleaning could be a risky behavior since gobies were observed cleaning species that were also known to eat them (i.e., wrasses, personal observations). If increased visitation rates were determined by a density independent factor (such as position on reef or an attribute of coral heads), and increased visitation rates resulted in increased cleaning behaviors, then variation in cleaning behaviors among sites may affect density independent mortality and result in lower quality sites experiencing lower per capita survival (Figure 2-2a). Alternatively, fishes may be more likely to clean if they are in a

39 place with low survival when they cannot do well otherwise, such as a coral head situated in areas of low flow and subsequent low zooplankton (i.e., food) supply. Thus, given these interesting results, further investigation is needed to better understand how cleaning relates to variation in habitat quality.

Overall, studies of this kind (Wilson and Osenberg 2002, Holbrook and Schmitt

2003, Shima and Osenberg 2003, this study) are particularly important because while previous work in these systems has recognized that variation in habitat types and environmental variables may affect settlement (Tolimieri 1995, Sweatman 1988, Schmitt and Holbrook 1996 ), and documented that patterns of growth and survival of fishes may differ on different habitat types or qualities (Nemeth 1996, Tupper and Boutilier 1997,

Caselle 1999, Shima 1999), to date, few studies have considered how settlement variation may covary with post-settlement processes (except see Steele and Forrester 2002,

Holbrook and Schimtt 2003, and Shima and Osenberg 2003). This is particularly troublesome in survey studies which do not randomize assignment of treatments to experimental sites, and therefore, can not remove confounding effects of habitat quality

(Meekan 1988, Doherty and Fowler 1994a, b, Williams et al. 1994), and can possibly result in biased estimates of density dependence (Wilson and Osenberg 2002, Shima and

Osenberg 2003). Recognizing variation in post-settlement process and covariance between different life stages emphasizes the fact that dynamics driving reef systems are not shaped only by settlement patterns and subsequent density independent loss nor are they driven by density dependent post-settlement processes alone. By considering covariance in parameters that govern the performance of different life stages, we can conceptually link and provide a cohesive framework to evaluate processes that occur

40 during different phases of the life history of organisms (also see Chesson 1998, Hixon

1998, Schmitt et al. 1999, Doherty 2002, Osenberg et al. 2002).

Table 2-1. Summary of coral heads used in survival experiments in 2000, 2001 and 2002. Note: n = number of coral heads. Experimental Coral Heads Experiment Year Area n Size-class Coral Surface Low Medium High of Fishes Species Area of Density Density Density (mm) Coral (cm2) (mean & range S.L.) 1 2000 Patch 24 12.5 Diploria 525-2650 0.003 0.01 reefs (10.1-16.2) strigosa fishes/cm2 fishes/cm2 2 2001 Back- 24 11.7 Montastrea 1775-6725 0.0005 0.001 reef (8.3-16.4) annularis fishes/cm2 fishes/cm2 3 2002 Back- 24 10.5 Montastrea 1775-6725 3 6 11 reef (8.5-12) annularis fishes/coral fishes/coral fishes/coral head head head 4 2002 Back- 4 10.9 Montastrea 2200-3850 3 41 reef (8.8-12) annularis fishes/coral head 5 2002 Back- 4 20.7 Montastrea 3075-6725 3 reef (16.6-27.2) annularis fishes/coral head

Table 2-2. Coral heads surveyed for settlement during a settlement pulse in July of 2000 and June of 2001. Note: n = number of coral heads. Year Area n Coral Species Corals Settlers Cleared Removed? Before Settlement Started? 2000 Patch reefs 24* Diploria Yes Yes strigosa 2001 Back-reef 36ψ Montastrea No No annularis *same coral heads used for survival experiment in 2000 (see Table 2-1). ψincludes coral heads used for survival experiment in 2001 (see Table 2-1) plus additional coral heads that varied in initial Elacatinus density.

Table 2-3. Results of the survival analysis. a) survival analysis coefficients (γ) from full model with P-values for the main effects and their interactions. b) estimates from the survival analysis without interactions and P-values for the main effects. Note: the significant P-value for “Experiment” demonstrates that the survival coefficients for the different experiments were significantly different from zero; however, the confidence intervals for all five estimates overlap. a) Interaction Coefficient Standard X 2 Df P-value (γ) Error

Habitat quality 0.141 -0.07 – 0.35 1.34 1 P = 0.18 Density -0.08 -0.20 – 0.03 1.20 1 P = 0.16 Experiment 2.46 4 P = 0.29 1 3.09 1.54 – 4.62 2 2.78 0.67 – 4.89 3 1.77 0.27 – 3.27 4 1.17 -0.64 – 2.98 5 1.14 -0.16 – 2.44 Scale 0.90 0.83 – 0.98 P = 0.02 Habitat quality 2.86 1 P = 0.10 x Density Habitat quality 0.19 4 P = 0.91 x Experiment Density x 3.48 4 P = 0.18 Experiment Habitat quality 0.69 4 P = 0.71 x Density x Experiment

b) Factor Coefficient Standard Error X 2 Df P-value (γ) Habitat quality 0.034 0.0073 – 0.060 6.27 1 P = 0.01 Density -0.059 -0.10 – -0.019 8.16 1 P = 0.004 Experiment 16.51 4 P = 0.002 1 1.97 1.33 – 2.61 2 1.46 0.83 – 2.09 3 1.59 0.93 – 2.25 4 1.78 0.93 – 2.63 5 1.88 1.28 – 2.49 Scale 0.92 0.84 – 1.0 P = 0.05

Table 2-4. Loadings of the six variables (log transformed) on the first two discriminant functions (DF) for the canonical discriminant function analyses for 2001 and 2002. 2001 2002 Variable Loadings Loadings Loadings Loadings on DF 1 on DF 2 on DF 1 on DF 2 Height 0.25 -0.10 -0.04 -0.16 Depth 0.31 0.52 0.60 -0.36 Surface Area 0.53 -0.47 -0.05 0.62 Minimum distance of shrimp cloud 0.33 0.71 0.62 -0.23 No. of competitors -0.07 0.43 0.09 0.48 No. of predators -0.33 -0.10 0.51 0.49

' Table 2-5. Estimates from the log additive model of the strength of density independence (αi ) and the strength of density dependence ' ( βi ) in Eq. 2-3. • Main Effect γ•* Var(γ•) γ 0 ' ' ' ' e αi S.E (αi ) βi S.E ( βi ) (range from lowest (range from lowest to highest quality) to highest quality) Quality -0.036 0.00012 Density 0.062 0.00048 Average -1.89 0.046 0.15 Low: 0.146 Low: 0.032 Low: 0.009 Low: 0.004 Experiment High: 0.079 High: 0.025 High: 0.005 High: 0.002 *note: estimates of γ• were transformed from coefficients (γ) (see Appendix A) from the survival analysis in Table 2-3b.

Best ) +1 t Good

Poor VENILES ( U J Worst gradient of habitat quality

SETTLERS (t )

Best ) +1 t Good

Poor JUVENILES ( Worst gradient of habitat quality

SETTLERS (t )

Figure 2-1. Graphical representation of survival of settlers at time t to time t+1 over habitats of different quality. a) positive correlation between settlement (solid circles) and habitats quality thus masking the underlying the effect of density (curved lines) and resulting in a linear relationship between juvenile and settler density and subsequent survival (dotted line). b) experimental design to test for variation in quality by examining differences in survival at a common density. The design allowed me to evaluate the effects of density (by comparing survival under low and high density) and putative habitat quality (by comparing survival in different putative quality sites at a common density).

Figure 2-2. The main effects of a) quality, b) density, and c) experiment on the survival of gobies as estimated with survival analysis. The survival function for each 1 (−[t e−γxi ]σ ) main effect was calculated as Si (t) = exp i . Means and 95 % confidence intervals are shown. Note: natural log scale on y-axis.

a) 0

-2

-4 e) iv l A n -6 o i t por

ro -8 P quality 18 quality 14 Ln ( -10 quality 12 quality 9 quality 6 quality 3 -12 quality 1

24681012

Time (days) b) 0

-5

-10 e) -15 Aliv n

rtio -20 2 fishes/head

po 3 fishes/head

ro 4 fishes/head P -25 5 fishes/head ( 6 fishes/head Ln 7 fishes/head -30 8 fishes/head 9 fishes/head -35 10 fishes/head 11 fishes/head

-40 024681012 c) Time (days) 0

-1 e) Aliv

n -2 rtio po ro P

( -3 Ln experiment 1 experiment 2 experiment 3 -4 experiment 4 experiment 5

024681012

Time (days)

49 )

20 l head cora

/ s r 15 e l

lers (sett 10 t

5 Number of Set l a t 0 To

0 2 4 6 8 101214161820 Original Number of Resident Fishes Present (fishes / coral head)

Figure 2-3. The relationship between the original number of fishes present on coral heads (surrogate of habitat quality) during initial surveys in 2000 and 2001 and the total number of settlers to those coral heads during a July 2000 and a June 2001 settlement event (n = 60 coral heads).

50 s ator

a) ea

2 ed distance h ace ar d t f u p o e l ight & pr d sur c he

rimp 1 h

s 1 on 1

4 surface area inant Functi

Discrim 3 2 predators & competitors 5 6

-1 -2 -1 0 1 2 Discriminant Function 2 ce n

b) t 2 a gh i e d dista are h h & rface u pt s mp clou i de

1 shr shrimp cloud distance

on 1 1 i 3 depth & predators

6 Funct 0 5 inant 2 4 surface area height

Discrim -1

-2 -1 0 1 2 Discriminant Function 2

Figure 2-4. Relationship between the mean scores for each habitat quality on the first two discriminant functions in a) 2001 and b) 2002 from the canonical discriminant function analyses. Note: the number next to each symbol represents a category (“level”) of habitat quality (1=low habitat quality and 6=high habitat quality). The arrows represent the loadings of the original variables.

CHAPTER 3 SETTLEMENT DYNAMICS AND COMPETITIVE ABILITY OF TWO SPECIES OF GOBIES, ELACATINUS EVELYNAE AND E. PROCHILOS

Introduction

Understanding the diversity and variability in the distribution and abundance of marine organisms has been the focus of much debate. Historically, there have been two classes of processes that have been argued to structure marine communities: density dependent processes versus chance events (i.e., settlement, or the addition of planktonic larvae to the benthic reef habitat). For instance, spatial and temporal variation in settlement and subsequent density independent loss were thought to be the main factor driving dynamics in reef systems (Doherty 1981, 1991, Doherty and Williams 1988).

Conversely, it has been argued that post-settlement processes (such as density dependent mortality due to habitat limitation, food resources and/or predation) can re-shape initial settlement patterns and thus be key factors driving the distribution and abundance of marine organisms (Jones 1987, Olafsson et al. 1994, Forrester 1995, Steele 1997b, Hixon and Carr 1997, Webster and Hixon 2000). More recently, however, the accepted paradigm is that settlement variation and density dependence work in concert to affect population dynamics of reef fishes (Warner and Hughes 1988, Caley et al. 1996, Chesson

1998, Hixon 1998, Schmitt et al. 1999, Osenberg et al. 2002)

While these dynamics include intraspecific interactions as well as interspecific interactions, most reef fish studies have concentrated on a single species (except see

Hixon and Carr 1997, Forrester and Steele 2000, Stewart and Jones 2001, Webster 2002,

51 52

Holbrook and Schmitt 2003). Since reef fish communities are known for their high degree of diversity (Smith and Tyler 1972, Emery 1978, Talbot et al. 1978), sometimes supporting hundreds of species within a given local area (i.e., patch reef) (Goldman and

Talbot 1976), settlement variation of different species and intraspecific and interspecific competitive interactions may play important roles in maintaining such diversity. Thus, understanding the ecology of different species is ultimately tied to understanding mechanisms that allow multiple species to coexist and, therefore, maintain diversity.

Classic niche partitioning has historically been viewed as the primary mechanism promoting coexistence of multiple species (MacArthur 1972, Ricklefs 1973, Pianka 1974,

Schoener 1974, Anderson et al. 1981). However, it has also been argued that many coral reef species, especially reef fishes, are generalists and exhibit little resource partitioning in either food or living space (Sale 1977, 1978; but see Sale 1974, Bell and Galzin 1984,

Sale et al. 1984, Wellington 1992, Tolimieri 1995 for examples of differences in habitat use). Thus, many reef fishes, especially those within habitat types, have been viewed as ecologically similar, suggesting that classic niche partitioning may not be a major factor contributing to coexistence in marine systems (Sale 1977, 1978). Indeed, if species have similar competitive abilities then classic niche partitioning theory cannot explain species coexistence reef fish communities.

However, the lottery model of coexistence suggests that ecologically similar species are able to coexist in the absence of habitat partitioning due to dispersive larvae, which compete for the random allocation of space over time (Sale 1977, 1978). This model was later revised and formalized by Chesson and Warner (Chesson and Warner

1981, Warner and Chesson 1985) and was extended to plant communities (Chesson and

Huntly 1989, 1993, 1997, Hubbell 1979, 1997, 2001). Chesson and Warner’s work showed that coexistence is promoted by temporal variation in the supply of larvae to a given area. Their work demonstrated that settlement variation, in addition to overlapping generations, can promote coexistence; however patterns of settlement variation had to differ between species.

These lottery-type models of coexistence assume that different species have equivalent competitive abilities. Competitive ability can be decomposed into competitive effect (ability to suppress other individuals) and competitive response (ability to avoid being suppressed: Goldberg and Werner 1983, Goldberg and Fleetwood 1987, Goldberg and Landa 1991). The strength of the effect and the response of each species relative to other species can influence whether two species coexist (Goldberg and Landa 1991).

Because competitive effects and responses can vary according to size/age class, we need to consider age-structure as well as species assemblage. This is particularly true in marine systems where new individuals (or settlers) enter the reef habitat and “settle” onto the benthic habitat (i.e., transform from a larvae to small, juvenile fishes or settler) where they encounter not only other settlers, but also older residents.

Thus, in order to better understand processes that structure reef fish communities, we need to identify mechanisms that maintain diversity. While much work has been done on settlement patterns of different species (Victor 1983, Cowen 1985, Sweatman

1988, Doherty 1991, Booth 1992) and many studies have quantified competitive interactions (or the lack thereof) among reef fishes (Doherty 1981, 1983, Doherty and

William 1988, Doherty and Fowler 1994, Steele 1997b, Schmitt and Holbrook 1999,

Shima 2001, Wilson and Osenberg 2002), little work has addressed how spatial and

54 temporal patterns of settlement, habitat use, and competition combine to maintain coexistence among species in marine systems (except see Chesson and Warner 1981,

Warner and Chesson 1985, Chesson 2000b, Munday 2004). Therefore, in this study I described patterns of variation in habitat use and settlement of two species of marine gobies (Elacatinus evelynae and E. prochilos). I also investigated the competitive effects and responses using a “target/neighbor” design in which I varied the density, species and age class of neighbors and monitored survival of target individuals (Goldberg and Werner

1983, Olson et al. 1995). My specific goals were 1) to determine if E. evelynae and E. prochilos differed in their use of available coral substrates; 2) to quantify the spatial and temporal patterns in settlement and determine if the two species exhibited correlated responses to the environment; and 3) to estimate the relative competitive effects and responses and to ascertain if they differed between the two species. Investigating the competitive ability of the two species and settlement variability can help gain insight into the mechanisms potentially driving coexistence in this system.

Methods

Study System

Elacatinus evelynae and E. prochilos are small (< 34 mm standard length, SL) cleaning gobies that can remove ectoparasites from larger fishes (Colin 1975). The two species co-occur down to depths of 50 m on live coral in St. Croix of the U.S.V.I.

Settlement of each species begins as early as the last quarter moon, peaks around the new moon, and continues as late as the first quarter moon (a period as long as two weeks, but typically much less). I conducted settlement surveys on a series of patch reefs located in

Tague Bay on the northeast coast of St. Croix during the summer months of 1996, 2000,

2001, and 2002 for a total of thirteen settlement episodes. I also conducted a competition

55 experiment, during the summer of 2002 along the backreef in Tague Bay to quantify the competitive effects and responses of two size classes of the two species.

Settlement Patterns

In order to assess whether or not the two species used the environment in the same way, I first examined temporal covariation in settlement of the two species. Within each month I summed settlement for each species across all coral heads on the three patch reefs. Then I determined the correlation in settlement for the two species across the

13 months that I had settlement data.

I also determined spatial covariation in settlement by exploring the correlation of settlement of the two species to the same coral heads for each of the 13 months (I did a sequential Bonferroni test (Holm 1979) to adjust P-values for the multiple correlations).

Another way to determine spatial covariation in settlement between the two species was to use an Analysis of Variance (ANOVA) on the natural log transformed settlement data to partition the variance components due to the interactions of species by space (i.e., spatial variation), species by time (i.e., temporal variation) and species by time by space

(i.e., spatiotemporal variation) (Chesson 1985). I added 0.1 to coral heads that did not receive new settlers.

I next examined patterns of habitat use by calculating the preference (αi,t) of settlers for different coral species in each year (1996, 2000, 2001, and 2002) on three patch reefs in Tague Bay. Because coral cover was similar between years (Wilson unpublished), I simply summed the settlement to different substrates across all times within a year and compared this to the coral availability using Manly’s index (Manly

1974)

ui,t ei,t αi,t = (3-1) k u j,t ∑ j=1 e j,t where αi,t is the preference for substrate i in year t, k is the number of substrate categories, ui,t is the total number of settlers of a given species for a given year using substrate i, and ei,t is the availability of substrate i (i.e., the proportion of surface area of a particular coral species out of the total surface area available of live coral). I restricted my analysis to a six meter band around the outer edge of each patch reef (i.e., from the edge of the patch reef to four meters onto the reef and from the edge of the patch reef to two meters off the reef) because most fishes settled close to the edge or just off the patch reef (see Wilson

1998). Coral species never used by the gobies (e.g., Favia fragum, Porites porites) were not included in the analysis. I averaged preference over the four years to determine an average preference for a given settlement substrate for each species.

Experimental Design

I experimentally evaluated the competitive effect and competitive response of the two gobies using a “target/neighbor” design (Goldberg and Werner 1983, Olson et al.

1995) in which I monitored the survival of targets across five neighbor treatments: 0 neighbors or five neighbors that were one of the two species (E. evelynae or E. prochilos) and one of two age classes (settlers or older fishes) (see Table 3-1). The targets consisted of 3 E. evelynae and 3 E. prochilos settlers. "Settlers" were < 16 mm (which corresponds to fishes that have settled within the previous two weeks) and “older fishes” were > 16 mm (which corresponds to fishes that had settled more than two weeks previously). In addition, there was a sixth treatment that consisted of only 3 E. prochilos settlers.

Experimental fish numbers were chosen to bracket the natural range in competitive

57 environments: the average mean crowding index (Lloyd 1967) based on surveys of coral heads in 2001 was 7.06 ± 0.11 S.E. (range: 1 to 16), which indicated that a goby, on average, experienced six other Elacatinus on a coral head. By comparing how each species in the target assemblage survived under the different treatments that varied in species and age class composition, I explicitly tested if these two species had similar competitive effects (i.e., ability to suppress other individuals). By comparing survival of each species in the target assemblages when exposed to the same neighbor assemblage, I tested if settlers of the two species had similar competitive responses (i.e., ability to avoid being suppressed).

My previous work in this system showed that coral heads varied in the strength of processes that affected density independent survival (Wilson and Osenberg 2002, Chapter

2). In addition, higher quality sites (those with the weakest density independent mortality) also received greater levels of settlement and therefore had higher resident densities. Therefore, I blocked treatments by the initial number of Elacatinus on the coral head, a correlate of habitat quality (Chapter 2). I used Montastrea annularis coral heads (the most preferred substrate by these species; see Wilson 1998) and conducted several surveys in which I counted the initial number and age class of gobies. Habitat quality was estimated by the average number of Elacatinus initially present in these surveys. All resident gobies were then removed by hand using small aquarium nets and clove oil. Habitat quality was used as a covariate in this study, and treatments were replicated six times along a gradient of habitat quality.

Fish of each species were collected from Montastrea annularis heads in an adjacent bay (Boiler Bay) and immediately taken to the backreef experimental sites in

Tague Bay where they were measured, tagged with an acrylic paint color underwater (to differentiate “target” from “neighbor” and the two age classes), and then released onto the appropriate coral head. Each coral head was stocked with fishes for two consecutive days (to rectify initial handling losses). The second day of stocking was considered "day

1". Coral heads were then surveyed on days 2, 3, 4, 6, 8, 10 and 12, and any missing tagged individuals were replaced during each survey to maintain densities. Replacement fishes were tagged with different colors to differentiate them from the original fishes.

Surrounding areas were searched for tagged fishes that may have moved from experimental sites. Because few tagged but missing fishes (12 out of 318) were found away from experimental sites, I assumed the disappearance of tagged individuals represented mortality. Any tagged fish remaining on day 12 were collected, measured, euthanized, and preserved in 95% ETOH.

Analyses

I explored the initial patterns of survival of the targets in each treatment by estimating longevity or the average number of days individuals of each species in the target assemblage survived in a given treatment (methods in Wilson and Osenberg 2002) blocked by habitat quality (1=lowest quality or coral heads with the fewest resident

Elacatinus and 6=highest quality or coral heads with the most resident Elacatinus). I found that survival of E. evelynae and E. prochilos in the target-only treatment (treatment

2 in Table 3-1) in the three highest quality levels (i.e., levels “4,” “5,” and “6” in Figure

3-1) was significantly lower than expected (P = 0.009). In fact, the fishes on these three coral heads had the poorest survival despite being on putatively high quality sites and being one of the treatments with the lowest densities (Figure 3-1). These results are inconsistent with previous work in this system that showed that survival decreased with

59 increasing density (Wilson and Osenberg 2002, Chapter 2) and that putatively high quality sites yielded higher survival (Chapter 2). Therefore, I concluded that these three coral heads were outliers, and I excluded them from all the following analyses.

Competitive Ability

I used a series of survival analyses (SAS v8.02) to determine the survival of E. evelynae and E. prochilos in the target assemblages under the different treatments across different habitat qualities. In all analyses I used a parametric model with a Weibull distribution. The survival analyses estimated the coefficients, γ, for each covariate, x, in a given model. The generalized log-survival time model for the Weibull models was

logT = γ 0 + γ 1x1i + γ 2 x2i + γ 12 x1i x2i + ...γ p x pi + σε (3-2) where γ0 is the intercept, σ is the scale parameter (assumed constant across treatments), and ε has a Weibull distribution (Collett 1994, Allison 1995) (note: if σ=1, this Weibull model simplifies to the exponential model).

In the first survival analysis I determined if the survival of E. evelynae and E. prochilos in the target assemblage was affected by density. There were six main factors in the model: “habitat quality,” “evelynae.settlers,” “evelynae.older,” “prochilos.settlers,” and “prochilos.older,” and a “target” factor. The first five factors were used as continuous variables in the model, where habitat quality was the average number of

Elacatinus initially present on experimental coral heads (included in the analysis) and ranged from 1.5 to 16 fishes/coral head. The four factors, which estimated a density effect and distinguished per capita effects of species and age class (i.e.,

“evelynae.settlers,” “evelynae.older,” “prochilos.settlers,” and “prochilos.older”), were the number of fish per species of a given age class on a coral head (see Table 3-1). The

“target” factor (“prochilos” or “evelynae”) was used as a categorical variable and determined whether there was a difference in each species’ response (i.e. survival) to the different neighbor assemblages.

However, comparing survival of treatment 1 (i.e., “prochilos.only”) to survival of targets in treatments 3-6 to determine competitive response and effect of the different neighbor assemblages confounds species and age class effects. Therefore, I ran a second analysis, which only included treatments 3-6 (see Table 3-1), to directly estimate the competitive effect and competitive response of each species for the different neighbor assemblages while accounting for habitat quality. The four neighbor assemblages in treatments 3-6 (see Table 3-1) formed a cross-classified design with species (E. evelynae or E. prochilos) crossed with age class (“settlers” or “older fishes”), and these two main factors were used as categorical variables in the model. The factor “target” was also used as a categorical variable and compared each target species’ response (i.e. survival) to the same neighbor assemblage, thus measuring each species competitive response. As in the previous analysis, habitat quality was a continuous variable and ranged from an average of 1.5 to 16 fishes initial resident Elacatinus per coral head.

Results

Settlement Patterns

Settlement is known to be extremely variable over time for reef fishes; however this temporal variation can be different for each species. Indeed, settlement for E. evelynae and E. prochilos within a given month was not strongly correlated for settlement data pooled over all years (r = 0.11; Figure 3-2). This suggests that a “good” settlement event for one species was not necessarily a “good” event for the other species. However, when each year is examined separately, in three of the four years, there was a positive

61 correlation between settlement of the two species (i.e., 2000, 2001, 2002; Figure 3-2). In

1996, however, where there was also much more variability in settlement, there was a negative correlation between settlement of the two species (Figure 3-2). Taken together, these results suggest that the two species potentially have differential responses in reproduction and/or settlement to temporal variation in the environment.

To determine if the two species spatially used the environment in similar ways, I examined if the two species settled to the same coral heads and if they preferred the same species of coral for settlement substrate. There was a significant correlation between settlement of E. evelynae and E. prochilos to coral heads during each month; however, the correlation for each month was low, ranging from 0.238 to 0.544. Yet, while the correlations were significant, demonstrating that both species of gobies settled to some of the same coral heads during each month, their spatial use of the environment was not identical (Table 3-2). However, the ANOVA on the log-transformed settlement data demonstrated that the settlement surveys did not reveal any significant spatial or spatiotemporal variation in settlement between the two species (Table 3-3), suggesting that the two species predominantly use the same settlement sites. In addition, only temporal variation in settlement between the two species was significant (Table 3-3), further suggesting that the two species may have different responses to temporal variation, rather than spatial variation, in the environment.

While the two species may predominantly use the same coral heads, they may differ in their micro-habitat preferences (i.e., the differential use of rarer species; see Eq.

3-1). This could potentially lead to microhabitat specialization (in terms of coral species) for the two goby species. Unfortunately, preferences for different coral species were

62 variable for the two goby species, and there was no clear and consistently highly preferred coral species for either goby species (Figure 3-3). Within patch reefs, however, species tended to prefer the same species of coral; the most preferred coral by both species was Montastrea cavernosa on reef 5 (Figure 3-3a). However, overall, M. cavernosa was more preferred by E. evelynae, M. annularis was more preferred by E. prochilos with only E. prochilos settling to S. michilini on reef 5 (Figure 3-3a, Table 3-4).

Within reefs 7 and 18 both species had similar preference patterns (Figure 3-3b, c), except only E. evelynae settled on D. labyrinthiformis on reef 18 (Figure 3-3c). In general, more highly preferred coral species consistently received higher numbers of settlers (except for D. strigosa on reef 7 and M. cavernosa on reef 18; Table 3-4, Figure

3-3). Thus, there was no strong evidence for segregation of the two species amongst different species of corals.

Competitive Ability

To test for 1) an effect of density and 2) to estimate the per capita effects of each species, I first included all main factors (“habitat quality,” “evelynae.settlers,”

“evelynae.older,” “prochilos.settlers,” and “prochilos.older,” and a “target” factor) and all their interactions in the survival model. I then excluded all non-significant interactions (P > 0.10) and re-ran the model. The refined model showed that there was a significant positive effect of habitat quality (i.e., survival was higher on higher quality sites) (Table 3-5, Figure 3-4). In addition, there was a significant negative effect of density of older and settler E. prochilos neighbors. However, Elacatinus prochilos and

E. evelynae targets’ survival was lowest with older E. evelynae neighbors, due to a significant interaction between habitat quality and older E. evelynae (the effect of older

E. evelynae gets disproportionately larger as habitat quality increases) (Table 3-5, Figure

3-4). But, E. prochilos and E. evelynae targets also experienced low survival with older

E. prochilos in the lowest habitat quality (Table 3-5, Figure 3-4a, b). Finally, the highest survival occurred at the lowest density: i.e., in the three E. prochilos settlers-only treatment (Figure 3-4b), thus demonstrating competition decreased with decreasing density.

Another way to interpret quantitative survival coefficients is to translate them into per capita effects on the instantaneous mortality rate (i.e., hazard rate). That is, the survival coefficients can be translated into the percent increase in the expected time to mortality for each one-unit increase in the covariate, xi, according to the following transformation: 100%(eγi - 1) (see Allison 1995). For example, each additional E. evelynae settler resulted in a 4.46% increase in the hazard (i.e., increasing E. evelynae increased mortality rate). Similarly, each additional older E. evelynae resulted in a 1.69% increase in the hazard rate (note that comparing the per capita effect of older E. evelynae with other effects is difficult due to an interaction with habitat quality). However, E. prochilos resulted in the largest increase in the hazard where each additional E. prochilos settler and older E. prochilos resulted in a 9.37% and a 12.19% increase in the hazard rate, respectively.

However, in the above analysis, I was not able to make a direct comparison of competitive effects and competitive response; the inclusion of the “prochilos.only” treatment confounded species and age class effects. Thus, I made an explicit comparison of the competitive effects and responses of each species by only including treatments 3-6

(see Table 3-1) in the second analysis. As in the previous analysis, I first ran the model with all the main factors (“habitat quality,” “age class,” “species,” and a “target” factor)

64 and their interactions. I then excluded all non-significant interaction terms (P > 0.10) and re-ran the model. The refined model demonstrated no significant effects of age class or neighbor species on either target’s survival (Table 3-6, Figure 3-5). Therefore, the two species (and age classes) had similar competitive effects. There was also a significant positive effect of quality for E. evelynae targets. However, due to a significant interaction between quality and E. prochilos targets, higher quality did not translate into higher survival for E. prochilos targets (Table 3-6, Figure 3-5c, d). In addition, E. evelynae and E. prochilos targets had similar survival when exposed to the same neighbor assemblage (P = 0.23; Table 3-6; Figure 3-5). Thus, the two species had similar competitive responses.

Discussion

Elacatinus evelynae and E. prochilos showed similar spatial settlement patterns

(Table 3-2), have similar planktonic larval durations (Chapter 5), substrate preferences

(Figure 3-3) and competitive effects (Table 3-5 & 3-6). The species also have similar color patterns, similar body types, and feed on similar prey (i.e., zooplankton and ectoparasites: Colin 1975, Wilson, personal observation). Thus, these two species are ecologically and morphologically similar. Interestingly, past work done by Colin (1975) had suggested that these two species may be hybridizing in the field. However, recent genetic work (based on the conserved region of the first 400 bp of cytochrome b) showed no shared haplotypes between E. evelynae and E. prochilos from St. Croix. Indeed, the two species from St. Croix are approximately 9% divergent, which is about the same level of divergence that occurs Caribbean-wide (M. Taylor, personal communication).

Consequently, there is no genetic evidence for hybridization (and populations of the blue/yellow color morphs of E. evelynae found at Barbados and Curaçao and separated

65 by 1000 km have been estimated as being isolated from each other for 75,000 to 103,000 years and are only 3.04% divergent; Taylor and Hellberg 2003). As a result, I have concluded that the two species have likely coexisted for many generations since divergence and secondary contact.

Yet, despite the substantial amount of time since secondary contact, this study has demonstrated that the two species had similar competitive effects and similar competitive responses (however, I acknowledge the lack of power in this study indicated by the large confidence intervals on the survival parameters – Table 3-6). How, then, do these morphologically and ecologically similar species coexist? Competitive equivalence alone will not lead to coexistence; rather competitively equivalent species should go through a very slow, random walk to competitive exclusion (Hubbell 1979, 1997). While it is possible that E. evelynae and E. prochilos may be undergoing a random walk to exclusion, I think it is valuable to explore if other factors may contribute to their long- term persistence, such as exploring what factors might provide the requisite “niche” for coexistence (Chesson 1991).

Given the two species have different temporal settlement patterns (Figure 3-2), suggesting differential responses to the environment, these two species might be exhibiting “temporal partitioning” of resources (Warner and Chesson 1985). For example, if peak reproduction occurs for the two species at different times, then coexistence can occur because each species can take advantage of resources during a favorable subsequent settlement event (i.e. high settlement after peak reproduction) when settlement density of other species is low. This would lessen competition for resources between species during particular settlement events (see Warner and Chesson 1985,

Chesson 2000a). However, I only have settlement data during summers of four different years; ideally settlement data over longer time periods with estimates of species specific female fecundity and better estimates of species specific adult longevity will give better insights into how these species coexist.

However, many marine ecologists have argued that coexistence in open systems can result from fixed levels of settlement into local populations (Warner and Hughes

1985, Hixon 1998). No doubt, this explains local persistence of many species. However, this becomes a circular argument if extended to the larger scale without explaining what maintains settlement at these larger scales. Given the high level of species diversity on coral reefs, we must consider how other processes might contribute to their coexistence.

In particular, instead of just focusing on settlement variability, we need to consider 1) how variation in settlement of different species is correlated over time and space and 2) what processes affect these patterns in the post-settlement environment. For example, the

“storage effect,” which is a revised lottery model, predicts stable coexistence depending on the relationship between settlement variation and the strength of competition in the post-settlement environment (Chesson 2003). More specifically, ecologically similar species can coexist if they respond differently to the common varying environment (in terms of reproduction and the magnitude of subsequent settlement), and if the relationship between settlement variation and the strength of competition in the benthic environment differs for different species (Chesson 2000a, 2003). Therefore, settlement variation and competition in the post-settlement environment can play important roles in species coexistence; however, it is the covariation of these processes, and how this

67 covariation differs among particular species, which is critical for the diversity of reef fishes (Chesson 1985, 2003).

This system is particularly promising for studying how settlement variation and competition can interact to maintain species diversity (see Chapter 6). Settlement of these species is variable through time (Figure 3-2), as well as there is competition in the post-settlement environment (Figure 3-4). However, variation in post-settlement processes leading to variation in habitat quality has not been considered within the mechanistic framework of coexistence. Is a differential response to habitat quality (i.e., the “common” varying environment) by the two species an important component of coexistence for these species? Or, does the mechanism which determines variation in habitat quality affect the two species differently (i.e., variation in habitat quality is not the

“common” varying environment that the fishes are responding to)? However, it should be noted that variation in habitat quality is due to variation in density independent processes in this system, where density dependent processes are more uniform across space (Chapter 2). Since theory predicts (e.g. Chesson 2003) that coexistence between similar species depends on the relationship between species’ settlement patterns and the strength of competition in the benthic environment, perhaps variation in the strength of density independent mortality will not be important for coexistence. Rather, if species differ in their response to habitat quality, then maybe the mechanisms driving variation in the strength of density independent mortality (i.e. predation) affect the two species differently (e.g., if differences in predation among sites drives variation in density independent mortality as is suggested in Chapter 2, then maybe E. evelynae are more susceptible to predation than E. prochilos, resulting in E. evelynae “responding” more to

68 variation in habitat quality). Conversely, if E. evelynae is the more abundant species on average (see Chapter 6), then such a scenario might suggest more “classic” mechanisms of coexistence where similar competitors can coexist through frequency-dependent predation or disturbance (Hutchinson 1959, Connell 1978). In either case, further empirical investigation in these types of systems will give us better insight into mechanisms maintaining complex and diverse coral reef fish communities.

Table 3-1. Experimental design for competitive ability experiment. Each treatment was replicated six times, and treatments were placed along a gradient of habitat quality (ranging from an average of 1.5 to 16 resident Elacatinus fishes). Treatment Target Assemblage Neighbor Assemblage E. evelynae Older E. prochilos Older No. of Fishes / E. prochilos E. evelynae settlers E. evelynae settlers E. prochilos Coral Head 1 3 0 0 0 0 0 3 2 3 3 0 0 0 0 6 3 3 3 5 0 0 0 11 4 3 3 0 5 0 0 11 5 3 3 0 0 5 0 11 6 3 3 0 0 0 5 11

Table 3-2. Correlation between settlement of E. evelynae and E. prochilos to the same coral heads on three patch reefs (#5, 7 & 18) in Tague Bay of St. Croix over four different years: a) 1996, b) 2000, c) 2001, and d) 2002, and n is the number of coral heads. a) 1996 E. prochilos n = 147 May June July E. evelynae May 0.238 P < 0.0037 June 0.382 P < 0.0001 July 0.584 P < 0.0001

b) 2000 E. prochilos n = 151 June July August E. evelynae June no E. prochilos settlement July 0.425 P < 0.0001 August 0.473 P < 0.0001

c)2001 E. prochilos n = 169 June July August E. evelynae June 0.477 P < 0.0001 July 0.363 P < 0.0001 August 0.544 P < 0.0001

d) 2002 E. prochilos n = 181 June July August September E. evelynae June 0.371 P < 0.0001 July 0.299 P < 0.0001 August 0.409 P < 0.0001 September 0.289 P < 0.0001

Table 3-3. Analysis of variance of the natural log of settlement for the two species on three patch reefs over 13 settlement events. “Species” was a fixed factor whereas all other factors were random. Note: estimates of variance components for “species x space” and “species x time x space” were originally negative. Negative estimates of variance components can result when the analysis of variance method is used for variance estimation. However, since variances are nonnegative values, I assumed that the negative estimates indicated that the variance components were really zero, and set the variances of species by space and species by time by space equal to 0; see Montgomery 1997. a) Source DF Mean Square F-value P-value Variance

Model 3093 1.12 1.06 0.38 Error 78 1.06

Species 1 4.35 0.27 0.62 Space 118 8.37 12.07 <0.0001 Time 12 15.73 0.96 0.53

Species x 12 16.34 22.93 <0.0001 0.1314 Time Species x 118 0.69 0.98 0.55 0 Space Species x 2832 0.70 0.67 0.99 0 Time x Space

Table 3-4. Average settlement of E. evelynae and E. prochilos over four years to different species of coral to three separate patch reefs. Note: “-“ signifies that a species of coral was not present on a particular patch reef. Patch Reef Coral Species Average E. evelynae Average E. prochilos settlement (± SE) settlement (± SE)

5 D. clivosa - - D. labyrinthiformis 0 0 D. strigosa 0 0 M. annularis 2 ± 1.68 10.5 ± 2.18 M. cavernosa 34.25 ± 20.25 21.25 ± 3.33 Millepora spp. 0 0 P. asteroides 0.25 ± 0.25 0.50 ± 0.50 S. michilini 0 0.25 ± 0.25 S. radians - - S. siderea 0 0

7 D. clivosa - - D. labyrinthiformis - - D. strigosa 2.5 ± 1.84 4.75 ± 0.47 M. annularis 16.75 ± 13.79 9.5 ± 2.90 M. cavernosa 0 0 Millepora spp. 0.5 ± 0.28 0.25 ± 0.25 P. asteroides 8.75 ± 6.76 11.25 ± 4.64 S. michilini - - S. radians - - S. siderea 4 ± 3.08 1.25 ± 0.25

18 D. clivosa 5.75 ± 4.11 4.5 ± 0.5 D. labyrinthiformis 0.5 ± 0.5 0 D. strigosa 25.25 ± 19.61 29.25 ± 17.58 M. annularis 19 ± 14.0 6 ± 1.08 M. cavernosa 4.75 ± 3.77 3 ± 1.47 Millepora spp. 0 0 P. asteroides 0 0 S. michilini - - S. radians 1.25 ± 1.25 0.5 ± 0.5 S. siderea 23 ± 12.02 12.75 ± 3.25

Table 3-5. Results from survival analysis to determine effect of density. Note: “Quality” and “Neighbor Species Per Capita Effects” are continuous variables whereas “Target Species Response” is a categorical variable. Main Effect Coefficient 95 % CI X 2 Df P-value (γ) Quality 0.088 0.043 – 0.133 5.13 1 <0.0001

Target 0.031 1 0.87 Species Response E. evelynae 1.57 1.07 – 2.07 E. prochilos 1.59 1.34 – 1.83

Neighbor Species Per Capita Effects E. evelynae -0.046 -0.103 – 0.011 0.036 1 0.87 settlers

Older E. -0.017 -0.137 – 0.103 10.3 1 0.11 evelynae

E. prochilos -0.098 -0.027 – -0.027 1.65 1 0.005 settlers

Older E. -0.13 -0.20 – -0.061 11.89 1 0.0001 prochilos

Quality* -0.026 -0.044 – -0.008 7.55 1 0.0041 Older E. evelynae

Scale 0.76 0.68 – 0.84 <0.0001

Table 3-6. Results from survival analysis to determine competitive effects and competitive responses. Note: “Quality” is a continuous variable whereas “Age class Effects”, “Neighbor Species Effects”, and “Target Species Response” are categorical variables. Main Effect Coefficient 95 % CI X 2 Df P-value (γ) Quality 0.071 0.011 – 0.13 8.60 1 0.003

Age class Effects 1.84 1 0.18 Settlers 0.89 0.39 – 1.39 Older Fishes 0.46 0.21 – 0.71

Neighbor Species 2.97 1 0.085 Effects E. evelynae 1.67 1.17 – 2.17 E. prochilos 0.89 0.39 – 1.39

Target Species 1.46 1 0.23 Response E. evelynae 0.35 -0.15 – 0.85 E. prochilos 0.89 0.39 – 1.39

Quality*Neighbor 0.12 0.06 – 0.18 11.14 1 0.0008 Species

Quality*Target -0.088 -0.148 – -0.028 5.84 1 0.016 Species

Scale 0.71 0.58 – 0.84 <0.0001

a) E. evelynae

6 "high" density (11) "medium" density (6) (targets only) 5

4 y t i gev n

o 3 L an

Me 2

0 01234567 Index of Habitat Quality (1 = low quality, 6 = high quality)

b) E. prochilos

"high" density (11) "medium" density (6) 7 (targets only) "Low" density (3) (E. prochilos only) 6

5 y t vi 4 nge Lo

n 3 Mea 2

0 01234567 Index of Habitat Quality (1 = low quality, 6 = high quality)

Figure 3-1. Mean longevity of targets (the average number of days targets remained alive on coral heads) for the two species on coral heads of different quality. Designation of quality was based on the number initial residents found on coral heads. Quality ranged from “one” to “six” (“one” being heads with the fewest residents initially present and “six” being coral heads with the highest number of residents initially present. a) mean longevity of E. evelynae targets with either neighbors present (“high” density) or absent (i.e., “targets only”=“medium” density), and b) mean longevity of E. prochilos targets with either neighbors present (“high” density) or absent (“medium” density) or E. prochilos only present (“low” density). Means and standard errors shown.

160 1996 2000 140 2001 2002 120 ttlement e 100 S

hilos 80 proc . 60 E

40 Monthly 20

0 0 50 100 150 200 250

Monthly E. evelynae Settlement

Figure 3-2. Variation in settlement over time. Total monthly settlement on three patch reefs in Tague Bay for E. prochilos versus total monthly settlement for E. evelynae within four different years (1996, 2000, 2001, 2002). Linear regression was fitted for each year separately (1996: y = 160.87-0.45x; 2000: y = -27.46+4.05x; 2001: y = 22.23+0.39x; 2002: y = 15.52+2.09x).

Figure 3-3. Average preference of settlers of each goby species for different coral species on three patch reefs in Tague Bay over four years (1996, 2000, 2001, 2002). ui,t ei,t Preference calculated according to αi,t = ; see Eq. 3-3 in text: k u j,t ∑ j=1 e j,t a) corals present on patch reef 5 (k = 8), b) corals present on patch reef 7 (k = 6), and c) corals present on patch reef 18 (k = 9). The dotted lines on each panel give the expected preferences (α = 1/k) assuming random use of corals. ND = no data available because the coral species did not occur on the particular patch reef, and “0,0” indicates no preference. Mean and standard errors are shown.

a) Reef 5 E. evelynae 1.0 E. prochilos 0.9

) 0.8 i α (

e 0.7 c n 0.6 ere f e r 0.5 e P 0.4 erag 0.3 Av 0.2 0.1 ND 0,0 0,0 0,0 0 ND 0,0 0.0 a h. a is a p. s ni s a os t os ar os p de ili n re iv in g l n s i h ia e cl yr ri nu er ra ro ic ad d . ab st n v o te m . r . si D . l . . a ca p as . S S D D M . ille . S M M P Coral Species b) Reef 7 0.8 E. evelynae 0.7 E. prochilos ) i 0.6 α ( e c 0.5 n ere f 0.4

ge Pre 0.3 era

Av 0.2

0.1 ND ND 0,0 ND ND 0.0 a h. a is a p. s ni s a s t os ar os p de ili an re ivo in g l n s i i e cl yr tri nu r ra ro ich ad id . ab s n ve o te m . r . s D . l . . a ca p as . S S D D M . ille . S M M P

Coral Species c) Reef 18 0.6 E. evelynae E. prochilos 0.5 ) i α 0.4 ce ( en

ef 0.3 r e P ag r 0.2 e v

A 0.1

0 0,0 0,0 ND 0.0 a . a is . s i s a s th s r sa pp e ilin n re ivo in go la no s id ia e cl yr ri nu er ra ro ich ad d . ab st n v o e m . r . si D . l . . a ca p ast . S S D D M . ille . S M M P Coral Species

Figure 3-4. Survival of targets according to the main effects in the survival analysis −γQ xQ,i +−γ e.set xe.set,i +−γ e.old xe.old,i +−γ p.set xp.set,i +−γ p.old xp.old,i +−γ tar +−γ e.old*Q xe.old,i xQ,i 1/σ Si (t) = exp{−[te ] where γQ is the coefficient for habitat quality, γe.set is the coefficient for E. evelynae settlers, γe.old is the coefficient for older E. evelynae, γp.set is the coefficient for E. prochilos settlers, γp.old is the coefficient for older E. prochilos, γtar is the coefficient for the target assemblage, and γe.old*Q is the coefficient for the interaction between older E. evelynae and habitat quality: a) survival of E. evelynae targets, and b) survival of E. prochilos targets. Only means are shown for clarity of presentation. Closed symbols represent survival in the highest quality habitats, and open symbols represent survival in the lowest quality habitats. Coefficient values and effects of factors are shown in Table 3-5. Note y-axis on natural log scale.

a) 0 s)

-2 Target elynae v -4 e E. Targets (3 E. evelynae + 3 E. prochilos) (higest quality) e of Targets + 5 E. evelynae settlers -6 Targets + 5 older E. evelynae Aliv Targets + 5 E. prochilos settlers n o

i Targets + 5 older E. prochilos Targets (lowest quality)

port -8 Targets + 5 E. evelynae settlers Targets + 5 older E. evelynae Targets + 5 E. prochilos settlers

Ln (Pro Targets + 5 older E. prochilos -10 123456789101112 Time (days)

b) 0 s) rget a -2 T los i

-4 proch E. f

o 3 E. prochilos settlers (highest quality) Targets (3 E. evelynae + 3 E. prochilos) -6 Targets + 5 E. evelynae settlers Targets + 5 older E. evelynae Targets + 5 E. prochilos settlers

ion Alive Targets + 5 older E. prochilos rt 3 E. prochilos settlers (lowest quality) -8 Targets (3 E. evelynae + 3 E. prochilos) Targets + 5 E. evelynae settlers Targets + 5 older E. evelynae Targets + 5 E. prochilos settlers Targets + 5 older E. prochilos Ln (Propo -10 123456789101112 Time (days)

Figure 3-5. Survival of targets according to the main effects, species and age class, in the survival analysis −γQ xQ,i +−γ age +−γ species +−γ tar +−γ species. pro*Q xQ,i +−γ tar. pro*Q xQ,i 1/σ Si (t) = exp{−[te ] , where γQ is the coefficient for habitat quality, γage is the coefficient for age class, γspecies is the coefficient for species, γtar is the coefficient for the target assemblage, γspecies.pro*Q is the coefficient for the interaction between E. prochilos and habitat quality, and γtar.pro*Q is the coefficient for the interaction between E. prochilos targets and habitat quality: a) survival of E. evelynae targets with different age class neighbors, b) survival of E. evelynae targets with different species of neighbors, c) survival of E. prochilos targets with different age class neighbors, and d) survival of E. prochilos targets with different with different species of neighbors. Only means are shown for clarity of presentation. Closed symbols represent survival in the highest quality habitats, and open symbols represent survival in the lowest quality habitats. Coefficient values and effects of factors are shown in Table 3-6. Note y-axis on natural log scale.

a) age-class effects b) neighbor species effects 0 0 e) e) iv iv -2 -1 Al Al ae ae n n ely ely v -4 -2 E. e E. ev settler neighbors;

highest quality n E. evelynae neighbors; highest quality rtio rtion settler neighbors; o o lowest quality E. evelynae neighbors; lowest quality older neighbors; -6 -3 highest quality E. prochilos neighbors; Ln (Prop Ln (Prop highest quality older neighbors; lowest quality E. prochilos neighbors; lowest quality

-8 -4 24681012 24681012

Time (days) Time (days) 82

d) neighbor species effects c) age-class effects 0 0 e) e) iv iv -1

Al -2 Al hilos hilos oc oc r r -2

E. p E. p E. evelynae neighbors;

n settler neighbors; n highest quality

o -4 o highest quality E. evelynae neighbors; settler neighbors; lowest quality lowest quality -3 E. prochilos neighbors; older neighbors; highest quality

Ln (Proporti highest quality Ln (Proporti -6 older neighbors; E. prochilos neighbors; lowest quality lowest quality

-4 24681012 24681012

Time (days) Time (days)

CHAPTER 4 AGE CLASS COMPETITIVE INTERACTIONS IN A MARINE GOBY, ELACATINUS PROCHILOS

Introduction

Most marine organisms are characterized by a bipartite life history with a pelagic larval stage followed by a benthic dwelling juvenile and adult stage (Sale 1980, Thresher

1984, Mapstone and Fowler 1988, Booth and Brosnan 1995, McEdward 1995). Much research has focused on the transition from the larval stage to the benthic stage and the processes that operate post-settlement. However, most of these studies remain focused on single cohorts: e.g., quantification of settlement pulses, subsequent survival, and the effect of settler density. This approach has at least two shortcomings. First, there can be profound ontogenetic shifts during the benthic (or larval) stage, including changes in habitat and diet and changes in the strength of processes that affect survival or growth

(Eggleston 1995, McCormick and Makey 1997, Jones 1987, 1991, Robertson 1998,

Schmitt and Holbrook 1999). These within-stage ontogenetic shifts could be at least as important as the larval-benthic transition (as has been shown in many freshwater systems:

Werner 1986, Spencer et al. 1991, Osenberg et al. 1992, 1994).

Second, intraspecific interactions may not be restricted to within cohorts. For example, older age classes can facilitate (Schmitt and Holbrook 1996, Tolimieri 1998) or suppress settlement (Tupper and Hunte 1994, Schmitt and Holbrook 1996, Wilson and

Osenberg 2002) and can reduce survival of recently settled fish (Jones 1987, Schmitt and

Holbrook 1999, Wilson and Osenberg 2002). In many cases, age class effects are likely

83 84 to be asymmetric, with older age classes having stronger effects on younger age classes

(Schmitt and Holbrook 1999), suggesting that important processes may be missed by focusing on intra-cohort effects. Inter-cohort interactions can be particularly important when settlement and post-settlement processes are temporally consistent, leading to carry-over effects across settlement pulses. Additionally, if processes involving settlement and post-settlement loss (e.g., habitat quality) positively covary over time and space (see Chapter 2), higher quality coral heads will consistently support higher densities and multiple age classes over time.

As a result of these two issues, there is a clear need to incorporate age (or size or stage) structure to better understand post-settlement survival and the processes influencing population dynamics (e.g., Jones 1987, Olson et al. 1995, Ohman et al. 1998,

Schmitt and Holbrook 1999, Persson et al. 2000, St. Mary et al. 2000, Bolker et al. 2002).

Therefore, in this study I explored interactions among new settlers and older fish of the marine goby, Elacatinus prochilos. All age classes of this fish occupy the same habitat

(i.e., live coral substrate) after settlement, and therefore, each age class potentially experiences and interacts with all other age classes. I determined the strength of age class interactions using a version of a “target/neighbor” design in which I varied the density and age class of different “neighbors” and monitored survival of “targets” (Goldberg and

Werner 1983, Olson et al. 1995). I focused on two age classes: those that had recently settled and those from previous settlement periods. My previous work suggested spatial variation in the strength of density independence drove spatial variation in habitat quality among coral heads. Therefore, my specific goal was to quantify and compare per capita effects of the two age classes on the survival of each age class in habitats of different

85 quality. The work was designed to determine if “age-structured interactions” mattered to the dynamics of this fish and whether models of density dependent survival needed to incorporate age-structure or could simply focus on intra-cohort interactions (or treat all age classes as having equivalent effects).

Methods

Experimental Design

An experiment was conducted on the backreef in Tague Bay of St. Croix, U.S.V.I. during the summer of 2002 to estimate the strength of age class interactions in habitats of different quality. I manipulated the density of two age classes: settlers and older fish of

E. prochilos. "Settlers" were < 16 mm (which corresponds to fish that have settled within the previous two weeks) and “older fishes” were > 16 mm (which corresponds to fish that had settled more than two weeks previously). Fish were categorized into these two classes based on the natural history of E. prochilos; new settlers enter the benthic environment around the new moon of each month and settle to live coral substrate that is already occupied by older individuals (i.e., juveniles and adults; Colin 1975, Wilson

1998). Throughout this chapter I will refer to “age” even though the two classes also differ in their size and stage. My goal here is to quantify differences in effects and responses of these two groups, rather than to ascertain if the differences are the result of age, size or stage-specific effects.

I varied the density of settlers and older fish and monitored the survival of settlers and older fish along these density gradients (see Table 4-1). The density of settlers ranged from 0 to 11 fish per coral head, and the density of older fish ranged from 0 to 8 fish per coral head (Table 4-1). In all treatments there were at least three individuals of each age class present, enabling me to look at the simultaneous responses of each age

86 class. Densities were chosen to bracket the natural range in competitive environments of the two age classes. The average mean crowding index (Lloyd 1967) based on surveys of coral heads in 2001 was 1.82 ± 0.15 (range: 0 to 2.3) for settlers on settlers, 1.64 ± 0.24

(range: 0 to 3.65) for older fish on older fish, 0.49 ± 0.08 (range: 0 to 0.735) for settlers on older fish, and 3.21 ± 0.10 (range: 0 to 3.3) for older fish on settlers. For example, a settler, on average, shared its coral head with two other settlers and three older fish.

Results from other years gave slightly higher crowding indices: e.g., in 1996 (when overall settlement was higher) a settler had an average of 6.25 settlers (range: 0 to 10.95) and 3 older fish (range: 0 to 4.8) as neighbors.

My previous work in this system showed that coral heads vary in the strength of processes that affects density independent survival (Wilson and Osenberg 2002, Chapter

2). Higher quality sites (those with the weakest density independent mortality) also receive greater levels of settlement, and therefore, have higher resident densities.

Consequently, I assigned treatments along a gradient based on the initial number of

Elacatinus sp. (i.e., E. evelynae and E. prochilos) on coral heads, the best correlate of habitat quality (Chapter 2). I used Montastrea annularis coral heads (the most preferred substrate by this species; see Wilson 1998) and conducted several surveys in which I counted the initial number and age class of gobies. Habitat quality was estimated by the average number of Elacatinus initially present in these surveys. All resident gobies were then removed by hand using small aquarium nets and clove oil. Each treatment was replicated four times, and habitat quality was used as a covariate (i.e., treatments were blocked by habitat quality).

Experimental Set-Up

Fish were collected from Montastrea annularis heads in an adjacent bay (Boiler

Bay), and fishes were immediately taken to the backreef in Tague Bay, measured and tagged with an injected acrylic paint color underwater (to differentiate “settler” from

“older fish” assemblages), and then released onto the appropriate coral head. Each coral head was stocked with fishes for two consecutive days (to rectify initial handling losses).

The second day of stocking was considered "day 1,” and the number of fish present per coral head at this time was considered the starting or initial density. Coral heads were then surveyed on days 2, 3, 4, 6, 8, 10 and 12, and any missing tagged individuals were replaced during each survey to maintain densities. Replacement fishes were tagged with different colors to differentiate them from the original fishes. Surrounding areas were searched for tagged fishes that may have moved from experimental sites. Because few tagged but missing fish were found away from experimental sites, I assumed the disappearance of tagged individuals represented mortality. Any tagged fish remaining on day 12 were collected, measured, euthanized, and preserved in 95% ETOH.

Analyses

To explore the initial patterns of survival of the gobies, I explored patterns of survival of each age class assemblage in each treatment by estimating longevity or the average number of days an individual of each age class assemblage survived in a given treatment (methods in Wilson and Osenberg 2002). However, because survival data is not normally distributed (i.e., the error distribution follows a Weibull or gamma-model distribution), and it is usually right and interval-censored, I used survival analysis (SAS v8.02) to quantify the effects of density and habitat quality on the survival of E. prochilos in the each age class. Survival analysis estimates parameters based on maximum

88 likelihood estimates and accommodates right and interval-censored data (Collett 1994,

Allison 1995). I used a parametric model with a Weibull distribution to estimate the coefficients, γ, for each covariate, x, in the survival model. The generalized log-survival time model for the Weibull models was

logT = γ 0 + γ 1x1i + γ 2 x2i + γ 12 x1i x2i + ...γ p x pi + σε (1) where γ0 is the intercept, σ is the scale parameter (assumed constant across treatments), and ε has a Weibull distribution (Collett 1994, Allison 1995) (note: if σ=1, this Weibull model simplifies to the exponential model).

There were four main factors in the model: “habitat quality,” “settler density,”

“older fish density,” and a “target” factor (which referred to the age class whose survival was being modeled). The first three factors were used as continuous variables in the model. Habitat quality was the average number of Elacatinus initially present on experimental coral heads and ranged from 1.5 to 16 fishes/coral head. Settler (or older fish) density was the number of fish of a given age class on a coral head (see Table 4-1).

The “target” factor (“settler” or “older fish”) was used as a categorical variable to determine whether there were differences in the responses (in terms of survival) of the two age classes when experiencing the same neighbor assemblage. To estimate the per capita effects of each age class on itself and on each other, I ran an additional survival analysis for each target assemblage (“settlers” or “older fish”) separately.

Results

Initial patterns of longevity showed that longevity tended to decrease with increasing fish density. In addition, each age class had comparable effects on itself as well as one another (Figure 4-1a, b). The survival analysis demonstrated that increasing

89 density of older fish significantly reduced the survival of both older fish and settlers.

This effect was most pronounced in lower quality sites (Table 4-2, Figure 4-2a, b).

Increasing density of settlers also decreased survival. Although this effect was not significant (Table 4-2, Figure 4-2), the per capita effect of settlers was not distinguishable from the per capita effect of older fish (i.e., older fish did not have larger per capita effects). Finally, there was a significant effect of habitat quality (i.e., survival was higher on coral heads that had more initial resident Elacatinus present) (Table 4-2, Figure 4-2).

However, there were a number of significant interactions (Table 4-2). A significant interaction between response of age class and habitat quality indicated that higher quality did not translate into higher survival for the older fish targets (Table 4-2 [i.e., the negative coefficient on the interaction between response of targets and habitat quality means older fish targets were less affected by increases in quality than were settler targets], Figure 4-

2b). In addition, a significant interaction between settler density and habitat quality indicated that per capita effects of settlers were stronger in sites with low habitat quality

(Figure 4-2b). However, a significant interaction between settler density and response of age class indicated that older fish were less affected by settlers than were older fish

(Table 4-2 [i.e., the positive coefficient for the interaction between settler density and response of age class means older fish targets were less negatively affected by settler density compared to settler targets], Figure 4-2b). The similar age class effects and differential effects of quality by age class are best demonstrated by examining the per capita effects of each age class on itself and one another (Table 4-3). The coefficients for effects of settlers on settlers and older fish on settlers are similar (Table 4-3a), demonstrating that settlers and older fish have similar effects on settlers. In addition, the

90 effects of quality are significant for settler targets. However, while the coefficients for the effects of settlers on older fish and older fish on older fish appear different, confidence intervals on these estimates overlap (Table 4-3b). It must be noted, however, that these confidence limits are large, so my ability to demonstrate that settlers and older fish have similar effects on older fish may be a question of power. In addition, the effect of quality was not significant when older fish targets were considered separately, thus explaining the significant interaction between target age class and habitat quality (Table

4-3b).

Another way to interpret the quantitative survival coefficients is to translate them into per capita effects on the instantaneous mortality rate (i.e., the hazard rate) of both age classes. This can be done by the transformation of 100%(eγi-1) (see Allison 1995), where the percent increase gives the increase (or decrease) in the expected mortality rate for each increment increase in covariate, xi. For example, each additional settlers have 8.6% increase and each additional older fish has a 7.13% increase in settler mortality (Table 4-

3c). Similarly, each additional increment in quality has a 6.9% decrease in settler mortality but only a 1.9% decrease in older fish mortality (Table 4-3c).

Discussion

As with many reef fishes, E. prochilos settle on a monthly basis following a lunar cycle, such that different cohorts generally occur together on live coral substrate (Wilson

1998, Wilson and Osenberg 2002). In an extreme case, this can result in fish that range in size from 6 to 34 mm co-occurring on the same coral head. This species does not undergo an ontogenetic habitat shift except when reproductive individuals leave live coral heads and build nests in small holes within the reef; however, young fish and fish of

91 reproductive size are often present on coral heads together (Wilson, personal observation). This study has shown that there was no difference in the competitive effects within and between age classes (within the limits of resolution of this study). So, while competition was operating in this system (given the significant, negative effects of adult density; Table 4-2), this population is essentially “unstructured”. Determining the strengths of such interactions is important, however, because differences in age class interactions can have important population dynamic consequences (Beddington 1974,

May et al. 1974, Tschumy 1982, Nisbet and Gurney 1982). For instance, in populations where there are differences in age class interactions, smaller individuals tend to be stronger competitors due to lower per capita metabolic requirements (McCauley et al.

1996, Persson et al. 1998). Therefore, while older individuals may have larger competitive effects due to bigger body size and higher resource requirements; smaller individuals may have stronger competitive responses (Persson and Crowder 1998,

Persson et al. 1998). These asymmetric interactions can result in oscillating population dynamics in closed systems (e.g. DeRoos et al. 1992, Persson et al. 2000).

However, in this study, I am considering an “open” system, where within a given locale competitive effects on reproduction are not translated into decreased local production. Therefore, asymmetric interactions may not result in oscillatory dynamics in these “open” populations. In addition, this population lacked differential age class effects

(i.e. the interactions were “symmetric” within the level of resolution for this study); yet even without this layer of complexity, the dynamics of the system are still far from

“simple”. First, both density independent and density dependent interactions will affect the dynamics of any particular system. Second, the strength of density dependent and

92 density independent processes can vary over space and time. Past work in the system has suggested that the strength of density dependence (i.e., interspecific and intraspecific competition) is spatially uniform, but the strength of density independence varies over space (and it is this variation that drives variation in habitat quality among coral heads;

Chapter 2). However, the results of this current study suggest that, in fact, habitat quality affects the strength of density dependent processes. That is, the interaction between settler density and habitat quality suggest that settler density has larger impacts in lower quality sites (Table 4-2). So, why the difference in results? First, the analysis in Chapter

2 did not include the majority of the data in this study, which was responsible for driving the pattern of spatial variation in density dependence (the analysis in Chapter 2 only included treatments 1 and 2 from this work). Second, the total habitat quality effect (i.e., habitat quality effect times its associated variation) is two orders of magnitude larger than the habitat quality by settler density interaction effect (Table 4-2; i.e., 0.86% decrease in mortality for each incremental increase in habitat quality and only a 0.006% increase in mortality for each additional settler across quality). Thus, the spatial variation in the strength of density independent mortality driving differences in habitat quality may swamp out the relatively minor effect of variation in the strength of density dependence among sites.

In addition, the interaction between target assemblage and habitat quality suggested that the two age classes responded differently to quality (with older fish responding less to variation in habitat quality than settlers; Table 4-2, Figure 4-2). It was speculated in Chapter 2 that spatial variation in density independent mortality among coral heads may be due to differences in cleaning behaviors among sites; more “risky”

93 cleaning behaviors (i.e., behaviors resulting in higher mortality) were observed on low quality sites. If older fish were 1) too large to be eaten by potential predators while cleaning or 2) learned not to engage in “risky” cleaning behavior, then they would incur less mortality among coral heads of different quality than smaller or “naïve” settlers.

Thus, they would not respond as much to differences in quality (or variation in the strength of density independent mortality) as settlers.

Finally, the interaction between target age class and settler density effects demonstrated that older fish were less affected by settler density than were other settlers.

This could be due to a number of things. First, while the two age classes co-occur on coral heads, there is some spatial segregation occurring within a given coral head

(Wilson, personal observation). Settlers tend to be separated from older fishes on individual coral heads. If the segregation allowed older fish to interact more intensively with one another, this would explain the target by settler density interaction as well as the significant effect of older fish density. But this would not explain the lack of a significant settler density effect that I found in this study. However, if predation is largely occurring on the smaller age classes (due size vulnerability or naïve cleaning behaviors) on a fast-enough time scale, then perhaps a form of apparent competition is occurring where settler density is quickly reduced through predation before it can have negative effects on settlers or older fish (Holt et al. 1994). While these explanations are speculative, they aim to highlight areas of new research and give possible new insight to how this system works. Such additional empirical work paired with a modeling approach that integrates variation in habitat quality, density dependence, similar age class effects

94 and different species interactions can help to better explain the complex dynamics of this system.

Table 4-1. Experimental set-up for age class experiment. Each treatment was replicated four times and placed along a gradient of habitat quality. Treatment Settler Assemblage Older Fish Total No. of Fish Assemblage per Coral Head 1 3 0 3 2 0 3 3 3 3 3 6 4 3 5 8 5 3 8 11 6 8 3 11 7 11 3 14

Table 4-2. Coefficients and results from the survival analysis to test for the responses and effects of different age classes. Main Effect Coefficient 95 % CI X 2 Df P-value (γ) Quality 0.139 0.076 – 0.120 16.92 1 <0.0001

Target Age class 1.77 1 0.99 Response Settlers 1.198 0.70 – 1.70 Older Fish 1.199 0.76 – 1.64

Settler Neighbor -0.0417 -0.096 – 0.012 0.43 1 0.51 Effects

Older Fish -0.109 -0.154 – -0.065 23.14 1 <0.0001 Neighbor Effects

Quality*Target -0.068 -0.12 – -0.017 6.90 1 0.009 Age class Response

Quality*Settler -0.0088 -0.015 – -0.0025 7.54 1 0.006 Neighbor Effects

Target Age class 0.050 0.002 – 0.098 4.21 1 0.040 Response*Settler Neighbor Effects

Scale 0.68 0.62 – 0.74 <0.0001

Table 4-3. Results from survival analysis on per capita effects on the instantaneous mortality rate of each age class on itself and on one another. a) coefficients for the effects of settlers on settlers and older fish on settlers, b) coefficients for the effects of settlers on older fish and older fish on older fish, and c) per capita effects of density in terms of percent increase in the hazard (i.e. increase in mortality) for each additional fish, and per capita effects of quality in terms of percent decrease in the hazard (i.e., decrease in mortality) for each additional fish. Numbers in parentheses below percent increase or percent decrease in the hazards are the 95% CI for the different hazard rates. Main Effect Coefficient 95 % CI (γ) a) Settler Targets Settlers Density Effects -0.098 -0.13 – -0.063 Older Fish Density Effects -0.074 -0.14 – -0.0071 Effect of Quality 0.067 0.029 – 0.11

b) 97 Older Fish Targets Settlers Density Effects -0.057 -0.092 – -0.022 Older fish Density Effects -0.14 -0.20 – -0.083 Effect of Quality 0.019 -0.015 – 0.054

c) Settlers on Settlers Older Fish on Settlers Settlers on Older Fish Older Fish on Older Fish Per Capita Effects of Density 8.6% 7.13% 5.54% 13.19% (12.2% – 6.1%) (13.6% – 0.71%) (8.79% – 2.18%) (18.1% – 7.96%) Per Capita Effects of Quality -6.9% -6.9% -1.9% -1.9% (-2.9% – -11.6%) (-2.9% – -11.6%) (1.49% – -5.54%) (1.49% – -5.54%)

a) 6 older fish on older fish settlers on older fish

3 s remained alive)

2 target fish 1 Longevity (average number of days older 0

01234567891011 Experimental "Neighbor" Density (no. settler or older fish neighbors / coral head)

b) 6 settlers on settlers older fish on settlers 5 days

4 alive) ined

a 3

2 (average number of rgets rem a

ler t 1 sett Longevity 0

01234567891011 Experimental "Neighbor" Density (no. settler or older fish neighbors / coral head)

Figure 4-1. Mean longevity of “targets” (the average number of days targets remained alive on coral heads) for each age class assemblage versus the number of fish on each coral head in each treatment. a) mean longevity of older fish targets with either older fish or settlers as neighbors, and b) mean longevity of settler targets with either settlers or older fish as neighbors. Least square means and standard errors shown. Note: data shown at “Experimental ‘Neighbor’ Density = 3” in each panel is one data point estimated from treatment 3 in Table 4-1 (and analyzed as such). For clarity of presentation, two data points are shown in each panel.

a) 0.0

e) -0.3 liv

s A -0.6 et -0.9 Targ -1.2 r Fish -1.5 older fish on older fish;

Olde highest quality f -1.8 older fish on older fish; lowest quality ion o -2.1 rt settlers on older fish; -2.4 highest quality ropo settlers on older fish; -2.7 lowest quality Ln (P -3.0 01234567891011 Experimental "Neighbor" Density (no. settler or older fish neighbors / coral head)

b) 0.0

-0.3 e) liv -0.6 s A

get -0.9 Tar

r -1.2 e l t -1.5 Set

of -1.8 ion

rt -2.1 o settlers on settlers; highest quality

rop -2.4 settlers on settlers; lowest quality P older fish on settlers; highest quality Ln ( -2.7 older fish on settlers; lowest quality -3.0 01234567891011 Experimental "Neighbor" Density (no. settler or older fish neighbors / coral head)

Figure 4-2. Survival of targets (older fish or settlers) according to the main effects in the survival analysis according to the following survival model on day 1:

−γ Q xQ,i +−γ tar +−γ old.den xold.den,i +−γ set.den xset.den,i +−γ tar*Q xQ,i +−γ tar*set.den xset.den,i +−γ set.den*Q xset.den,i xQ,i 1/σ Si (t) = exp{−[te ]

where γQ is the coefficient for habitat quality, γtar is the coefficient for the target assemblage, γold.den is the coefficient for older fish density, γset.den is the coefficient for settler density, γtar*Q is the coefficient for the interaction between target assemblage and habitat quality, γtar*set.den is the coefficient for the interaction between target assemblage and settler density, γset.den*Q is the coefficient for the interaction between settler density and habitat quality. a) survival of older fish targets, and b) survival of settler targets. Only means are shown for clarity of presentation. Closed symbols represent survival in the highest quality habitats, and open symbols represent survival in the lowest quality habitats. Coefficient values and effects of factors are shown in Table 4-2. Note y-axis on natural log scale.

CHAPTER 5 AGE AND GROWTH OF TWO SPECIES OF MARINE GOBIES BASED ON OTOLITH ANALYSES

Introduction

Back-calculation methods, which yield a time series of sizes for individuals, have been valuable tools for both fisheries research and fish ecology (Francis 1990, Vigliola et al. 2000, Bergenius et al. 2002). The resulting size at age relationships can be used to compare growth rates among different cohorts (Beacham 1981, Rijnsdorp 1993), sexes

(Iglesias et al. 1997) or among populations (Osenberg et al. 1988, Rijnsdorp 1993).

Back-calculation models can also be used to estimate growth or size during life history stages that are difficult to study directly: e.g., growth of larvae or size at settlement. As a result, processes can be examined throughout the entire life history rather than at particular, easily studied stages, which may not be the key stages influencing population dynamics. For instance, growth rates of pelagic larvae are one of the primary determinants of recruitment success of fishes (Anderson 1988, Leggett and DeBlois

1994, Meekan et al. 1998). In addition, mortality of young fishes is size-selective, such that large size-at-hatching and high growth move fishes through more vulnerable sizes more quickly, thus reducing their cumulative larval mortality (Miller et al. 1988, Leggett and DeBlois 1994). Consequently, through the use of back-calculation methods, mortality of young post-settled fishes has been traced back to larval growth history

(Bergenius et al. 2002, Vigliola et al. 2000). Therefore, back-calculation methods can

100 101 quantify differences in larval size initiated at hatching and in growth so that we can better understand and predict distribution and abundance patterns in the benthic habitat.

A variety of methods for back-calculation of size at age have been proposed, each making different assumptions about the relationship between otolith and fish growth (see

Francis 1990). However, all back-calculation models are based on two key assumptions:

1) that there is periodicity in the formation of otoliths on an annual or daily basis

(Campana and Nielson 1985, Campana and Jones 1992), and 2) that relative fish growth is proportional to relative otolith (or scale) growth (Carlander 1981, Campana 1990).

This second assumption can be expressed by the equation

(1 (L − a)) * dL dt = (c R) *dR dt (5-1) where L is fish length and R is otolith radius at time t, a is the fish length at the time of otolith formation (a > 0: Fraser 1916, Lee 1920), and c is the proportionality coefficient.

Evidence for proportionality between relative somatic growth and otolith growth is usually derived from a strong correlation between fish size and otolith size (Campana

1990), and most studies have not been able to demonstrate a complete lack of proportionality between otolith size and fish size (e.g., Vigliola et al. 2000, but see Secor and Dean 1989, 1992, Reznick et al. 1989, Molony and Choat 1990, Francis et al. 1993).

The first back-calculation models were simplistic in that they assumed a constant linear relationship between otolith size and body length. For instance, one of the first accounts of back-calculation was the Dahl-Lea equation (Lea 1910), which assumed that otolith and body length grew in exact proportion (Francis 1990) such that

L = bR (5-2)

102 where L and R are defined above and b is the slope of the relationship. Similarly, the

Fraser-Lee model (Fraser 1916, Lee 1920) assumed a linear relationship between body length and otolith size where otolith growth was, on average, in constant proportion with somatic growth. However, in the Fraser-Lee model, the intercept of the relationship between fish length and otolith size was not assumed to be zero; rather, the intercept was the value from the regression

L = a + bR (5-3) where a is the intercept and b is the slope of the relationship (Francis 1990, Secor and

Dean 1992).

In addition to these regression approaches to back calculation, proportional methods, also known as the Body Proportional Hypothesis (BPH) and Scale Proportional

Hypothesis (SPH), have been developed (Whitney and Carlander 1956, Francis 1990).

The BPH assumes that the deviation of body length of a fish from the average sized fish for that otolith size is constant through time (see Figure 5-1b), while the SPH assumes that the deviation of otolith size of a fish from the average sized otolith for a fish with that body size is constant through time (Francis 1990). Therefore, these models assume some constant proportional deviation from the mean body size (BPH) or mean otolith size (SPH) (Francis 1990).

However, studies have shown that changes in the otolith-body size relationship may occur through time (Secor and Dean 1992, Sirois et al. 1998, Vigliola et al. 2000).

For instance, growth rates can vary between ontogenetic stages due to environmental changes and/or habitat shifts. This can result in a non-linear relationship between otolith and body size, thus making models which assume an underlying linear relationship

103 inappropriate. Fry (1943) proposed a non-linear back-calculation model that is based on the body-otolith relationship

L = a + bR c (5-4) where a and b are described as above, and c is the proportionality coefficient (as in Eq. 5-

1), which can describe an allometric relationship between body length and otolith radius

(Francis 1990). Sirois et al. (1998) developed another model, the Time-Varying Growth

(TVG) model, to address variation in growth rate over time explicitly. Their model weights the contribution of each growth increment on an otolith (according to different developmental stages) in the length back-calculation using a growth effect factor (Table

5-1; Sirois et al. 1998). This, however, assumes that the underlying relationship between otolith size and body size should be linear; by weighting the contribution of individual increments, the model retains a linear relationship between otolith size and fish body length through ontogeny, despite changes in growth rate (Sirois et al. 1998, Vigliola et al.

2000).

In addition to changes in growth rates through time, studies have shown that otolith size may depend on absolute growth rate such that slow-growing fishes can end up with disproportionately larger otoliths. This is known as a “growth effect” (Reznick et al.

1989, Secor and Dean 1989, Secor et al. 1989, Sirois et al. 1998). Some models have been developed to eliminate the bias arising from growth effects. For example, Campana

(1990) proposed a modified version of the Fraser-Lee model, called the Biological

Intercept (BI) model, which incorporates a fixed point based upon the population’s mean fish length and otolith radius at hatching (L0,p, R0,p) (see Figure 5-1a) that is based on the following body-otolith relationship for a population of fish

104

L = L0, p − bR0, p + bR . (5-5)

In addition, Vigliola et al. (2000) developed a modified version of the Fry model that could deal with variation in growth rates over time (such as an allometric relationship between otolith growth and fish length; see Figure 5-1a) as well as problems associated with growth effects. Similar to the Campana (1990) approach in Eq. 5-5, the back- calculation model developed by Vigliola et al. (2000) incorporated a biological intercept into Eq. 5-4 (see Figure 5-1a) such that the body-otolith relationship is represented as

c c L = L0, p − bRo, p + bR . (5-6)

The back-calculation model also has a term for fish length at otolith formation (a in

Figure 5-1b; see Vigliola et al. 2000 for details). This additional parameter, a, provides three known fish lengths (fish length at otolith formation, the biological intercept and fish length at time of capture) such that a non-linear relationship can be estimated between otolith size and fish length (Figure 5-1b).

Finally, Morita and Matsuishi (2001) developed an Age Effects (AE) model that addressed a similar bias, an “age effect,” which occurs when otolith size increases but there is no subsequent increase in somatic growth. The age effect has similar properties to the growth effect, and these two effects are not mutually exclusive (Morita and

Matsuishi 2001). The AE model assumes that otolith size increases with both fish body length and age, thus allowing for increases in otolith size with no increase in fish length and avoids overestimating fish size. In addition, their model follows the assumptions of

SPH, which assumes a constant proportional deviation of otolith size of a fish from the average for a fish of that length and age (see Morita and Matsuishi 2001).

105

The focus of this study was to examine the relationship between otolith size and fish body length, and to determine appropriate back-calculation models of growth for two species of gobies. More specifically, we validated daily increment formation on otoliths for two goby species, Elacatinus evelynae and E. prochilos, and we determined the presence of and categorized the morphology of a settlement mark on the otoliths of these two species. Validation of otolith increment periodicity is essential for accurately aging fishes and for the application of growth models. In addition, determining the presence of a settlement mark can prove valuable for determining age and size at settlement. Finally, we evaluated the efficacy of different back-calculation models (BI, BPH, MF, TVG and

AE) to predict size at age estimates from known growth trajectories from a detailed study of tagged fishes. In doing this, we explicitly tested if the relative otolith growth rate was proportional to the relative somatic growth rate. In addition, by monitoring individual growth trajectories, we were able to examine whether or not the relationship between otolith size and body size conformed to the specific assumptions of different back- calculation models. We also discuss the implications of violating such assumptions for back-calculating fish length from daily otolith increments.

Methods

Study System

Elacatinus evelynae and E. prochilos are small (< 34 mm standard length, SL) cleaning gobies that can remove ectoparasites from larger fishes (Colin 1975). The two species are ecological and morphologically similar, relatively sedentary, dwell on live scleractinian corals (and occasionally on rock surfaces and the outer surface of sponges), and occur at depths from zero to 50 m (Colin 1975). Settlement of each species begins as

106 early as the last quarter moon, peaks around the new moon, and continues as late as the first quarter moon (a period as long as two weeks, but typically much less) (Wilson, personal observation). New settlers lack pigmentation for approximately 24 hours after settling on coral heads, allowing settlers to be easily distinguished from older fishes

(Wilson, personal observation).

Sampling

Approximately 150 fishes (75 E. evelynae and 75 E. prochilos) were collected by hand from patch reefs in Boiler Bay and the backreef in Tague Bay on the northeast part of St. Croix, U.S.V.I. (17° 45′ 40′′ N, 65° 35′ 30′′ W) using quinaldine and small aquarium nets approximately one week after a new moon in May, 2001. Therefore, collected fishes were not older than one week post-settlement, and ranged in size from

8.5 to 12.3 mm for E. evelynae and 9.2 to 12.9 mm for E. prochilos.

Fishes were submerged in Alizarin Red S (300 mg/L) to create a fluorescent mark on the otoliths (Beckman and Schulz 1996). After 24 hours fishes were removed, placed in fresh seawater, marked subcutaneously with one of eight different colors of non-toxic acrylic paint (see Wilson and Osenberg 2002), and randomly assigned to one of four different food (mysid shrimp) treatments: 1) high, 2) ambient , 3) low, and 4) varying level of food (2 wks high food, 2 wks low food). The “ambient” food level was adjusted

(and varied as fishes grew) so that the number of mysids per fish were completely consumed in a 24-hour period. “High” food had 50% more shrimp per fish, and “low” had 50% fewer shrimp per fish than the “ambient” food treatment. Mysid shrimp is a natural food item (Wilson, personal observation) and was collected daily from Tague

Bay.

107

After the first day of tagging, dead individuals were replaced with similarly tagged fishes. After this day, dead fishes were recorded but not replaced. Each treatment was replicated three times (each treatment consisted of 3, 5-gallon buckets, each with four individually marked fish of each species). Fishes were measured every two weeks to monitor somatic growth at which time food levels were also increased to accommodate growth of fishes. A total of six body length (i.e., standard length) measurements were made over the course of the study. Due to mortality over the 11 weeks of this study, the total number of fishes was reduced from 96 to 45 fishes (16 E. evelynae and 29 E. prochilos).

Fishes were submerged in Alizarin Red S for a total of three different 24-hour periods (approximately every four weeks over the 11 wk study) to provide three marks on the otoliths to validate daily increment formation during the first two months post- settlement. At the end of 11 weeks, fishes were euthanized, preserved in 95% ethanol, and shipped to the University of Florida for otolith analysis.

Otolith Analysis

Left and right sagittae were dissected from fishes, cleaned of tissue, mounted on a glass slide with thermoplastic glue (Crystalbond), and stored in a microscope slide case to prevent fading of any fluorescent marks through prolonged exposure to light. Only left sagittae were used in the analyses unless the left sagitta was destroyed during preparation, in which case the right sagitta was used. Otoliths were prepared according to Hernaman et al. (2000) except that each otolith was prepared so that a thin transverse section that contained the nucleus was obtained, and otoliths were ground on 1000 grit sandpaper,

108 and polished on 9,3,and 1 µm 3M lapping film. Slides containing ground, polished otoliths were kept in a light-proof microscope slide box.

Alizarin Red S was detected in the otoliths by viewing them under an inverted epifluorescence compound microscope (Olympus IX70) fitted with a 100W mercury lamp and a DAPI/FITC/TRITC triple band filter set (Chroma Technology Corp.).

Alizarin Red S appeared violet-red while using a 525/25 excitation filter (Chroma

Technology Corp.). Digital pictures were taken with a 3.34 megapixel digital camera

(Nikon Coolpix 990) while viewing the otoliths under immersion oil at 1000x magnification. The digital images were imported into an image analysis system

(Optimas, Inc., v6). The number of growth increments was counted between the successive fluorescent marks or from the last fluorescent mark to the margin of the otolith along the longest axis of each ground otolith. Reader error was adjusted for by comparing estimated age of fishes with similar sizes at capture. If age estimates were more than 10% different, then each otolith was re-read a second and third time. If the second and third estimates were not larger than 10%, then the third estimates was used as an estimate of age for a particular individual. If the discrepancy was larger than 10%, then the otolith was excluded from the analysis (this only occurred for one otolith).

Validation of Daily Increments

By marking the otoliths with a fluorescent tag and holding the fishes for a known period of time, we were able to determine if the two species of gobies laid down daily rings up to two months post-settlement. The three Alizarin Red S tags provided three intervals over which we counted the number of rings visible on the otolith under a compound microscope and compared the number of rings with the known number of

109 days the fishes were held in the lab (i.e., 27 days between tags 1 and 2; 26 days between tags 2 and 3; and 12 days between tag 3 and the edge of the otolith).

We used a linear mixed-effects model (LME) (Pinheiro and Bates 2000), with a fixed factor (species by food treatment) and a random factor (each individual fish), to test if the deviation of the observed value (the counted number of increments in each time period on each otolith) from the expected value (the known number of days in each interval) varied among treatment groups or showed an overall deviation from zero

yi, j,k = β i + b j + ε i, j,k , i = 1,…,8, j = 1,…,45, k = 1,…,3, (5-7)

where yi,j,k was the number of observed increments minus the actual number of days elapsed for fish j, in treatment i, during each Alizarin interval k, βi is the effect of factor i,

th 2 bj is the random effect associated with the j individual, where b j ~ Ν(0,σ b ) , and εi,j,k is

2 the error, where ε i, j,k ~ Ν(0,σ ) (Pinheiro and Bates 2000). We estimated the overall mean of the treatment groups to test for an overall bias in yi,j,k using Helmert contrasts

(Pinheiro and Bates 2000). The parameters of the above model (Eq. 5-7) were estimated in R (v 1.5.0) using Restricted Maximum Likelihood (REML) (Pinheiro and Bates 2000).

In addition, we ran a linear mixed-effects model to test for a bucket effect; however, there was no significant variation associated with differences among buckets; therefore, we present only the results from Eq. 5-7.

Settlement Marks

Changes in otolith microstructure, such as abrupt transitions in the width of growth increments, can occur during settlement (Wilson and McCormick 1997, 1999).

Identification and categorization of a settlement mark in these species provides a visible

110 marker for calculating age and back-calculating size at settlement. Therefore, seven settlers (< 24 hours post-settlement) and seven older individuals (> 2 weeks post- settlement) of both species were collected in Tague Bay in 2001. We examined the otoliths of just settled fishes and compared them to the otoliths of older fishes to test for presence or absence of a mark that would be associated with settlement. Fishes were collected and otoliths prepared as described above (see “Otolith analysis”). Otoliths were viewed under immersion oil with transmitted light using a polarizing compound microscope (Olympus BX50) under 1000x magnification. Increment number, and the radius and width of each increment were measured along the longest axis of the transverse section of the otoliths using an image analysis system (Optimas, Inc., v6). We assumed that increments were deposited on a daily basis during the pre-settlement phase

(Jones 1986) and that the first increment in the otoliths was formed at hatching (Tsuji and

Aoyama 1982). Any visible mark or change in microstructure that could have been associated with settlement was recorded in the image analysis program while increments were being counted.

For the older fishes, otolith increment width versus age of fishes was examined using the “transition-centered” method (see Wilson and McCormick 1997): i.e., we identified the first increment of the transition zone and analyzed the ten increments before and ten increments after that start of the transition zone. Then, the ten pre- settlement and ten post-settlement otolith increment profiles for each species were compared using a one-factor repeated measures ANOVA (SAS v 8.02). This analysis tested whether increment width changed before versus after the settlement mark and allowed categorization of observed settlement marks according to Wilson and

111

McCormick (1999). In addition, a two-way ANOVA tested if age at the settlement mark varied for species and age class, which would verify that the microstructural change in the otolith of older fishes indeed corresponded to settlement.

Application of Back-Calculation Models

Longitudinal records of size were back-calculated for each tagged individual using the five back-calculation models described in Table 5-1. Parameters used in the models were estimated as follows. The average length at hatching (L0,p) for the two species of cleaning gobies was set to 2.5 mm SL (Colin 1975). Otolith radii at hatching

(R0) were averaged from all ground otoliths for each species to obtain a mean value

(R0,p). Estimates of R0,p were 8.8 µm for E. evelynae (n = 16) and 9.2 µm for E. prochilos (n = 29). Additional parameters (see Table 5-1) were estimated according to species and food treatment using either linear regression, non-linear regression (using a

Gauss-Newton algorithm) or a multiple linear regression in SAS (v 8.02). For the TVG model, each life history stage was divided into 14 day intervals. This corresponded to the frequency at which standard length was measured in the lab, and food levels were subsequently adjusted (see “Sampling” above).

Comparison of Back-Calculation Models

To evaluate which of the five growth back-calculation models best predicted body size for each species under various food regimes, outcomes of the models were compared with each of the six measurements of size that were recorded for each individual in the experiment. Specifically, we calculated residuals from each back-calculation model by subtracting each observed length measurement Lobs from the corresponding back- calculated size Lpred. We then assessed the accuracy of size estimates provided by the

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various back-calculation models by calculating an accuracy index Ia for each model

(Vigliola et al. 2000)

−1 2 2 2 −1 I a = (SSTotal − SSRe sidual )SSTotal = (∑(Lobs − Lobs ) − ∑(L pred − Lobs ) )(∑(Lobs − Lobs ) ) . (5-8)

2 As with a regression r , a larger accuracy index Ia indicates a smaller residual sum square, and hence a better fit. The accuracy index, Ia, can reach a maximum of one when predictions from the model perfectly match observations, while it has a value of zero when the model has no predictive power. However, in contrast to regression, the residual sum of squares (SSResidual) from back-calculation models is not constrained to be smaller than the total sum of squares (SSTotal). Hence, Ia can reach negative values when size estimates from back-calculation are unrealistic.

As with the validation of daily increments, we used a linear mixed-effects model

(LME), which included a fixed factor (species by food treatment) and a random factor

(individual fish), to test if the deviation of the observed, standard length from the estimated back-calculated size varied among treatment groups or showed an overall deviation from zero

yi, j,t = β i + b j + ε i, j,t , i = 1,…,8, j = 1,…,45, t = 1,…,6, (5-9)

where yi,j,t is the deviation of the back-calculated size from the measured standard length for fish j, in treatment i, on day t. We estimated the overall mean of the treatments groups to test for an overall bias in yi,j,t using Helmert contrasts (Pinheiro and Bates

2000). Parameters of the model (Eq. 5-9) were estimated in R (v 1.5.0) using Restricted

Maximum Likelihood (REML) (Pinheiro and Bates 2000). This analysis was repeated on

113 residuals that were calculated on ranked deviations of observed standard lengths from predicted lengths to test if back-calculation models were able to accurately reconstitute size hierarchy among individuals. In addition, we ran a linear mixed-effects model to test for a bucket effect; however, there was no significant variation associated with differences among buckets; therefore, we present only the results from Eq. 5-9.

Results

Validation of Daily Increments

Otolith increments were laid down approximately every day over the first two months following settlement onto the reef for both species independent of food treatments (Figure 5-2, LME, F8,37 = 1.18, P > 0.33). Although the LME model indicated that average deviations between the number of increments deposited on the otolith and the number of days elapsed between successive Alizarin Red S tags did not significantly differ from zero, average deviations had negative values in all cases (Figure 5-2). This indicated that we were more likely to slightly underestimate the age of a given individual by misreading 2-3 otolith increments in each ~ four-week Alizarin interval (Figure 5-2).

As a result, cumulative deviation over the entire study duration (65 days) was substantial for some individuals (down to –14 and –12 days for E. evelynae and E. prochilos respectively) and, although small, its average was significantly different from zero for E. prochilos (E. evelynae: mean=-1.71 d, t13 = -1.44, P = 0.17, 95% CI = -4.28 to 0.85 d; E. prochilos: mean=-1.45 d, t28= -2.28, P = 0.029, 95% CI = -2.74 to -0.15 d).

Settlement Marks

One main application of back-calculation models is to back-calculate size at settlement. This is most easily accomplished if there is an indicator, such as a discrete

114 mark, on the otolith that corresponds to settlement. A discrete, dark, and optically opaque increment was observed in older fishes of both species (n = 7 for both species).

Fishes that settled the night prior to collection did not yet possess this mark. In addition, a two-way ANOVA on species by age class showed that age of older individuals at the putative settlement mark did not differ significantly from the actual age of the settlers

(species: F1,24 =6.24, P = 0.02, age class: F1,24 = 1.08, P = 0.31; species x age class:

F1,24 =0.17, P = 0.68). This result indicated that the microstructural change in the otolith of older fishes indeed corresponded to settlement. This corresponded to a planktonic larval duration (PLD: number of increments from the hatching mark to the putative settlement mark) of 28 days ± 0.90 for E. evelynae and 26 days ± 1.0 for E. prochilos.

In addition to visual changes in increment formation during settlement, abrupt transitions in the increment width can also be associated with settlement. The RPMS

ANOVA on the increment width profiles of older fishes of both species showed a significant decrease in mean increment width after the formation of a settlement mark

(Figure 5-3: E. evelynae: 6.14 µm ± 0.32 before vs. 4.06 µm ± 0.56 after, F1,6 = 44.55,

P = 0.0005; E. prochilos: 6.85 µm ± 0.28 vs. 4.76 µm ± 0.44, F1,6 = 83.49, P < 0.0001).

This 30-35% decrease in the mean increment width following settlement that occurred over approximately three to four days (Figure 5-3a, b) is typical of a Type Ib settlement mark (sensu Wilson and McCormick 1999).

Back-Calculation Models

When determining which model of growth back-calculation was most appropriate, we first had to assess the type of relationship between otolith and somatic growth rates.

In fact, there was a strong relationship of proportionality between somatic and otolith

115 relative growth rates for both species at the population level (E. evelynae: r2 = 0.71,

2 F1,73=181.48, P < 0.0001, n = 74; E. prochilos: r = 0.73, F1,144=394.58, P < 0.0001, n = 145; Figure 5-4). From the relative growth rates (Figure 5-4), we can calculate the proportionality coefficient c (see Eq. 5-1) for each species at the population level. The proportionality coefficient c indicated negative allometry (i.e., c was less than 1) for E. evelynae (c=0.82, t73=2.958, P=0.0042) and isometry (i.e., c was not different from 1) for

E. prochilos (c=0.997, t144=0.0676, P=0.9461). When we investigated the relationship between relative somatic and otolith growth at the individual level, this result was not preserved; both positive and negative allometry were observed for a large fraction of fish from both species (Figure 5-5a). However, due to the lack of power of our analysis

(small number of observations per species, especially for E. evelynae), significant departure from isometry was only observed for one E. prochilos (c=1.77, t4=2.84,

P<0.05; Figure 5-5a).

Next, when we only used data collected at capture (i.e., the end of the study), as is the case for routine growth back-calculation, there were strong, linear relationships

2 between fish length and otolith radius (see Eq. 5-6) (E. evelynae: r = 0.66, F1,29=958.24,

2 P<0.001; E. prochilos: r = 0.81, F1,42=2727.58, P<0.001) (c=1, P = 0.87 for E. evelynae and c=1, P = 0.35 for E. prochilos) (Figure 5-6). In contrast, when all data from tagging were used in the analyses performed at the population level, positive allometry was found for E. prochilos (Figure 5-6, c=1.25, P<0.001) while isometry remained for E. evelynae

(c=1, P=0.47). However, this latter result was not preserved at the individual level where most fish from both species displayed positive allometry (Figure 5-5b).

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Comparison of the results of the different back-calculation models showed that growth curves generated by the Modified Fry model (MF) gave a better fit to curves derived from tagging than those generated by the BPH, BI, TVG and AE models (Table

5-2). This result was consistent for the two species at all food treatments except for E. evelynae at varying food regime, where the BI model yielded the greatest accuracy index

Ia. Size estimates derived from the AE model were largely unrealistic for both species at all but at high food regime as indicated by large and negative Ia (Table 5-2). Other back- calculation models generated reasonably good predictions of fish size as indicated by Ia that were often greater than 0.5, while the MF model explained more than 80% of the observed variation in body size in most cases (Table 5-2).

The best fit provided by the Modified Fry model can also been seen from the results of the linear-mixed effects model (Figure 5-7, Table 5-3a). Average biases were of about minus 1 mm for the MF model, which corresponded to our accuracy in size measurements. However, 95% confidence intervals indicated that biases of minus 2-3 mm were not uncommon for the four back-calculation models that provided realistic size estimates (Figure 5-7, MF, BPH, BI, TVG). For the last model (AE), deviations between observed and predicted size were very large (up to 40 mm) but not always significant (t- statistic219, 0.05 = 1.03, P = 0.31) due to the high variability in the unrealistic size estimates derived from this model (Figure 5-7, 5-8b, 5-9b). However, all four models that gave realistic sizes systematically overestimated size such that the average deviation between the measured standard lengths and the back-calculated length estimates were significantly different from zero (Figures 5-7a-d, 5-8a, 5-9a; MF: t-statistic219,0.05 = -5.63, P < 0.0001;

BPH: t-statistic219,0.05 = -5.63, P < 0.0001; BI: t-statistic219,0.05 = -8.33, P < 0.0001; TVG:

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t-statistic219,0.05 = -7.99, P < 0.0001). Although the size bias for the individual combinations of food and species for each of the four models varied among the treatments and the different models (Figure 5-7a-d), there was no overall significant variation among combinations of food and species (MF: F7,37 = 1.79, P = 0.12; BPH:

F7,37 = 1.47, P = 0.21; BI: F7,37 = 0.42, P = 0.88; TVG: F7,37 = 0.48, P = 0.84).

When observed and predicted fish length were ranked prior to comparisons, fixed factor (species by food) in LME models were no longer significant for MF, BPH, BI and

TVG back-calculation models (Table 5-3b). The observed size hierarchy among individuals was therefore correctly inferred by these models with best inference obtained from the MF model that yielded the lowest negative log-likelihood (Table 5-3b). As expected, unrealistic size estimates derived from the AE model generated erroneous size hierarchy among individuals (Table 5-3b).

Discussion

This study demonstrated that growth increments were daily in nature for these two species of gobies. Therefore, these species can be aged on a daily basis for up to two months post-settlement. However, there were individuals whose age was underestimated by up to 14 days over the entire study duration. In such cases, this cumulative deviation, although small on average, ended up being significant for E. prochilos. While this does not mean that increments were non-daily, it demonstrates that otoliths can give biased age estimates. Since all back-calculation methods depend on accurate age estimates (in order to accurately predict growth trajectories), it is important to recognize and consider such biases since they will ultimately influence back-calculation estimates.

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Overall, we found evidence for an allometric relationship between somatic length and otolith size (Figure 5-5b). This explains why the MF model gave the least biased back-calculation size estimates. However, allometry was only evident at the individual level. At the population level, with the typical length-at-capture data, an allometric relationship could not be discerned from an isometric relationship. This also explains why the BI model gave similar results to the MF model. The BI model is equivalent to the Modified Fry model if there is isometric growth. However, the value of the proportionality coefficient, c, varied depending on how it was estimated (via relative growth or via the L-R relationship; Figure 5-5a vs. 5-5b). Therefore, due to difficulty in assessing allometry (even with detailed, individual level data), the most conservative approach is to use the Modified Fry model.

In addition, each back-calculation growth model overestimated size at age compared to the observed standard length regardless of food treatment (Figure 5-7, 5-8,

5-9). This could have been due to a number of reasons. First, inaccurate size back- calculation can, in part, be due to a weak correlation between relative otolith growth and relative somatic growth. An uncoupling between otolith growth and somatic growth has been reported for other species (Reznick et al. 1989, Molony and Choat 1990, Mosegaard et al. 1988, Francis et al. 1993) making otoliths of these species unsuitable for back- calculation. However, the goby species had relatively strong somatic-otolith growth rate relationships (i.e., Figure 5-4). In addition, a weak correlation would not explain the consistent bias (i.e., overestimation of size) by all back-calculation models (Figures 5-8,

5-9).

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Rather, the models are more likely inappropriate because their underlying assumptions do not hold for these species. For instance, the AE model assumed that the deviation of the otolith length of a fish from the average fish of that size and age was constant through time (i.e., SPH) (Morita and Matsuishi 2001). This did not hold true for these two species (Figures 5-10, 5-11). The deviation of an individual’s otolith from the average did not remain constant through time; rather, individual otolith size fluctuated above and below the population line for a given treatment (Figures 5-10, 5-11). In addition, the BPH, BI, AE, and TVG models all assume that the relationship between otolith size and fish length is linear (Campana 1990, Francis 1990, Sirois et al. 1998,

Morita and Matsuishi 2001). However, a closer evaluation showed a decelerating relationship between fish and otolith size on an individual basis (Figures 5-10, 5-11); as fishes aged, otolith size did not increase as quickly as body size. As a consequence, the otolith size and body length followed a non-linear, allometric relationship rather than a linear one, highlighting again why Modified Fry model gave the most accurate length back-calculations.

Surprisingly, the TVG model gave poor estimates of size at age. Given the varying food treatment and the non-linear nature of the relationship between otolith size and body size, we expected the TVG and MF models would provide the best estimates.

This was not the case, and the TVG model provided estimates almost identical to the BI model (Figure 5-7c, d). This similarity in estimates of the TVG and BI models was also found by Sirois et al. (1998) and Vigliola et al. (2000). Finally, the Body Proportional

Hypothesis (BPH) and the Modified Fry (MF) model gave similar estimates (Figure 5-7a,

120 b). However, the BPH gave unrealistic, negative estimates of size at age because it lacks a biological constraint, and therefore is vulnerable to growth effects (Figures 5-8, 5-9).

However, even the MF model, which explicitly incorporated an allometric relationship between somatic and otolith growth, still provided somewhat biased estimates of back-calculated size at age (Figure 5-7a, 5-8a, 5-9a). In fact, all the models systematically overestimated size at age; this would suggest that such a bias does not necessarily come from the models themselves (i.e., different biases would be expected for different models formulas). Rather, a more plausible scenario may be due to the biased estimates of age from the otoliths. As already mentioned, although increments were formed on a daily basis, there was a slight tendency to underestimate fish age from the otoliths. Hence, when we estimated size for a given age by back-calculation, the fish was actually older than the otolith-derived age estimate. This could result in a back- calculated size that was larger than the true size of a fish for a given age (Figure 5-12).

However, despite these results, the ranked study (Table 5-3b) showed that the biases were systematic and constant among individuals. This means that back-calculation could be suitable for a comparative approach. And, since these species exhibited a clear decrease in increment width that coincided with settlement (Figure 5-3), these species are amenable for determining size at settlement. Back-calculating size at settlement, a time period which is often difficult to directly observe, can have important insights for understanding and predicting reef fish dynamics. For instance, determining size at settlement can have important implications for size-selective mortality (Houde 1987,

Booth and Hixon 1999, Bergenius et al. 2002, Vigliola and Meekan 2002) and differential condition and quality (with respect to size) of larvae and settlers among

121 habitats. Differences in condition of larvae and potentially quality of larvae arriving at different habitats is poorly understood (but see McCormick 1994, Meekan and Fortier

1996, Searcy & Sponaugle 2000, 2001); however, a better understanding of this phenomena may help in understanding differences in the abundance and distribution of reef fishes among habitats.

Thus, while this study focuses on two particular species, the results can be put into a broader context. This study demonstrated that there was an allometric relationship between somatic length and otolith size for both species. Such a pattern is common in fishes (e.g. Lombarte and Lleonart 1993, Sirois et al. 1998), but rarely considered in back-calculation models (Francis 1990, Vigliola et al. 2000). Therefore, models which incorporate such growth patterns (i.e., the MF) should be considered for back-calculation in addition to the more well known BI and proportional models (i.e. BPH and SPH).

However, this study highlights the need for caution when using otoliths in reef fish population studies (i.e., validation and verification of age estimates and appropriate growth models are needed). Otoliths have been used to re-construct settlement patterns and infer reproduction events for many species of reef fish (e.g. Victor 1983, 1986,

Robertson 1990, 1992). However, if otolith techniques become widely used to for back- calculating size at settlement and estimating larval growth and size-selective mortality, it is imperative that potential biases are recognized. Such recognition can avoid incorrect conclusions about the importance of these different processes in shaping the distribution and abundance of reef fishes and influencing reef fish dynamics.

Table 5-1. Five back-calculation models investigated in this study: Biological Intercept (BI) (Campana 1990), Modified Fry (MF) (Vigliola et al. 2000), Time-Varying Growth (TVG) (Sirois et al. 1998), Body- Proportional Hypothesis (BPH) (Francis 1990), and Age Effects (AE) (Morita and Matsuishi 2001). Back-calculation models

BI (Ri − Rcpt ) Li = Lcpt + (Lcpt − L0, p ) * (Rcpt − R0, p )

MF (ln(Ri ) − ln(R0, p )) Li = a + exp(ln(L0, p − a) + (ln(Lcpt − a) − ln(L0, p − a))* (ln(Rcpt ) − ln(R0, p )) c c c a = L0, p − bR0, p ; constants b and c estimated from the non-linear regression of L = L0, p − bR0, p + bR

t TVG (Lcpt − L0, p ) Li = L0, p + ∑Wi + Ge (Wi −W ))* i=1 (Rcpt − R0, p ) 122

Growth effectGe is estimated as in Sirois et al. 1998.

BPH (a + bRi ) Li = * Lcpt (a + bRcpt ) constants a and b were estimated from the linear regression of L = a + bR

AE α α γ Ri γ Li = − + (Lcpt + + Tcpt ) * − ti β β β Rcpt β constants α, β, and γ were estimated from the multiple linear regression of R = α + βL + γt

Note: L, standard fish length; R, otolith radius; L0,p, standard fish length at biological intercept; Li, standard length at age i; Lcpt, final length at capture; R0,p, otolith radius at biological intercept; Ri, radius at age i; Rcpt, otolith radius at capture; W, mean increment

width during each developmental stage; Wi, increment width at age i; Tcpt, final age of fish at capture; ti, fish at age i;Ge , the slope from the regression of the slope of the fish length and otolith length relationship on absolute growth (details in Sirois et al. 1998).

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Table 5-2. Index of accuracy, Ia, of back-calculation for 5 different back-calculation growth models for the two species of gobies experiencing different food treatments. Modified Fry (MF) (Vigliola et al. 2000), Body- Proportional Hypothesis (BPH) (Francis 1990), Biological Intercept (BI) (Campana 1990), Time-Varying Growth (TVG) (Sirois et al. 1998), and Age Effects (AE) (Morita and Matsuishi 2001). Species Food MF BPH BI TVG AE Treatment E. evelynae Ambient 0.83 0.75 0.55 0.54 -3.30 High 0.93 0.91 0.88 0.86 0.86 Low 0.96 0.94 0.86 0.87 -2.17 Vary 0.53 0.41 0.77 0.75 -1.83 E. prochilos Ambient 0.92 0.89 0.75 0.74 0.58 High 0.92 0.90 0.78 0.45 0.87 Low 0.66 0.60 0.65 0.64 -0.57 Vary 0.83 0.44 0.71 0.41 -5.13

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Table 5-3. Results from the LME model to compare the deviation of the observed, standard length measurements from the predicted back-calculated estimates from the five different back-calculation growth models. Note: all data (i.e., both species) lumped together. a) unranked deviations of observed standard lengths from predicted lengths., and b) ranked deviations of observed standard lengths from predicted lengths. Modified Fry (MF) (Vigliola et al. 2000), Body- Proportional Hypothesis (BPH) (Francis 1990), Biological Intercept (BI) (Campana 1990), Time-Varying Growth (TVG) (Sirois et al. 1998), and Age Effects (AE) (Morita and Matsuishi 2001). Transformation Model Negative Log- F-value P-value Likelihood a) unranked deviations MF 396 7.82 <0.001 BPH 426 7.86 <0.001 BI 437 12.52 <0.001 TVG 460 5.36 <0.001 AE 1031 9.06 0.0002

b) ranked deviations MF 1133 0.434 0.89 BPH 1152 0.431 0.89 BI 1156 0.477 0.86 TVG 1183 0.299 0.96 AE 1495 2.35 0.037

125

30 a) biological intercept (L0,p, R0,p) allometric, nonlinear (MF) linear (BI) 25

20 mm) ( h t ng 15 Le rd da 10 Stan

0 0 50 100 150 200 250 300 350 400 Otolith Radius (µm)

regression line

biological intercept (L0,p,R0,p) a, body size at otolith formation BI 30 b) MF TVG BPH AE 25

) 20 m Lcpt m

( L (BI, MF, TVG) h i t 15

ng Li(BPH) Le 10 rd

da Li(AE) an t 5 S a 0

-5 R R 0 100 200 300 i 400 cpt Otolith Radius (µm)

Figure 5-1. Relationship between otolith size and fish length and back-calculation of size at age. a) schematic of body-otolith relationship for Biological Intercept model (BI) (solid line) (Eq. 5-5, Campana 1990) and the Modified Fry model (MF) (dashed line) (Eq. 5-6, Vigliola et al. 2000). The biological intercept was L0,p = 2.5 mm and R0,p = 9.2 µm. b) example of back-calculation methods using data from E. prochilos. The standard length at capture (Lcpt) was 18.6 mm, the otolith radius at capture (Rcpt) was 410.9 µm, and Ri was 324 µm. The bold line is the regression line for the observed standard length versus otolith radius (solid symbols, •). The broken lines, and one solid line for the Age Effects model, are used to illustrate back-calculated standard lengths (Li’s) for a given Ri for the BI model (Campana 1990), the MF model (Vigliola et al. 2000), the Time-Varying Growth model (TVG) (Sirois et al. 1998), the Body-Proportional Hypothesis model (BPH) (Francis 1990), and the Age Effects model (AE) (Morita and Matsuishi 2001). The body size at otolith formation (a) (see Table 5-1, Vigliola et al. 2000) was 2.34 mm. The biological intercept was L0,p = 2.5 mm and R0,p = 9.2 µm.

126

1 pected x

0 days) ements-E r c n -1 ements ( ber of I of Incr m

u -2 N

Number -3 Observed

-4

n b h y b h y w r w r a g g m i o a m i o a e l l a h - v a h - v - - - - m - e - s e e a e s s o s ll l a a n a o lo i lo a il i i r n n y n h y l y h h c h e ly l l e c c o c v e e v e o o r o o v v e v r r p r e e e p p p

Treatments

Figure 5-2. Deviation of the observed number of increments from the expected number of increments for the overall mean ( ) and for the two species of gobies (E. evelynae (●) and E. prochilos (○)) under the four different food treatments (ambient food, high food, low food and vary food). The mean deviation with 95% confidence intervals are shown.

127

a) E. evelynae 9

m) µ ( 6 h t

5 Wid

4 crement n I 3

1 -11-10-9-8-7-6-5-4-3-2-11234567891011 Increment Number From Settlement Mark

9 b) E. prochilos

7 m) µ (

h 6 Widt 5

4 Increment

2 -11-10-9-8-7-6-5-4-3-2-11234567891011 Increment Number From Settlement Mark

Figure 5-3. Transition-centered profile for the two species of gobies. Mean increment width (± SE) for a) E. evelynae and b) E. prochilos. The vertical dashed line is the first increment of the settlement mark (= pelagic larval duration + 1 day).

128

a) E. evelynae 0.04 ) -1 mm -1

0.02 mm day th Rate ( ow tic Gr

a 0.00 Som

0.000 0.005 0.010 0.015 0.020 0.025 0.030 Otolith Growth Rate (µm day-1 µm-1)

0.04 b) E. prochilos ) -1 mm -1

0.02 mm day te ( a owth R c Gr 0.00 Somati

0.000 0.005 0.010 0.015 0.020 0.025 0.030 Otolith Growth Rate (µm day-1 µm-1)

(L − L ) Figure 5-4. Relationship between relative somatic growth ( t t−1 versus relative (Lt *t) (R − R ) otolith growth rates ( t t−1 ) for the two species of gobies. Linear (Rt *t) regression for a) E. evelynae (L=0.819*R) and b) E. prochilos (L=0.996*R).

129

a) 35

E. evelynae 30 E. prochilos

20 ncy (%)

15 Freque

0 0.0 0.5 1.0 1.5 2.0 2.5 Coefficient c of allometry

b) 30 E. evelynae E. prochilos

Frequency (%) 10

0 0.5 1.0 1.5 2.0 2.5 Coefficient c of allometry

Figure 5-5. Proportionality coefficient c estimated at the individual level. a) frequency of individuals that had a particular proportionality coefficient c as estimated from relative growth (see Eq. 5-1), and b) frequency of individuals that had a particular proportionality coefficient c as estimated from the L-R relationship (see Eq. 5-6). White bars are for E. evelynae and black bars are for E. prochilos. Arrows indicate isometry.

130

a) E. evelynae 25

m SL) 15 th (m ng 10 Le h length at capture data Fis regression for only length at capture data 5 all data regression for all data

0 150 200 250 300 350 400 450 500 Otolith radius (µm)

b) E. prochilos 25

20 )

m SL 15 (m h t ng 10 Le length at capture data sh

Fi regression for only length at capture data 5 all data regression for all data

0 150 200 250 300 350 400 450 500 Otolith radius (µm)

Figure 5-6. Length versus otolith size relationship for each species according to Eq. 5-6. Closed circles are the observations at capture only and closed and open circles are all observations. The dashed line considers the relationship for only the open circles (“typical” data that is available). The solid line represents the relationship considering all data. a) E. evelynae (dashed line: Lcpt=2.5- (1.029) (1.029) (0.908) 0.037*8.8 +0.037*Rcpt ; solid line: L=2.5-0.073*8.8 + (0.908) 0.073*R ), and b) E. prochilos (dashed line: Lcpt=2.5- (1.109) (1.109) (1.25) 0.024*9.2 +0.024*Rcpt ; solid line: L=2.5-0.0097*9.2 + 0.0097*R(1.25)).

Figure 5-7. Deviation of the back-calculated size at age from the measured standard fish length for the overall mean ( ) and for the two species of gobies (E. evelynae (●) and E. prochilos (○)) under the four different food treatments (ambient food, high food, low food and vary food) for the five back-calculation models. The mean deviation with 95% confidence intervals are shown. a) Modified Fry (MF) (Vigliola et al. 2000), b) Body-Proportional Hypothesis (BPH) (Francis 1990), c) Biological Intercept (BI) (Campana 1990), d)Time-Varying Growth (TVG) (Sirois et al. 1998), and e) Age Effects (AE) (Morita and Matsuishi 2001).

132

2 e a) MF Ag

h a s e

z 1 Si rd Fi d a e d t n a a t S cul

l 0

a -c ck a asured

B -1 Me m o r of n F ) o i t m a -2 vi (m h De gt

Len -3

2 b) BPH e Ag

h at s i e z F i 1 d S

r ed da at an ul c 0 Treatments cal ed St - r k u c as

Ba -1 Me f o

n From ) o i m at -2 m vi ( h t De g n

L -3

1 c) BI Age at sh i e z 0 ed Si dard F t la an u c St d e -cal r k

u -1 c s X Data Ba n of Mea From )

io -2 m at i (m

th Dev ng

Le -3

1 e d) TVG g A

at sh e z 0 d Si ard Fi te a l and u c l St a

-c X Data

ured -1 s Back m o r F n of Mea

)

io -2 t m a i v (m

e h D

ngt

Le -3

8 e e) AE Ag t 6 h a s e z i Fi d S 4 r ed nda

at 2 a ul c l

a 0 c - k

c X Data a asured St -2 B

Me f -4 o n From ) o i

m -6 at vi (m h

t -8 De g

n e

L -10

n b h y b h w r w ry a g o g m i l a m i lo a e h - v - - - -h -v m -a e -a s e e a e s s o s ll l a a a o o i lo n l l i a n n n i i h r ly y y y h h c h e l l l e c c o c v e e e v o o r o o v v e v r r p r e e e p p p Treatments

133

a) 26

20 th (mm)

ng 18

d Le 16 te a l

u 14 observed standard length alc Biological Intercept -c 12 k Modified Fry Body-Proportional Hypothesis

Bac 10 Time-Varying Growth 8

6 6 8 10 12 14 16 18 20 22 24 26 Observed Standard Length (mm)

80 b)

40 (mm)

gth 20

0 lated Len

cu -20 -cal

ck -40 observed standard length Ba Age Effects -60

-80 6 8 10 12 14 16 18 20 22 24 26 Observed Standard Length (mm)

Figure 5-8. Relationship between the back-calculated size at age for the different back- calculation models versus the observed standard length measurements for E. evelynae. a) four back-calculation models, Biological Intercept model (Campana 1990), Modified Fry model (Vigliola et al. 2000), Body- Proportional Hypothesis model (Francis 1990) and Time-Varying Growth model (Sirois et al. 1998) and b) Age Effects model (Morita and Matsuishi 2001).

134

a) 30

25 gth (mm) 20 ted Len

15 cula observed standard length Biological Intercept Modified Fry ck-cal

a Body-Proportional Hypothesis B 10 Time-Varying Growth

5 8 10121416182022242628 Observed Standard Length (mm)

35 b)

m) 25 m (

20 Length 15 ated l 10 observed standard length

ck-calcu 5 Age Effects Ba

-5 8 10121416182022242628 Observed Standard Length (mm)

Figure 5-9. Relationship between the back-calculated size at age for the different back- calculation models versus the observed standard length measurements for E. prochilos. a) four back-calculation models, Biological Intercept model (Campana 1990), Modified Fry model (Vigliola et al. 2000), Body- Proportional Hypothesis model (Francis 1990) and Time-Varying Growth model (Sirois et al. 1998) and b) Age Effects model (Morita and Matsuishi 2001).

450 a) vary 450 b) ambient

400 400

350 m) m) 350 µ µ ( ( 300 us us 300

h Radi 250 h Radi t t i i

ol ol 250 Ot 200 Ot

200 150

100 150 10 12 14 16 18 20 22 24 8 10121416182022

Observed Standard Length (mm) Observed Standard Length (mm)

340 c) low 450 d) high

320 135 400

300

m) m) 350 µ 280 µ ( ( s s u u i i d d

a 260 a 300

ith R 240 ith R ol ol t t 250 O O 220

200 200

180 150 10 12 14 16 18 20 22 24 10 12 14 16 18 20 22 Observed Standard Length (mm) Observed Standard Length (mm)

Figure 5-10. Relationship between otolith radius versus observed standard length for the four different food treatments for E. evelynae. a) varying food treatment, b) ambient food treatment, c) low food treatment and d) high food treatment. Individuals are plotted separately for each food treatment. Each symbol and dotted line in each plot corresponds to one individual. The solid line in each panel is the “population” line determined for each treatment based on a simple linear regression of otolith radius versus observed standard length for all individuals lumped together for each treatment.

450 500 a) vary b) ambient

450 400

400 m) m) 350 µ µ ( ( 350 300 300 h Radius h Radius

olit 250 olit Ot Ot 250

200 200

150 150 10 12 14 16 18 20 22 24 26 10 12 14 16 18 20 22 24 26

Observed Standard Length (mm) Observed Standard Length (mm)

450 c) low 550 d) high

500 136 400 450 m)

m) 350 µ µ ( 400 (

300 350 h Radius h Radius 300 olit olit 250 Ot Ot 250

200 200

150 150 10 12 14 16 18 20 22 8 10121416182022242628 Observed Standard Length (mm) Observed Standard Length (mm)

Figure 5-11. Relationship between otolith radius versus observed standard length for the four different food treatments for E. prochilos. a) varying food treatment, b) ambient food treatment, c) low food treatment and d) high food treatment. Individuals are plotted separately for each food treatment. Each symbol and dotted line in each plot corresponds to one individual. The solid line in each panel is the “population” line determined for each treatment based on a simple linear regression of otolith radius versus observed standard length for all individuals lumped together for each treatment.

True growth trajectory (observed length) Size Estimated growth trajectory (back-calculated length)

Estimated

size at agei True size

for agei 137

Age Estimated age True age

Figure 5-12. Depiction of how underestimating true age can overestimate back-calculated size at age. The gray line is the true growth trajectory based on the true age of the fish. The black line is the estimated growth trajectory based on the underestimated age of fish from the otolith.

CHAPTER 6 SUMMARY, IMPLICATIONS, AND CONCLUSIONS

Summary and Overview of Experimental Work

1983, McFarland et al. 1985, Robertson et al. 1988, 1993, Robertson 1990, Sponaugle and Cowen 1994, 1997). However, while settlement has been recognized as being notoriously variable, post-settlement processes, such as the strength of density independent and/or density dependent processes, have been assumed to be more homogenous over space and time. One aspect of my dissertation research was to quantify the strength of post-settlement processes and determine whether or not they were uniform over space. In fact, one set of experiments demonstrated that the strength of density independence varied among corals and drove variation in habitat quality (Chapter 2).

However, identifying the mechanism(s) that drove such variation was more difficult; there were no clear correlates of habitat quality (Chapter 2). Potential predator and competitors did not vary among sites nor did size, height, or depth of coral heads. The only distinguishable correlate was cleaning rate: gobies on lower quality sites had significantly higher cleaning rates. Therefore, it was hypothesized that cleaning was a

“risky” strategy (see Chapter 2) and was adopted only when other possible feeding strategies were not available. Thus, it was suggested that cleaning was a possible

138 139 indication of low site quality and could lead to high mortality by increasing exposure to possible predators.

In addition, settlement was greater to sites of higher quality (i.e., sites receiving the most settlers also yielded weaker density independent mortality). This positive covariance between settlement and habitat quality can mask the underlying effect of density dependence in observational studies (see Wilson and Osenberg 2002, Shima and

Osenberg 2003). Indeed, density had much stronger effects in this system than inferred from spatial correlations between density and survival (Wilson and Osenberg 2002).

Density had significantly negative effects on survival of both species; however, the negative effects of increased density were more offset by increased quality for E. evelynae than for E. prochilos (Chapter 3).

Experimental work with these species also suggested that mortality rate declined through time, even when fish density was kept constant (by replacing fish that died): i.e., a greater proportion of the fish died at the beginning of the experiment than towards the end of the experiment. Several scenarios can give rise to the same pattern where mortality rates change over time. For instance, all individuals may have the same mortality schedule (i.e., individuals from a given genetic cohort); however, mortality rate for the entire cohort may vary over time (i.e., a time-dependent mortality rate or hazard which depends on age of the entire cohort). For example, there may be a high hazard, or high probability of death, for all individuals in a cohort when the cohort is very young, due to vulnerability to predation. However, the probability of death decreases as the entire cohort becomes older and larger, and reaches a size refuge from predation, therefore, lowering the hazard of the cohort. Alternatively, higher mortality at the

140 beginning of the experiment could suggest that individuals can differ in size at settlement, condition or genetic make-up, and therefore have inherently different mortality schedules

(e.g. “weaker” individuals may die early whereas “stronger” individuals die off more slowly). Such heterogeneity within a cohort could be due to handling artifacts, which may have led to higher mortality rates at the beginning of the experiment; however, other studies have suggested that most mortality of new settlers occurs within the first 24 – 48 hours, even in the absence of handling (Schmitt and Holbrook 1999, Steele and Forrester

2002, Webster 2003). Indeed, my work is one of the first to suggest that there are differences among individuals of the same cohort in their survival probabilities (except see Miller et al. 1988, Houde 1989, Davis et al. 1991, Booth and Hixon 1999, Vigliola and Meekan 2002). This individual variation can have important consequences on the dynamics of reef fish systems; however, to date, most studies assume all new settlers are identical.

In addition to differences among individuals of the same cohort, mortality rates and interactions can also differ across cohorts. I therefore explored age-structured interactions for E. prochilos. However, there were no differences in the competitive effects within and between age classes of younger and older fish (however, there was some evidence that older fish were less affected by settlers than settlers were by other settlers – see Chapter 4). This result will greatly simplify modeling the dynamics of this species in future work (see below). In addition, work on growth patterns of the two species in the lab suggested that both species experienced similar allometric growth patterns as determined from otolith analyses. Otolith techniques and a Modified Fry model of growth can be used in future work to investigate possible variation in larval and

141 settler quality (e.g., estimated via variation in back-calculated size at settlement).

Otoliths can also be used to estimate adult longevity, age at reproduction, and dispersal abilities of these species (estimated via determining age at settlement) (Chapter 5).

Finally, my experimental work demonstrated that both species had similar competitive effects and responses to one another’s densities (Chapter 3). Indeed, the two species are very similar ecologically. For instance, settlement of each species begins as early as the last quarter moon, peaks around the new moon, and continues as late as the first quarter moon (a period as long as two weeks, but typically much less). Both species remain in the plankton for similar amounts of time (~27 days: see Chapter 5), settle onto coral heads at similar sizes (8.5 to 12.3 mm for E. evelynae and 9.2 to 12.9 mm for E. prochilos) and become sexually mature between 22 and 25 mm SL (Colin 1975). The two species also have similar morphology and occupy similar habitats (often co- occurring on the same coral heads where their distributions overlap: i.e., throughout the central Caribbean). They do, however, have different biogeographic distributions.

Elacatinus prochilos is found throughout much of the Caribbean, from as far north as the

Gulf of Mexico to Venezuela, whereas Elacatinus evelynae ranges only from the

Bahamas southward to Venezuela (Colin 1975).

Implications: Speculation About Mechanisms of Coexistence

These similarities challenge conventional ideas regarding the mechanisms by which these species coexist. Historically, competition theory has emphasized the importance of niche divergence among co-occurring species thus limiting competitive interactions and preventing competitive exclusion (MacArthur 1972, Ricklefs 1973, Pianka 1974,

Schoener 1974). Niche divergence results in stable coexistence by concentrating intraspecific competition relative to inter-specific competition (Abrams 1983, Tilman 1994).

142

These mechanisms can promote coexistence in constant or fluctuating environments, and have therefore been called "fluctuation-independent" mechanisms (Chesson 2000a).

These mechanisms cannot however, give rise to coexistence of identical species: over long enough time scales -- one species will always be excluded (Hubbell 1979, 1997,

2001).

Recent theoretical work has sought to clarify the ways in which similar species may coexist in the absence of classic niche divergence (Chesson and Warner 1981, Chesson

1985, 1997, 2000a,b, Warner and Chesson 1985, Hubbell 2001, Munday 2004). For example, coexistence between similar competitors can still arise through frequency- dependent predation or disturbance (Hutchinson 1959, Connell 1978) or resource patchiness (Pacala and Tilman 1994, Bolker and Pacala 1999). Alternatively, the lottery model describes how ecologically similar species compete for space; however, in such instances, competitive exclusion is inevitable, but the time required may be so long that competing species may appear to coexist on ecologically relevant time scales (Sale 1977,

1978, Hubbell 1979, 1997). In contrast, the stable coexistence of ecologically similar species can be facilitated by environmental variation that together with slight differences in the way species respond to the environment can provide the requisite “niche” divergence (Chesson and Warner 1981, Warner and Chesson 1985, Bolker and Pacala

1999, Chesson 2000a, b). Such mechanisms are inherently dependent on fluctuations in the environment, and therefore can be thought of as “fluctuation-dependent” mechanisms

(Chesson 2000a).

Fluctuation-dependent coexistence can arise through temporal, spatial or spatiotemporal variation (Chesson 1985). Models of coexistence in temporally varying

143 environments assume that species use the same resources but at different times

(Armstrong and McGehee 1976, Abrams 1984, Chesson and Huntly 1997), while models of coexistence via spatial variation give rise to stable coexistence when species live in different habitats, limiting interactions with one another (MacArthur 1972, Ricklefs 1973,

Pianka 1974, Schoener 1974). However, recent work suggests that strict segregation over space is not needed for coexistence (Levin 1974, Lavorel and Chesson 1995, Bolker and

Pacala 1999). Competitively equivalent species (in which per capita intra- and interspecific effects are equal) can coexist without spatial segregation if they either respond differently to the common varying environment (Chesson 1985, 1991, Iwasa and

Roughgarden 1986, Butler and Chesson 1990) or have different relative fitnesses over space (Chesson 1985, Iwasa and Roughgarden 1986, Butler and Chesson 1990, Pacala and Tilman 1994).

All three kinds of environmental variation (spatial, temporal, and spatiotemporal) can promote stable coexistence among competing species (Chesson 1985) via the

"storage effect". The storage effect relies on three main processes (Chesson 2000a,

2003). First, species must differ in their responses to the environment giving rise to temporal and/or spatiotemporal variation in settlement. Second, persistent life history stages must buffer settlement variation and prevent catastrophic population declines during poor settlement events. As a consequence, a population at low density grows more during favorable settlement events than it declines during periods of poor settlement

(Chesson 1994). Third, the effects of the environment and competition must covary

(Chesson 1990). The covariance between environment and competition will be greater for a species experiencing mostly intraspecific competition (i.e., a common species)

144 versus a species experiencing mostly interspecific competition (i.e., a rare species)

(Chesson 1994). The growth rate for a rare species will be greater than expected following a good settlement event because a species at low density is not as limited by intraspecific competition as the high density species. As a result, the rare species is expected to have a positive growth rate at low density, thus promoting coexistence

(Chesson 2000a, b).

Despite the well-known theory of the storage effect (e.g., Chesson 1978, 1982,

1985, 1994, 2000a, b, Chesson and Warner 1981, Warner and Chesson 1985) there has been little empirical evaluation of its role in promoting coexistence (but see Chesson and

Huntly 1989, 1993, 1997, Kelly and Bowler 2002). Elacatinus evelynae and E. prochilos are coexisting gobiid fishes that compete and exhibit temporal and spatial variation in settlement (see Chapter 3). Although my studies were not originally designed to study coexistence, they can be used to begin exploring this issue. Indeed, given the theoretical importance of the storage effect and the lack of empirical tests, one of my future goals is to use my data to evaluate the storage effect and to clarify how the storage effect might be tested. Here, I use settlement data for the two species collected over four years to three patch reefs in Tague Bay of St. Croix to evaluate if this system has all components of the storage effect and to try to evaluate if it is a plausible mechanism facilitating coexistence in this system.

The Storage Effect: Linking Theory with Empirical Aspects of Fish Settlement

The empirical approach necessary to evaluate the storage effect depends on the form of environmental variation. An Analysis of Variance (ANOVA) on the natural log transformed settlement data (i.e., the "environment") can be used to partition the variance components due to the interactions of species by space (i.e., spatial variation), species by

145 time (i.e., temporal variation) and species by time by space (i.e., spatiotemporal variation)

(Chesson 1985). This was done in Chapter 3 (see Table 3-3). Based on this ANOVA, there was no significant spatial or spatiotemporal variation (Table 3-3), suggesting that only temporal variation could contribute to the storage effect. This is not surprising given only three patch reefs in one bay of St. Croix were monitored for settlement, which is only one small area of the larger distribution of these species. Therefore, I concentrated on how aspects of the temporal storage effect may be driving coexistence in this system.

The temporal storage effect depends on each species' environmental response, Ej(t)

(i.e., settlement to the benthic environment), the response to competition, Cj(t) (which can be thought of as the reduction in recruitment due to competition), and the covariance between these factors, Cov(Ej(t),Cj(t)). According to the storage theory, covariance between the environment and competition will be greater for species experiencing more intraspecific competition relative to interspecific competition (Chesson 1994). This is important for the recovery of a species from low density, and acts to stabilize the species’ presence in the system by allowing a species at low density to experience higher per capita growth rates compared to more abundant species that are more limited by intraspecific competition. Therefore, critical to the storage effect is difference in the

Cov[Ej(t),Cj(t)] between one species at high density versus another species at low density.

If species show differential responses to the environment and differences in

Cov[Ej(t),Cj(t)], then there are several ways to quantify the storage effect (for examples see Chesson 1985, 2003). Typically, coexistence is considered in terms of invasibility criteria: if each species exhibits positive growth when at low density, then they will each

146 persist in the system (i.e., exclusion requires that the long-term growth rate be <0 when densities are low: Turelli 1981, Chesson 1994). However, the storage effect can be quantified from survey type data, such as the settlement surveys that I have for the two species of gobies (also see Kelly and Bowler 2002). The long-term low density growth rate of species i can be written as

ri ≈ ri′− ∆N i + ∆I i (6-1)

where ri′ is to the growth due to fluctuation-independent mechanism (i.e., classic

resource partitioning), ∆Ni measures the effects of relative nonlinearity (which will not

be discussed here; see Chesson 2000a), and ∆Ii is the difference between the resident’s and invader's covariance between the environment and competition (i.e. Cov(Er(t),Cr(t)) -

Cov(Ej(t),Cj(t)): Chesson (1994)). The term ri′ sums to zero over species, making it negative for some species and positive for others (unless it is zero for all species). The challenge arises for species with ri' < 0, indicating that in the absence of a storage effect,

they would be eliminated from the system. In such cases, ∆Ii might be sufficiently

positive to counteract negative values of ri′. In this situation, the storage effect will promote stable coexistence (Chesson 2003). Since the covariance term is expected to be smaller for species at low density than a species at high density (i.e., when a species is at low densities, a "good" settlement event does not lead to appreciable increases in

competition with conspecifics), ∆Ii will be tend to be positive when a species is rare.

If variances and covariances of the environmental responses’ are symmetric (i.e.,

2 2 V(Ei)=σ and Cov(Ei,Ej)=ρσ , for all species pairs, i≠j; see Chesson 2003) then the storage effect reduces to

147

σ 2 (1− ρ)(1− d)B ∆I = (6-2) i n −1 where B defines the form of competition (see appendix of Chesson (2003)), d is the fraction of adults dying during one unit of time, and , n is the number of species. If we assume that the species are competitively equivalent and adult longevity is equivalent among species, then the storage effect for species i becomes proportional to the species- specific component,[σ2(1-ρ)], of the variance of that species’ environmental response,

V(Ei(t)) (Chesson 2003).

(s≠i) (s≠i) Next, assume that ∆Ni is zero, and replace ri′ with µi − µs , where µs is the

(s≠i) average fitness over all resident species (see Chesson 2003). The term, µi − µs , can be thought of as the average fitness disadvantage of the invader in the absence of environmental fluctuations relative to its competitors. Given these assumptions and substitution, Eq. 6-2 can be rewritten as:

(s≠i) 2 ri = µi − µs + σ (1 − ρ) * c (6-3)

(1 − d)B where c = , and c is assumed to be equivalent for both species and is n −1 subsequently considered a constant. Therefore, if there is a large enough value of σ2(1-ρ)

to overcome any fitness disadvantage, then all species will have positive values of ri and coexist (Chesson 2003).

Given this theoretical framework, I can evaluate if the temporal storage effect is promoting stable coexistence in the goby system using my settlement surveys of the two goby species. From my settlement surveys of three patch reefs of the two species, I can estimate Ej(t). From previous competition studies, I can measure Cj(t), and given these

148

estimates, I can directly estimate Cov[Ej(t),Cj(t)] (note t is one month or 28 days) to determine if there are aspects of the storage effect operating in this system. Additionally, using an ANOVA on my natural log transformed settlement data, I can quantify the proportional contribution of the temporal storage effect in this system (Chesson, personal communication). By estimating mean mortality of each species and mean mortality over

(s≠i) all species as a surrogate of fitness to assess the value of µi − µs , I can evaluate if the proportional estimate of the temporal storage effect is large enough to outweigh any fitness disadvantages and produce coexistence in this system.

Empirical Evidence of the Temporal Storage Effect

If the temporal storage effect is an important mechanism of coexistence in this system, then three conditions must be satisfied: 1) there must be overlapping generations to buffer population growth of each species; 2) there must be differences in the

Cov(Ej(t),Cj(t)) between species, and 3) the two species must have different responses to the environment (Ej(t)). Using my empirical data from settlement surveys and experimental studies in my dissertation, I will next determine if these three conditions are met in the goby system.

Buffered Population Growth

Overlapping generations are critical for the storage effect to promote existence

(Chesson 2000b). Because E. evelynae and E. prochilos can become reproductive within one month of settlement (Colin 1975, Wilson, personal observation), I determined if older fish persisted from one settlement event to the next, indicating that generations overlapped. On average, 6.7% of coral heads had adult E. evelynae present one lunar month following a settlement peak (Figure 6-1), while 2.5% had adult E. prochilos

149 present (Figure 6-1). Thus, generations overlap to a small degree, which potentially buffers population growth.

Covariance Between the Environment and the Strength of Competition

I determined settlement (i.e., Ej(t)) for each species during each month by summing up the total number of new settlers of each species to my study sites in the patch reef system of Tague Bay (reefs 5, 7, 18) within a given month.

Next, the strength of competition was estimated as the recruitment in the absence of density dependent survival relative to that with density dependence (see Chesson 2003)

0 ∑ Ri, j (t) Ci, j (t) = (6-5) ∑ Ri, j (t)

0 where Ri, j (t) is the recruitment rate on coral head i of species j from time t to t+1 in the absence of competition (i.e. but with the inclusion of density independent mortality) and

Ri,j(t) is the recruitment rate with both density independent and density dependent

0 mortality included (see Chesson 2003). The terms Ri, j (t) and Ri,j(t) were summed across all coral heads for a given month, and then the ratio of these summed values was used as the estimate of the strength of competition for a given month. The term, Ri,j,(t), was based on the integrated form of the Beverton-Holt settlement function (see Chapter 1,

Osenberg et al. 2002 and Bolker et al. 2002)

−αit e S0 Ri, j (t) = (6-6) β (1 − e−αit )N 1 + i, j,k 0 αi where βi,j,k is the effect of one individual of species j on the instantaneous mortality rate of species k on coral head i (coral head per fish per day: coral head fish-1d-1; see Chapter

2), αi, is the density independent mortality rate on coral head i, S0 is the initial number of

150

settlers, N0 is the total initial number of fishes on a coral head (both species and all age classes), and the time interval was one month (i.e., 28 days).

I estimated the necessary terms in Eq. 6-6 by drawing from my experimental results and striving for a relatively simple approach (in which I emphasized general patterns).

Because the strength of density dependence was relatively uniform in space, and similar among species and age classes, I assumed that β i,j,k = 0.012 for all coral heads, species and age classes (this is the average of the per capita effects estimated for each age class and species in Chapter 3). Because the strength of density independence varied among coral heads (Chapter 3), I defined αi as

αi, = 2.85+0.34*Q (6-7) where Q was the number of fishes present just prior to settlement (a correlate of habitat quality), and the constants were taken from the regression in Figure 2-3 in Chapter 2. To

0 estimate Ri, j (t) , I took an identical approach, except that I set βi,j,k = 0. Cov(Ej(t), Cj(t)) was calculated by regressing the strength of competition for each month on total settlement for each month (Ej(t)) for each species.

Settlement surveys demonstrated that Elacatinus evelynae and E. prochilos had similar (albeit variable) overall settlement through time with an average of 52.84 ± 23.85

(S. E.) settlers for E. evelynae and an average of 46.84 ± 9.35 (S. E.) settlers for E. prochilos. Despite the similar densities, there were differences in the strengths of the relationships between the strength of competition and total settlement (i.e., the environment), where E. prochilos had a weaker covariance (r = 0.09) between the strength of competition and the environment than E. evelynae (r = 0.75) (Figure 6-2).

151

Differential Responses to the Environment

Settlement of E. evelynae and E. prochilos within a given month was not strongly correlated (r = 0.11), suggesting that a “good” settlement event for one species was not necessarily a “good” event for the other species (see Figure 3-2, Chapter 3). While there was a positive relationship within three of the four years between settlement events of each species, there was a negative relationship in one year (1996), which also had the most variation in settlement (see Figure 3-2, Chapter 3). This gives some evidence suggesting that the two species had different responses to the environment.

Quantifying the Temporal Storage Effect

The system has all elements of the temporal storage effect, but what does that mean in terms of coexistence? The variance components from the ANOVA on the log transformed settlement data in Table 3-3 of Chapter 3 can yield the proportional contribution of the temporal variation to the temporal storage effect (Chesson, personal communication). Therefore, I re-ran the ANOVA in Chapter 3 in Table 3-3, removing all non-significant interaction terms, and calculated the variance component of the temporal variation term (species by time interaction; see Table 6-1). The proportional contribution of temporal variation to the temporal storage effect on the population growth was 0.1312 per adult per month (Table 6-1). The temporal storage effect will produce stable coexistence if it can outweigh a fitness disadvantage of either species. Therefore, evaluating the role of the storage effect requires comparing the temporal variation to the fitness differential. Because this is an open system, in which post-settlement mortality is critical in determining benthic density, I estimated the mean fitness of each species in terms of mortality. If one species had greater average mortality than the overall average mortality for both species, it would presumably have a fitness disadvantage. Based on

152 these mortality estimates, E. evelynae had a higher mean mortality than the overall average mortality. However, the proportional estimate of the contribution of the temporal storage effect was large enough that it could, in fact, help overcome this disadvantage and produce coexistence (Table 6-2). Elacatinus prochilos, however, did not have a fitness disadvantage (at least in terms of mortality). Thus, the storage effect could potentially only add to its population growth. This is especially of interest given E. prochilos, on average, had fewer adults present on coral heads than E. evelynae (Figure 6-1), and thus, a larger population growth with fewer adults may help keep E. prochilos from being out- competed by E. evelynae. Again, these results are speculative given the small spatial extent of this study (i.e., E. prochilos may have more adults present elsewhere) and due to the approximate estimates of fitness and of the contribution of the temporal storage effect (i.e., Table 6-2).

Implications of the Storage Effect

This final chapter was meant as a preliminary examination to determine if the storage effect was a viable mechanism promoting coexistence in this goby system.

Theoretically, differences in the covariances between the environment and competition should allow the rarer species (which should also have a weaker covariance between the environment and competition) to have a higher per capita growth rate during favorable environmental conditions. Other studies that have taken a similar approach contrasting recruitment variation and growth rates between species pair that differed in density (see

Kelly and Bowler 2002). However, the similarity in overall densities of the two species in this study brings into question the appropriateness of the temporal storage effect for this system. Perhaps the temporal scale used in this study is not appropriate. For instance, the similarities in numbers may be due to the “snapshot” nature of this study.

153

These data were taken from only three-four month periods during four different years, and perhaps these months are not indicative of numerical differences between the species.

However, the two species did have differential responses to the environment within a given month (see Table 3-3 & Figure 3-2, Chapter 3), where one species had a low density and the other had a higher density within a given month. Therefore, these differences in density within a monthly time-scale may be enough to satisfy the requirements of differential densities for the storage effect.

Next, depending on how high a species’ average mortality was from the overall average mortality, it appears that the proportional contribution of the temporal storage effect may be large enough to “rescue” a species with a fitness disadvantage. Curiously, the species with the stronger covariance between competition and the environment, E. evelynae, had the greater fitness disadvantage (Table 6-2). However, E. prochilos, the species with the weaker covariance between competition and the environment, did not appear to have a fitness disadvantage (Table 6-2). Thus, this species might not need the temporal storage effect to remain in the system (i.e., other mechanisms of coexistence, such as resource partitioning may be sufficient to allow this species to persist over time).

However, these assertions must be made with some caution. First, this work required a number of assumptions (i.e., that adult numbers were consistent over time, and there were similar adult longevities, complete competitive equivalence between the two species, and similar effects of habitat quality on the two species). Violation of these assumptions can have important implications for the evaluation of the storage effect (see

Chesson 2003). Additionally, whether or not the storage effect is promoting coexistence does not preclude fluctuation independent mechanism from promoting coexistence.

154

Niche divergence and resources partitioning are classic mechanisms known to promote stable coexistence (MacArthur 1972, Ricklefs 1973, Pianka 1974, Schoener 1974).

These mechanisms could, in theory, be playing a role in maintaining coexistence given slight morphological differences between the two species; E. evelynae has a terminal mouth and rostral frenmum where E. prochilos has a subterminal mouth, which may allow for differences in dietary patterns.

Finally, many marine ecologists have argued that coexistence in open systems can result from fixed levels of settlement into local populations (Warner and Hughes 1985,

Hixon 1998). No doubt, this explains local persistence of many species. However, this becomes a circular argument if extended to the larger scale without explaining what maintains settlement at these larger scales. Such an explanation tells us little about the maintenance of diversity on a global scale, and ideally, we want to consider coexistence on a large enough spatial scale that the system is “closed” and is not influenced by migration across boundaries. However, this is logistically difficult for marine systems where little is known about the “openness” of systems and dispersal abilities of different species (but see Leis et al. 1998, Jones et al. 1999, Swearer et al. 1999, Taylor and

Hellberg 2003). However, understanding the dynamics of this system (in terms of settlement variation) over a larger spatial scale will help elucidate to what extent the spatial (and even spatiotemporal) storage effect may be acting to promote stable coexistence. Finally, while empirical tests of the storage effect have been conducted (e.g. see Warner and Chesson 1985, Kelly and Bowler 2002), the scope of data needed to critically evaluate and quantify the storage effect in marine systems is challenging.

Operationalizing the theory so that it can be tested empirically is still a work-in-progress.

155

The work presented here was intended to broaden the implications of my experimental work and synthesize these results within the theoretical framework of the temporal storage effect as a mechanism of coexistence.

Future Directions

In the future I plan to develop a population dynamics model in collaboration with

Craig Osenberg and Ben Bolker that will provide a conceptual framework to quantify how density dependence, interspecific interactions, and variation in habitat quality affect adult densities of E. prochilos. Estimates of these processes will be taken from the empirical studies in my dissertation that will be used to develop and parameterize the model, which will be based on the approach taken by Bolker et al. 2002 (see Chapter 1).

Thus, my dissertation research has provided the conceptual and empirical basis for this work. It was designed to quantify the strength of density dependence and density independence, estimate the spatial variation in these processes, and quantify differential age class and competitive interactions between the two species. For instance, empirical evidence from this work demonstrated that for the most part, interactions among age classes of E. prochilos are essentially unstructured. Thus, modeling the dynamics of E. prochilos can be simplified since the effects and responses of different age classes of E. prochilos are similar.

More importantly, since the multiple processes that shape the dynamics of E. prochilos do not act in isolation, it is critical to understand how multiple processes operate simultaneously (Schmitt et al. 1999, Osenberg et al. 2002). Therefore, to understand how multiple processes act in concert, I need to integrate settlement and post- settlement processes into a common framework to be able to extrapolate longer term dynamics (i.e., multiple generations) over larger spatial and temporal scales. The model I

156 develop will allow me to gain general insights into the dynamics of this system and to examine the population level implications of these interactions within habitats of different quality.

In addition, I can envision that further investigation of how different mortality rates among individuals (which can be one phenomenon driving the Weibull pattern of mortality in this system) could reveal important implications of individual variation on the dynamics of this system. Such an investigation will allow a better understanding of how individual factors, such as variation in condition, can translate into population level phenomena. For instance, what are the population effects of individual variation in condition (i.e. larger body size, higher fat reserves, etc., leading to “better” condition)?

Are better conditioned individuals less affected by other individuals (i.e., do they have superior competitive responses) and/or are they more able to suppress other individuals

(i.e., do they have superior competitive effects)? Differences in competitive abilities of individuals can have important implications on the dynamics of this system, which has mostly been ignored in marine reef fish systems.

In fact, settlement variation and the competitive abilities of these species is an important component of the maintenance of diversity in these systems (Doherty and

Williams 1988, Chesson and Warner 1981, Warner and Chesson 1985, Chesson 2003).

In future studies, I will also use my empirical data to more rigorously evaluate the storage effect and determine its role in promoting coexisting of E. evelynae and E. prochilos in collaboration with Peter Chesson, Craig Osenberg and Ben Bolker. However, in order to more quantitatively evaluate the storage effect, some additional information is needed. I need to quantify if adult density changes over space and time, and I need to estimate adult

157 longevity and per capita production for the two species. In addition, I need to know the appropriate spatial scale to consider the spatial and spatiotemporal storage effect in this system. In order to evaluate spatial and spatiotemporal variation, I need to identify a large enough spatial scale such that immigration is no longer an issue. This would most likely require a population genetics study (i.e., similar to that of Taylor and Hellberg

2003) to determine larval dispersal and at what spatial scale the goby system is essentially “closed”. Finally, more extensive temporal data (e.g., collected throughout the year) is needed.

158

Table 6-1. Refined model of the Analysis of Variance of Table 3-3 in Chapter 3 (main factors and only significant interactions included) on the natural log of settlement for the two species on three patch reefs over 13 settlement events. “Species” was a fixed factor whereas all other factors were random. Source DF Mean Square F-value P-value Variance

Model 143 9.72 13.56 <0.0001 Error 3028 0.72

Species 1 4.28 0.26 0.62 Space 118 8.37 11.67 <0.0001 Time 12 16.46 0.98 0.51

Species x 12 16.72 23.33 <0.0001 0.1312 Time

Table 6-2. Contribution of the temporal storage effect towards stable coexistence (see Eq. 6-3). Note: σ 2 (1− ρ) was taken (1 − d)B from variance term of the species x time interaction in Table 6-1, c = where (1-d) = 0.27/month (taken n −1 from Wilson and Osenberg 2002), B = 1 for competitively equivalent species (see Appendix in Chesson 2003), and 2 n = 2 for the two species considered here. Finally, the term µs − µ + σ (1 − ρ) * c is the increase in population growth rate due to the storage effect with units of per adult per month. 2 Species µ c 2 µ σ (1− ρ) s µs − µ µs − µ + σ (1 − ρ) *c -0.672 0.13121 E. evelynae -0.70 0.27 -0.028 0.0074 E. prochilos -0.66 0.27 0.012 0.0474

159

160

E. evelynae 125 E. prochilos

120

115

110

105

100 20 Frequency 15

0 01234

Average Number of Adults (average no. adults / coral head)

Figure 6-1. The average number of adults on coral heads for the two goby species just prior to settlement over 13 months during 4 years (1996, 2000, 2001 and 2002), and n=119 coral heads.

161

1.030

1.025 ion

it 1.020 et mp

Co 1.015 of h t 1.010 reng t

S E. evelynae E. evelynae regression 1.005 E. prochilos E. prochilos regression

1.000 0 50 100 150 200 250 300 Environmental Response (total monthly settlement)

Figure 6-2. The relationship between the mean strength of competition (calculated according to Eq. 6-5) per coral head each month and the environmental response (the total number of settlers during a given month) for 13 different settlement events. E. evelynae (• and regression line) and E. prochilos (o and dashed line). Note: there was no settlement for E. prochilos in June of 2000; thus, competition was undefined for this species during this month, resulting in only 12 data points for E. prochilos.

APPENDIX A APPROXIMATING AN ADDITIVE MODEL OF MORTALITY FROM THE LOG ADDITIVE MODEL (OR HAZARD) USED IN THE SURVIVAL ANALYSIS

The hazard function can be expressed as a log hazard function according to

Allison (1995) such that

• • • • • • • • Ln(hi[t]) = ρ * Ln(t) + γ 0 + γ QQi + γ DNi + γ E Ei + γ QDQi Ni + γ QEQiEi + γ DENiEi + γ QDEQi NiEi (A-1)

• • where γ i = −γ i /σ , ρ = (1/σ)-1 at time t, and γ 0 is the intercept (Allison 1995) and subscripts are defined as in Eq. 2-1.

In the Weibull model, the hazard function, or mortality rate, varies over time. The relative mortality rates of all treatments remain the same over time; thus for mathematical simplicity, I will derive the additive model of mortality at time t = 1 so that the term

ρ * Ln(t) in Eq. A-1 becomes zero. The coefficients from the log hazard model (γ • ’s)

(assuming that they are small in magnitude) can be used to derive an additive model of mortality from the log additive model by approximating the value of the function ( f (N ) ; estimating the hazard as a function density) using the Taylor series approximation (see

Hilborn and Mangel 1997) where

• • • f (N ) = eγ 0 +γ QQi +γ D Ni (A-2) which is an exponentiated form of the log hazard, but defined in terms of Eq. 2-2. Using the Taylor series approximation, we can take higher order derivatives of the function at a chosen point (in this case, N=0) and approximate the additive model using Taylor series approximation such that

162 163

2 2 γ • n n ∂f ∂ f N 0 ∂ f N f (N ) ≈ f (N = 0) + N =0.N + N = 0. e + ... + N = 0. ... (A-3) ∂N ∂N 2 2 ∂N n n!

Since the second derivative is small, we can ignore it and any higher order derivatives.

Thus, Eq. A-3 can be simplified such that

• • • • (γ 0 +γ QQi ) (γ 0 +γ QQi ) • fi (N ) ≈ e + e γ DN. (A-4)

The parameters in Eq. A-4 can be put into terms of αi and βi in Eq. 2-2 as

• • ' γ 0 +γ QQi αi = (e ) , (A-5)

• • ' (γ 0 +γ QQi ) • βi = e γ D (A-6) where Qi is “habitat quality” or the number of initial residents found on a particular coral head. Therefore, while the additive model allowed independent estimates of density

' ' independence (α) and density dependence (β), estimates of αi and βi from the log additive model are not independent from one another; the estimate of density dependence

' ' ( βi ) is dependent on the value of density independence (αi ). In addition, variation in

' ' αi is reflected in the estimate of βi . Differences in the estimates of these parameters between the two approaches are due to how the effect of density is interpreted in a

Beverton-Holt type of framework versus a survival analysis type of framework. In the

Beverton-Holt approach, the effect of density independence is added to the effect of density dependence (i.e., it is an additive model). However, in survival analysis, the effect of density independence is multiplied by the effect of density dependence (hence, it

' ' is a log additive model). Therefore, while equating estimates of αi and βi from a survival analysis approach to estimates of α and β from a Beverton-Holt approach allows

164 comparison of these results with those from other systems (i.e., estimates of density independence and density dependence has been published using a Beverton-Holt framework), it is important to recognize the differences in these approaches and how they translate into parameter estimates.

APPENDIX B ESTIMATING VARIANCE ON HAZARD (MORTALITY) (TAKEN FROM COLLETT 1994)

In order to estimate the variance of mortality within each habitat j, I first had to estimate the variance of each parameter in the log hazard model (Eq. A-1). Only the standard error of γi is calculated in a survival analysis (Eq. 2-1). To obtain the variance

• of each γ i , we can first consider the approximate variance of an arbitrary function ,g, of two parameters, θ1, θ2, as

∂g 2 ∂g 2 ∂g ∂g var(g) = ( ) var(θ1 ) + ( ) var(θ2 ) + 2( ) cov(θ1,θ2 ). (B-1) ∂θ1 ∂θ2 ∂θ1 ∂θ2

Now take

• γ i γ i = g(γ i ,σ ) = − σ where γi is the coefficient of factor i in the survival analysis (Eq. 2-1), and σ is the scale

• parameter estimated from Eq. 2-1. To calculate the approximate variance of γ i , we need to calculate the derivatives of g(γi, σ) such that

∂g 1 ∂g γ i = − , = 2 , ∂γ i σ ∂σ σ so we can use Eq. B-1, substituting the above derivatives as

γ 1 γ 1 γ var(− i ) ≈ (− )2 var(γ ) + ( i )2 var(σ ) + 2(− )( i )cov(γ ,σ ) . σ σ i σ 2 σ σ 2 i

This can be simplified to

165 166

1 4 var(γ • ) ≈ [σ 2 var(γ ) + γ 2 var(σ ) − 2γ σ cov(γ ,σ )]. (B-2) i σ i i i i

With estimates of the variance for the parameters in the log hazard model, we can then calculate the variance of the log hazard on day 1 within habitat i (var[ Ln(hi[1]) ]) as

• 2 • 2 • 2 • var(Ln(hi[1])) ≈ var(γ 0 ) + x1i var(γ1 ) + x2i var(γ 2 ) + ... + xki var(γ k ). (B-3)

Finally, the variance of the hazard on day 1 can be calculated from the variance of the log hazard model in each habitat i such that

2*Ln(h [1])+var(Ln(h [1])) var(Ln(h [1])) var(hi[1]) ≈ e i i * (e i −1) (B-4) where Ln(hi[1]) is from Eq. A-1 and var( Ln(hi[1]) ) is taken from Eq. B-3.

APPENDIX C ESTIMATING THE VARIANCE OF THE STRENGTH OF DENSITY INDEPENDENCE AND THE STRENGH OF DENSITY DEPENDENCE ESTIMATED FROM A LOG ADDITIVE MODEL

' ' The variance of αi and βi on day 1 can be estimated from the framework

' developed in Appendix A and Appendix B. First, given the definition of αi in Eq. A-5,

• • ' γ 0 +γ QQ the variance of αi is calculated by taking the log hazard of e . Using Eq. A-1, this is represented as

' • • Ln(.αi[1]) = ρ * Ln(1) + γ 0 + γ Q xQi

It should be noted that an average “Experiment” effect was incorporated in the model by

• using the parameter estimate for the average experiment (γ E ) in place of the model

• intercept, γ 0 .

' Next, the variance of the log hazard for αi can be estimated from Eq. B-3 such that

' • 2 • var(Ln(αi[1])) ≈ var(γ E ) + xQi var(γ Q ) .

' Finally, the variance of hazard, or mortality associated withαi , can be estimated from

Eq. B-4 as

' 2*Ln(α ' [1])+var(Ln(α ' [1])) var(Ln(α ' [1])) var(αi[1]) ≈ e i i * (e i −1) . (C-1)

167 168

' ' Since the estimate of βi includes the estimate of αi multiplied by the effect of

• ' ' density (γ D ), calculating the variance of βi is slightly different from that of αi (i.e., the elements were multiplied in Eq. A-6 rather than added as in Eq. A-5).

' Therefore, the variance of βi becomes

' ' • 2 • ' 2 var(βi ) = var(αi[1]) * (γ D ) + var(γ D ) * (αi ) (C-2)

' • ' where var(αi[1]) comes from Eq. C-1, var(γ D ) comes from Eq. B-2, and αi comes from Eq. A-5.

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BIOGRAPHICAL SKETCH

My main interests are in community ecology and population biology, and throughout my undergraduate and graduate career, I have had a strong interest in research. I received my Bachelor of Arts in aquatic biology from the University of

California, Santa Barbara (UCSB) in 1994. While attending UCSB, I received the Dean

Bazzi Memorial Scholarship from the Department of Biological Sciences for my work in environmental science. I also participated in several research programs as an undergraduate. I completed and published an independent research project under the direction of Dr. Alice Alldredge in which I investigated the impact of the copepod,

Calanus pacificus, on carbon cycling in the ocean. I received funding for this study from the May Company Scholarship. In addition, I worked in Dr. Alldredge’s lab studying impacts of other types of zooplankton on carbon cycling, and I worked in Dr. Robert

Warner’s lab studying behavioral ecology of marine fish in St. Croix of the U.S.V.I.

Finally, in the spring of 1995 I participated in an internship program at Mote Marine

Laboratory in Sarasota, Florida. There I assisted with field surveys of coastal shark species to investigate migration patterns and the effects of commercial fishing on particular shark species.

In the fall of 1995 I began my graduate work at the University of Florida in the lab of Dr. Craig Osenberg. My master’s research focused on spatial and temporal variation and density dependence in the recruitment and survival of two gobies (Elacatinus evelynae and Elacatinus prochilos) found in St. Croix. In May of 1998 I completed my

187 188 master’s work and continued with my dissertation in Dr. Osenberg’s lab. I spent two summers (1998 and 1999) working in the Florida Keys studying population dynamics of the bicolor damselfish, Stegastes partititus. However, due to difficulties in manipulating densities of this species, and given my background in the goby system in St. Croix, I returned to St. Croix during the summers of 2000 – 2002 for my dissertation research. I received an EPA STAR Fellowship to fund this work where I investigated post- settlement processes driving variation in habitat quality, recruitment patterns and differences in species and age class interactions between E. evelynae and E. prochilos.

Since the completion of my Ph.D., I have been looking for a research position in either a state or a federal management or a policy-based agency. While in such a position, I hope to address three major limitations I feel currently limit the quality of applied research. First, there is a tendency to base applied studies on poor experimental or study designs, which reduces confidence in the investigators’ conclusions. Second, these studies often do not rely on ecological theory, which limits the application of the results to new situations. Third, there is poor communication between scientists and policy-makers, which further limits the application of science. Scientists need to efficiently disseminate their results to policy-makers so that policies can be informed by sound science. In turn, this communication will also inform scientists of the questions of most relevance to policy-makers. Achieving these goals require that scientists interested in applied problems be well-trained in ecological theory and basic science and that they understand policy and the application of scientific results.