Population Ecology and Monitoring of the Endangered Devils Hole Pupfish Maria Dzul Iowa State University

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2011 Population ecology and monitoring of the endangered Devils Hole pupfish Maria Dzul Iowa State University

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Population ecology and monitoring of the endangered Devils Hole pupfish

Maria Christina Dzul

A thesis submitted to the graduate faculty

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

Major: Wildlife Ecology

Program of Study Committee: Stephen J. Dinsmore, Co-Major Professor Michael C. Quist, Co-Major Professor Philip M. Dixon

Iowa State University

Ames, Iowa

2011

TABLE OF CONTENTS

LIST OF TABLES iv LIST OF FIGURES vi ACKNOWLEDGEMENTS xi

CHAPTER 1. GENERAL INTRODUCTION 1 Thesis Organization 5 References 6

CHAPTER 2. IDENTIFYING SOURCES OF ERROR IN SURVEYS OF ADULT DEVILS HOLE PUPFISH 9 Abstract 9 Introduction 10 Methods 12 Results 16 Discussion 18 References 23 Tables 27 Figures 28

CHAPTER 3.USING VARIANCE COMPONENTS TO ESTIMATE POWER IN A HIERARCHICALLY NESTED SAMPLING DESIGN: IMPROVING MONITORING OF LARVAL DEVILS HOLE PUPFISH 30 Abstract 30 Introduction 31 Methods 34 Study Area 34 Survey Design 35 Statistical Analysis 36 Results 39 Discussion 40 Conclusion 44 References 47 Tables 52 Figures 53 iii

CHAPTER 4. DEVELOPING A SIMULATION MODEL OF THE DEVILS HOLE PUPFISH POPULATION USING MONTHLY LENGTH FREQUENCY DISTRIBUTIONS 58 Abstract 58 Introduction 59 Methods 62 Study Site 62 Estimation of length-frequency distributions 63 Evaluating length-frequency distributions using mixture models 65 Model Construction 66 Simulation Modeling 66 Estimating Reproduction 67 Fitting a Growth Model 70 Survival 72 Simulation Runs 74 Simulation Models 75 Choosing a baseline model 75 Assessing elasticity of model inputs 76 Results 79 Discussion 82 Conclusion 90 References 92 Tables 101 Figures 104

CHAPTER 5. GENERAL CONCLUSIONS 117

LIST OF TABLES

CHAPTER 2

TABLE 2.1. Evaluation of sources of error in estimates of size of the 27 population of Devils Hole pupfish (Cyprinodon diabolis) in Nye County, Nevada. Test statistics are shown for mixed-effects model assessing historical records of estimates, split-split plot ANOVA evaluating experimental dives, split-plot ANOVA examining experimental shelf surveys, and split-plot ANOVA analyzing combined estimates from experimental dives and shelf surveys.

CHAPTER 3

TABLE 3.1. . Variance components and their associated estimates of 52 statistical power in hierarchically nested surveys of Devils Hole pupfish (DHP) larvae, Cyprinodon diabolis, in Devils Hole, Nye County, NV. Values were attained from ln-transformed abundance estimates of DHP larvae from mid-March to mid-May. Power was estimated from sampling designs with five surveys, three events, and nine plots. Plots were treated either as fixed (F) or random (R) effects.

CHAPTER 4

TABLE 4.1. Summary of parameterizations used in simulation models 101 describing population dynamics of Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, Nye County, NV. Specifically, annual survival probabilities for adult, juvenile, and larval pupfish were increased by 5% to determine the effect of survival probabilities on the finite population growth rate (λ). Likewise, reproductive length and juvenile length were increased by 5% in the baseline model to evaluate the response of λ to uncertainty in these parameter estimates. One additional simulation which includes decreased estimates of the number of larvae per female and increased estimates of larval survival probabilities was run to determine response of λ to uncertainty in fecundity estimates. Importantly, because survival of juveniles and adults was modeled as a Type 2 survival curve, 5% annual increases in adult and juvenile survival rates corresponds to a 0.4% (or 1.051/12) increase in monthly survival probabilities.

TABLE 4.2. Summary of mixture model parameters describing monthly 103 length-frequency of the Devils Hole pupfish population, Cyprinodon diabolis, Devils Hole, Nye County, NV. For each month, mixture v

models with normal and lognormal distributions were compared and the top model was selected using the Bayesian Information Criterion (BIC). Sums of BIC values from mixture models fit to lognormal distributions were lower than the sum of BIC values fit to a normal distribution (∆BIC = -6.1).

LIST OF FIGURES

CHAPTER 2

FIGURE 2.1. Side view of Devils Hole, Nye County, Nevada, illustrating 28 the four levels used in SCUBA-dive surveys.. The entire geographic range of the Devils Hole pupfish (Cyprinodon diabolis) resides in this cavern system.

FIGURE 2.2. Mean number of Devils Hole pupfish (Cyprinodon 29 diabolis) in Nye County, Nevada, by: a) time of day × level; and b) net × level. Error bars represent SE estimated from ln-transformed estimates of size of population. The interval of the ln-transformed mean ±1 SE was then back-transformed so that it could be applied to estimates of abundance. Different letters represent contrasts that were statistically different (P <0.05).

CHAPTER 3

FIGURE 3.1. Sampling design structure for surveys of larval Devils Hole 53 pupfish, Cyprinodon diabolis, in Nye County, NV. The left photograph shows the Devils Hole spawning shelf with placement of fixed plots represented by numbers. In the upper left corner, there is a photograph of the sampling apparatus. The right diagram depicts the hierarchically nested structure of the sampling design.

FIGURE 3.2. Estimates of larval abundance per plot from mid-March to 54 mid-May for the Devils Hole pupfish, Cyprinodon diabolis, in Devils Hole, Nye County, Nevada. Average larval abundance per plot from 2007-2009 was estimated as the average number of larvae occurring on plots during each survey.

FIGURE 3.3. Statistical power to detect increases in the abundance of 55 Devils Hole pupfish larvae, Cyprinodon diabolis, in Devils Hole, Nye County, NV. Power was estimated for different sample size combinations in a hierarchically nested sampling design. Estimates of variance components and power were attained from pooling abundance data from five surveys days each year in mid-March thru mid-May in 2007 –2009. In each panel, the sample sizes of two levels of sampling were held constant to show how increasing sample size at a specific level of sampling influenced statistical power. Power was estimated from sampling designs with (a) 3 events and 9 vii

random plots, (b) 5 surveys and 9 random plots, and (c) 5 surveys and 3 events.

FIGURE 3.4. Comparison of power from sampling designs with fixed 56 plots and random plots in surveys of larval Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Power was calculated from pooled estimates of variance in spring 2007-2009 from sampling designs with 5 surveys and 3 events.

FIGURE 3.5. Statistical power of different sampling design structures to 57 detect a 30% increase population abundance in Devils Hole pupfish larvae, Cyprinodon diabolis, in Nye County, NV. Symbols on the graph represent the number of events in each survey. The dotted line represents a constant sampling effort of thirty plots partitioned differently among events (i.e., for 5 plots and 6 events versus 30 plots and 1 event). The line slopes gently upwards, indicating that maximizing the number of plots per event will result in a survey design with higher power. The number of surveys was held constant at five. Power of the previous (3 events, 9 plots) and proposed (2 events, 30 plots) sampling designs are illustrated by (*) and (†), respectively.

CHAPTER 4

FIGURE 4.1. Mixture models fit to monthly length-probability 104 distributions of the Devils Hole pupfish, Cyprinodon diabolis, endemic to Devils Hole, Nye County, NV. Observed length-probability distributions from stereovideo dives (solid line) are plotted against best-fit normal mixture models (dotted line) for March-February.

FIGURE 4.2. Von Bertalanffy growth models describing individual 105 growth of Devils Hole pupfish, Cyprinodon diabolis, endemic to Devils Hole, Nye County, NV. The fast-slow simulation model uses two growth curves to describe pupfish growth; individuals born in spring following a fast trajectory and individuals born during other times of year following the slow trajectory. In contrast, the mode model estimated growth from observed length-frequency distributions from stereovideo dives and early life stage surveys of Devils Hole pupfish.

FIGURE 4.3. Seasonal abundance of Devils Hole pupfish larvae, 106 Cyprinodon diabolis, Devils Hole, Nye County, NV. Points on the figure represent the sum of 3-5 mm larvae observed on twenty-seven 30 cm × 14 cm plots on the Devils Hole spawning shelf. The line on the figure is the best-fit generalized linear model with a Poisson viii

response. The best-fit model includes a fifth degree polynomial equation with time as the predictor variable.

FIGURE 4.4. Monthly estimates of the number of larvae per reproductive 107 female for the Devils Hole pupfish, Cyprinodon diabolis, endemic to Devils Hole, Nye County, NV. Numbers of larvae per female were estimated by dividing larval abundance estimates by predicted adult abundance estimates. Note that numbers of larvae per female were corrected to account for unequal sampling intervals..

FIGURE 4.5. Simulated and observed length-frequency distributions of 108 the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly- chosen iterations of a simulation model (light lines). The simulation model used a monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 4.7%, and the fast-slow model to describe pupfish growth.

FIGURE 4.6. Simulated and observed length-frequency distributions of 109 the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly- chosen iterations of a simulation model (light lines). To facilitate comparison between stereovideo dives and the simulation model output, length probability distributions only include fish with lengths greater than 18mm. The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 4.7%, and the mode model to describe pupfish growth.

FIGURE 4.7. Simulated and observed length-frequency distributions of 110 the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly- chosen iterations of a simulation model (light lines). To facilitate comparison between stereovideo dives and the simulation model output, length probability distributions only include fish with lengths greater than 18mm. The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 4.7%, and the mode model to describe pupfish growth.

FIGURE 4.8. Intra-annual abundance patterns of Devils Hole pupfish, 111 Cyprinodon diabolis, Devils Hole, in Nye County, NV. Simulation models were run with three different monthly adult and juvenile survival probabilities: 70% (top), 80% (middle), and 86% (bottom). Larval survival rates were 7.6% (top), 4.7% (middle), and 3.4% ix

(bottom). All abundance values were scaled by dividing by maximum observed annual abundance. Lines represent scaled monthly abundance estimates of Devils Hole pupfish predicted by the adult abundance model. Points represent scaled abundance (for fish greater than 18 mm total length) of from five random iterations of simulation models with different adult survival probabilities.

FIGURE 4.9. Summary of simulated population trends of the Devils Hole 112 pupfish, Cyprinodon diabolis, Devils Hole, in Nye County, NV. Median (dark line) and 2.5% and 97.5% quantiles (dotted lines) of population abundance trajectories of 2,000 iterations of the baseline simulation model. The baseline simulation model included constant monthly adult and juvenile survival rates of 80% and a larval survival rate of 4.7%. FIGURE 4.10. Mean discrete population growth rates (λ) for simulation 113 model parameters describing population dynamics of Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, in Nye County, NV. Summary of population growth rates from simulation models with 5% increases in annual larval, juvenile, and adult survival probabilities. Due to uncertainty in the current adult survival rate, we estimated finite annual population growth rates from simulation models with monthly adult survival rates of 70%, 80%, and 86%. Error bars represent 2.5% and 97.5% quantiles of population growth rates from 2,000 iterations. FIGURE 4.11. Intra-annual abundance patterns of a simulation model 114 with zero over-winter survival of larvae and juvenile Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Monthly adult and juvenile survival rates were set to 80% and larval survival was set to 7.0%. All abundance values were scaled by dividing by maximum observed annual abundance. Lines represent scaled monthly abundance estimates of Devils Hole pupfish predicted by the adult abundance model. Points represent scaled abundance (for fish greater than 18 mm total length) of from five random iterations of simulation models with different adult survival probabilities. x

FIGURE 4.12. Simulated and observed length-frequency distributions of 115 the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 7.0%, and the fast-slow model to describe pupfish growth. Furthermore, survival probabilities of juvenile and larval fish were set to 0 from November to January. FIGURE 4.13. Simulated and observed length-frequency distributions of 116 the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). To facilitate comparison between stereovideo dives and the simulation model output, length probability distributions only include fish with lengths greater than 18mm. The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 7.0%, and the fast-slow model to describe pupfish growth. Furthermore, survival probabilities of juvenile and larval fish were set to 0 from November to January.

ACKNOWLEDGEMENTS

I would like to thank my advisors: Dr. Michael Quist and Dr. Stephen Dinsmore.

Both Mike and Steve were always willing to help, and their insight helped me realize when I had over-thought a concept to the point where I had gone askew from the original intention of the project. Furthermore, both Mike and Steve have been supportive in allowing me to pursue various opportunities and side projects during my M.S. I think these experiences have greatly added to my ecological knowledge and experience. Additionally, I would like to thank Dr. Philip Dixon for his statistical insight and helpful nature. Whereas past Devils

Hole pupfish research has been primarily qualitative, I think Dr. Dixon’s advice helped take this thesis in a unique direction compared to previous studies. I thank Mike Bower for helping initiate this project. Mike Bower has a knack for asking good questions, many of which helped guide research objectives of this thesis. Dr. Kevin Wilson and Bailey Gaines were extremely helpful for providing “on the ground” opinions concerning Devils Hole pupfish management. Bailey and Kevin also helped on the practical end of things: field help, lending equipment, providing storage space, etc. Most of all, I am thankful that my thesis included insight from diverse academic backgrounds as well as from management agencies.

I believe completion of this thesis required finding a balance between ecological and statistical concepts. I think finding this balance has made me a better ecologist. I thank my fellow graduate students in the Department of Natural Resource Ecology and Management at

Iowa State University, for initiating countless ecological discussions which helped broaden my interests and knowledge. This thesis is dedicated to my parents, Andrew and Christina xii

Dzul. I would not have completed this thesis without their support and encouragement. I would also like to thank my fiancée, Chris Ebert, for his love, helpfulness, and patience. 1

CHAPTER 1. GENERAL INTRODUCTION

In the southwestern United States, large lakes present during the Pleistocene began to gradually disappear about 10,000 years ago. As the southwestern United States became increasingly arid, once contiguous aquatic environments became disconnected, effectively limiting dispersal and promoting speciation of aquatic biota. Consequently, geographic isolation in aquatic environments across the southwestern United States has resulted in a high degree of endemicity in native fishes (Soltz and Naiman 1978; Echelle et al. 2005).

Pupfishes (family Cyprinodontidae) are able to tolerate great fluctuations in water temperature and salinity and low dissolved oxygen concentrations. As such, pupfishes are well-suited for life in desert aquatic environments, which often exhibit large fluctuations in environmental conditions. Unfortunately, many North American pupfishes are threatened due to groundwater withdrawals (Deacon and Williams 1991; Dunham and Minckley 1998), competition with or predation by non-native species (Kennedy et al. 2005; Scoppettone

2005; Rogowski and Stockwell 2006), and hybridization with non-native fishes (Echelle and

Echelle 1997; Huxel 1999). Specifically, thirty-seven species and ten subspecies within

Cyprinodontidae are listed as imperiled or extinct in the American Fisheries Society’s most recent compilation of imperiled and extinct freshwater and diadromous species in North

America (Jelks et al. 2008). These forty-seven taxa represent 88% of Cyprinodontidae taxa in North America. Of these forty-seven taxa, twenty-three are endangered and eight extinct.

Perhaps the most-recognized pupfish species is the Devils Hole pupfish (Cyprinodon diabolis), which is thought to have the smallest geographic range of any vertebrate species. 2

The species only lives in Devils Hole, a small limestone cavern located in a discontiguous portion of Death Valley National Park adjacent to Ash Meadows National Wildlife Refuge

(Nye County, NV). The Devils Hole pupfish is one of the most morphologically distinct pupfish species; its adult morphological traits are similar to those exhibited by other pupfishes in their juvenile states (Miller 1948). It is thought that retention of juvenile morphological characteristics in the Devils Hole pupfish may be in response to the physiologically stressful conditions in Devils Hole (Lema and Nevitt 2006). Records of adult population size dating back to 1972 indicate that Devils Hole pupfish population size fluctuates seasonally, historically reaching a maximum of 400 -500 in early autumn and a minimum of 200-300 in mid-spring (Andersen and Deacon 1991). The Devils Hole ecosystem only receives direct sunlight eight months a year, and the maximum duration of direct sunlight hitting the shallow shelf is four hours per day. As such, primary production in

Devils Hole is light-limited during certain times of year (Wilson 2001). Devils Hole pupfish are omnivorous, feeding mainly upon diatoms that grow on the surface of calcium carbonate crystals (Minckley and Deacon 1975; Wilson 2001). They also feed on amphipods, ostracods, algae, cyanobacteria, beetles, flatworms, and snails (Minckley and Deacon 1975;

Wilson 2001). In the winter months when light is limiting, food becomes scarce and pupfish attain some energy from terrestrial sources of food that are wind-blown into Devils Hole

(Wilson 2001). Low-frequency disturbance events, such as earthquakes and torrential desert rains, impact nutrient cycling (Wilson and Blinn 2007) and substrate composition of the spawning shelf (Lyons 2005), although the impact of these disturbances on the Devils Hole pupfish population has not been formally examined. 3

In addition to its unique biology, the Devils Hole pupfish has played a pivotal role in conservation, because the pupfish’s near-extinction in the 1970s sparked controversy between conservationists and landowners opposing government intervention. In the late

1960s, Spring Meadows, a commercial farm, began to pumping water from the aquifer that supplies water to Devils Hole, thus greatly lowering the water level in Devils Hole and ensuring eventual extinction of the pupfish with continued water withdrawals. The near- extinction of the Devils Hole pupfish helped fuel conservation groups to challenge the legality of Spring Meadow’s actions in a suite of court cases. Eventually the lawsuit against

Spring Meadows made its way to the Supreme Court in Cappaert v. United States, in which the Supreme Court decision ruled the water level in Devils Hole must be maintained at a level of 0.82 m below a specified reference point. In so doing, the Supreme Court ruled against agricultural interests in favor of an endangered species. Cappaert v. United States set a precedent for future lawsuits involving endangered species, ensuring legal consequences for actions which jeopardized endangered species “for the enjoyment of future generations”

(Deacon and Williams 1991).

Monitoring of the adult Devils Hole pupfish population commenced in 1972 and continues to present. Because handling fish often increases the risk of mortality, all Devils

Hole pupfish monitoring is non-obtrusive. Consequently, population surveys are conducted by SCUBA divers who count adult Devils Hole pupfish. From the mid-1990s to the late

2000s, the estimates from population surveys indicated that the Devils Hole pupfish population size decreased substantially, reaching a low of 38 individuals in April 2006 and again in April 2007. In response to the population decline, management agencies (namely, the National Park Service, the U.S. Fish and Wildlife Service, and Nevada Department of 4

Game and Fish), began to supplement the diet of the Devils Hole pupfish population by regularly supplying fish food to Devils Hole in 2007. Since 2007, population size has increased gradually to approximately 100 individuals, although the most recent adult survey estimates (2010-2011) indicate no further growth in population size. Although almost forty years of population records exist for the adult Devils Hole pupfish population, consistent monitoring of Devils Hole pupfish larvae, invertebrate communities, and primary production were only initiated in the late 2000s. Accordingly, little is known about mechanisms causing the decline of Devils Hole pupfish population. In addition, although population records of the adult population are temporally extensive, the non-obtrusive methods used to estimate adult population size produce highly variable population estimates, thereby making it difficult to detect short-term population trends. More precise population estimates would help biologists evaluate effects of management actions.

Monitoring efforts focused solely on trend detection are of limited use in conservation, and such efforts have been criticized for misuse of conservation funds

(Campbell 2002; Nichols and Williams 2006). To improve its use, trend detection should be integrated into a larger framework in which monitoring is guided by a priori hypotheses designed to assess mechanisms attributed to species’ declines. Regrettably, although the

Devils Hole pupfish population is well-studied relative to other imperiled species, little is known about its population dynamics and life history characteristics due to the limitations of non-obtrusive sampling. In their review of recovery plans for 181 endangered species,

Campbell et al. (2002) write that for species with poorly understood biology, it is best to acquire basic biological knowledge as an early priority, and to use this baseline knowledge to focus future monitoring efforts on mechanisms associated with species’ declines. Continued 5

monitoring and evaluation of recovery efforts will lead to modifications and improvements in

monitoring plans, thus helping species recovery.

One of the long-term goals of this thesis is to help guide future monitoring and conservation efforts by 1) improving existing survey methodology (if possible) and 2) increasing understanding of Devils Hole pupfish population dynamics. With less variability in population estimates, managers will have more confidence in measured trends and will be better able to assess management actions. Furthermore, a greater understanding of population dynamics will help managers develop testable hypotheses about processes affecting Devils Hole pupfish population dynamics.

Thesis Organization

This thesis is comprised of three chapters. Chapter 2 uses a manipulative experiment to evaluate suspected sources of error in SCUBA surveys of adult Devils Hole pupfish.

Chapter 3 evaluates statistical power of the early life stage surveys of Devils Hole pupfish, and how changing allocation of sampling effort (e.g., changing the number of samples, subsamples, and sub-subsamples) affects statistical power of the resulting estimates. Chapter

4 uses simulation to assess patterns of Devils Hole pupfish survival, growth, and recruitment.

Simulated data are compared to observed length-frequency distributions in 2010 to explore the effects of variation in adult and larval survival rates on population growth, as well as to assess beliefs about Devils Hole pupfish population dynamics. Collectively, I hope this information improve understanding of Devils Hole pupfish life history and enable biologists to identify factors associated with the recent population decline.

REFERENCES

Andersen, M.E., and J.E. Deacon. 2001. Population size of Devils Hole pupfish

(Cyprinodon diabolis) correlates with water level. Copeia 2001:224-228.

Campbell, S.P., J.A. Clark, L.H. Crampton, A.D. Guerry, L.T. Hatch, P.R. Hosseini, J.J.

Lawler, and R.J. O’Connor. 2002. An assessment of monitoring efforts in

endangered species recovery plans. Ecological Applications 12: 674- 681.

Deacon, J.E., and C.D. Williams. 1991. Ash Meadows and the legacy of the Devils Hole

pupfish. Pages 69-99 in W.L. Minckley and J.E. Deacon, editors. Battle against

extinction. The University of Arizona Press, Tuscon, AZ.

Dunham, J.B., and W.L. Minckley. 1998. Allozymic variation in desert pupfish from natural

and artificial habitats: genetic conservation in fluctuating populations. Biological

Conservation 84:7-15.

Echelle, A.A., and A.F. Echelle. 1997. Genetic introgression of endemic taxa by non-native:

A case study with Leon Springs pupfish and sheepshead minnow. Conservation

Biology 11:153-161.

Echelle, A.A., E.W. Carson, A.F. Echelle, R.A. Van Den Bussche, T.E. Dowling, and A.

Meyer. 2005. Historical biogeography of the new-world pupfish genus Cyprinodon

(Teleostei: Cyprinodontidae). Copeia 2005:320-339.

Jelks, H. L., S. J. Walsh, N. M. Burkhead, S. Contreras-Balderas, E. Diaz-Pardo, D. A.

Hendrickson, J. Lyons, N. E. Mandrak, F. McCormick, J. S. Nelson, S. P. Platania,

B. A. Porter, C. B. Renaud, J. J. Schmitter-Soto, E. B. Taylor, and M. L. Warren, Jr. 7

2008. Conservation status of imperiled North American freshwater and diadromous

fishes. Transactions of the American Fisheries Society 33:372-407.

Kennedy, T.A., J.C. Finlay, and S.E. Hobbie. 2005. Eradication of invasive Tamarix

ramosissima along a desert stream increases native fish diversity. Ecological

Applications 15:2072-2083.

Huxel, G.R. 1999. Rapid displacement of native species by invasive species: effects of

hybridization. Biological Conservation 89:143-152.

Lema, S.C., and G.A. Nevitt. 2006. Testing an ecophysiological mechanism of

morphological plasticity in pupfish and its relevance to conservation efforts for

endangered Devils Hole pupfish. The Journal of Experimental Biology 209:3499-

3509.

Lyons, L.T. 2005. Temporal and spatial variation in larval Devils Hole pupfish (Cyprinodon

diabolis) abundance and associated microhabitat variables in Devils Hole, Nevada.

Master’s thesis. University of Nevada, Las Vegas.

Miller, R.R. 1948. The cyprinodont fishes of the Death Valley system of eastern California

and southwestern Nevada. Miscellaneous Publications, Museum of Zoology,

University of Michigan 68:1-155.

Minckley, C.O., and J.E. Deacon. 1975. Foods of the Devil’s[sic] Hole pupfish, Cyprinodon

diabolis (Cyprinodontidae). The Southwestern Naturalist 20:105-111.

Nichols, J.D., and B.K. Williams. 2006. Monitoring for conservation. TRENDS in Ecology

and Evolution 21:668-673. 8

Rogowski, D.L., and C.A. Stockwell. 2006. Assessment of potential impacts of exotic

species on populations of a threatened species, White Sands pupfish, Cyprinodon

tularosa. Biological Invasions 8:79-87.

Scoppettone, G.G., P.H. Rissler, C. Gourley, and C. Martinez. 2005. Habitat restoration as a

means of controlling non-native fish in a Mojave desert oasis. Restoration Ecology

13:247-256.

Soltz, D.L, and R.J. Naiman. 1978. The natural history of native fishes in the Death Valley

system. Natural History Museum of Los Angeles County, Science Series 30: 1-76.

Wilson, K.P. 2001. Role of allochthonous and autochthonous carbon in the food web of

Devils Hole, Nevada. Master’s thesis. Northern Arizona University, Flagstaff.

Wilson, K.P., and D.W. Blinn. 2007. Food web structure, energetics, and importance of

allochthonous carbon in a desert cavernous limnocrene: Devils Hole, Nevada.

Western North American Naturalist 67:185-198.

CHAPTER 2. IDENTIFYING SOURCES OF ERROR IN SURVEYS OF DEVILS HOLE PUPFISH (CYPRINODON DIABOLIS)

Modified from a paper accepted by The Southwestern Naturalist

Maria C. Dzul1, Michael C. Quist2, Stephen J. Dinsmore1, Philip M. Dixon3, Michael R. Bower44, Kevin P. Wilson55, and D. Bailey Gaines5

ABSTRACT—We assessed four potential sources of error in estimating size of the

population of Devils Hole pupfish (Cyprinodon diabolis); net, time of day, diver, and order

of diver. Experimental dives (3/day) were conducted during 4 days in July 2009. Effects of

the four sources of error on estimates from dive surveys were analyzed using a split-split plot

ANOVA. Diver and order of diver had no significant influence on estimates, whereas the effect of presence or absence of a net was significant. Effects of time of day and presence or

absence of a net showed a significant interaction with depth of water. Results indicated that

pupfish may move upward during the dive, and as a result, the standard methods of dive surveys may underestimate abundance.

RESUMEN—En este estudio, nosotros organizamos una serie de sesiones de buceo

experimentales para evaluar cuatro fuentes de error que posiblemente influyen los cálculos

aproximados de la población—la red, la hora del día, el buzo, y el orden de los buzos. Estas

sesiones de buceo experimentales incluían cuatro días de buceo en julio de 2009, con tres

1 Graduate student and Associate Professor, respectively, Department of Natural Resource Ecology and Management, Iowa State University. 2 Assistant Unit Leader, U.S. Geological Survey - Idaho Cooperative Fish and Wildlife Research Unit, University of Idaho. 3 Professor, Department of Statistics, Iowa State University. 4 Fish biologist, U.S. Forest Service – Bighorn National Forest. 5 Aquatic biologist and fish biologist, respectively, U.S. Park Service – Death Valley National Park. 10

sesiones de buceo cada día. Los efectos de estas fuentes de error sobre los cálculos aproximados de la población estaban analizados usando un “split split plot” para observar la variancia. El buzo y el orden de los buzos no influían mucho en los cálculos aproximados de la población, mientras la red influía los cálculos considerablemente. Además. Hora del día y la red demostraban una interacción importante con la profundidad del agua. Los resultados indican que los peces suben en el agua durante las sesiones de buceo, y como consecuencia el estudio típico de estas sesiones tal vez subestime la abundancia de los peces.

INTRODUCTION—According to a recent compilation of the conservation status of fishes developed by the American Fisheries Society, ca. 39% of taxa of freshwater and diadromous fishes in North America are imperiled, with 230 vulnerable, 190 threatened, 280 endangered, and 61 presumed to be extinct in the wild (Jelks et al., 2008). Rate of extinction in freshwater ecosystems is estimated to be five times greater than in terrestrial ecosystems

(Ricciardi and Rasmussen, 1999). In assessing loss of diversity of native fishes in California,

Moyle and Williams (1990) determined that some leading factors characterizing imperiled species were endemicity, small area of habitat, habitat in only one drainage basin, low diversity of the native assemblage, occurrence in isolated springs, or a combination of these.

Many of these characteristics are exhibited by aquatic environments in deserts. Although aquatic habitats in deserts may appear depauperate of aquatic fauna when viewed individually, they exhibit much greater diversity when viewed collectively because geographic isolation of habitats has resulted in speciation and endemicity.

The Devils Hole pupfish (Cyprinodon diabolis) is the poster child for preservation of aquatic ecosystems in deserts because it has been pivotal to legislation to conserve freshwater 11

fishes and endangered species (Deacon and Williams, 1991). Despite extensive research,

population dynamics are poorly understood because researchers cannot physically handle

pupfish due to the risk of mortality to the fish. As such, estimates of size of the population of

adult Devils Hole pupfish must be obtained using SCUBA-diver, visual-survey methods.

Routine monitoring of abundance of adult Devils Hole pupfish started in 1972 and continues

to present. During surveys, habitat in Devils Hole is divided into strata: the shallow shelf, a

boulder ca. 2 by 5 m in area submersed under 0.2-0.7 m of water, and the deep pool or deeper

waters of the cavern. Surveys include dive and shelf surveys; two SCUBA divers count

pupfish in the deep-pool habitat (i.e., dive survey) while observers count fish from a platform

overlooking the shallow shelf (i.e., shelf survey). Counts from the dive and shelf surveys are

summed to estimate size of the population of adult pupfish. Surveys are conducted in April

and September when the population is at its annual minimum and maximum, respectively.

Potential sources of error associated with visual assessments make attaining replicate counts challenging and may limit detection of trends in populations. Among potential sources of error are effects of movement of fish, time of day, order of diver, and diver. The effect of movement of fish is likely a source of error (Watson et al., 1995) due to tendency of fish to move as a school and linger at the boundary between the shelf and deep pool. Fish at the boundary can be double-counted or missed completely by both dive and shelf surveys. Managers have proposed placing a block net at the shelf-deep-pool boundary during the survey to impede movement of fish between the shelf and the deep pool and improve accuracy of counts. Time of day when the survey is conducted also may influence estimates. While surveys of adults that are conducted at different times of day during the same sampling date are meant to serve as replicated estimates, James (1969) noted that 12

Devils Hole pupfish avoid sunlight during midday. Likewise, order of diver may have an

effect on estimates, as the first diver may influence the count of the second diver by disturbing fish. Finally, variability in estimates also may be attributed to differences between divers. In ecological monitoring, multiple observers can produce dissimilar results based on differing abilities to detect organisms (Thompson and Mapstone, 1997; Bue et al., 1998;

Nichols et al., 2000; Diefenbach, 2003). For example, Thompson and Mapstone (1997) reported that bias of observers in dive surveys in the Great Barrier Reef of Australia varied with species of fish, and that while biases for some species could be corrected by calibration- training the diver, biases for other species persisted despite calibration-training efforts. The extent to which these four potential sources of error affect replicated samples needs to be either corrected, quantified, or have its presence acknowledged. Thus, the objective of this study was to identify and minimize (if possible) sources of error in surveys of adult Devils

Hole pupfish.

METHODS—Devils Hole, a fissure formed by tectonic activity, is adjacent to Ash

Meadows National Wildlife Refuge, an oasis in the Amargosa Desert in Nye County,

Nevada. Devils Hole is the hydrologic head of a deep and extensive carbonate aquifer.

Adult pupfish are typically in the upper 25 m of the deep pool and density of fish is greatest

in the upper 10 m. In the deep pool, temperature of water, pH, and conductivity remain fairly

constant at 32-33ºC, 7.1-7.5, and 820 µS/cm, respectively (Shepard et al., 2000). In contrast, the shallow shelf is more dynamic (Lyons, 2005). While temperature of water along the shallow shelf typically is similar to that of the deep pool, temperature of water on the shelf has reached extremes of 9 and 38ºC (Lyons, 2005). Concentrations of dissolved oxygen 13

typically are ca. 2 mg/L until the shelf is seasonally illuminated by the sun when

concentrations increase to ca. 8.0 mg/L in the afternoon (Shepard et al., 2000).

We designed a series of 12 experimental dives to examine effects of time of day (3 times/day), order of diver (two orders), diver (two divers), and net (two treatments) on estimates of size of the population of Devils Hole pupfish. Experimental dives consisted of 4 days of dives during 10-13 July 2009. Dives occurred each day at 0800 h (morning), 1100 h

(midday), and 1330 h (afternoon) and lasted ca. 1 h each. On 2 days of dives, we placed a

mesh block net at the boundary between the shelf and deep-pool habitats to prevent movement of fish. On dives with a block net, we stretched the net across the shelf-deep-pool boundary before divers began descending into the deep pool. Between dives, we drew ends of the net inward to allow movement of fish between habitats. The other 2 days of dives did not include a block net (no-net dives). Similar to standard dive surveys, the route for all

dives was divided into four levels that corresponded with consistent changes in depth (Fig.

1). Divers recorded number of fish encountered at each level. Unlike standard surveys,

divers switched order three times during the dive at transition points between levels in Devils

Hole. Switching orders during the dive provided greater replication for testing effects of

diver and order of diver. The same two divers counted fish on every dive; both divers were

experienced and had participated in surveys for multiple years. As with historical surveys,

divers swam down to ca. 30 m, waited 10 min, and then ascended to count fish.

Design of the experimental dive also included experimental shelf surveys to assess

effects of time of day and presence or absence of a net. All experimental shelf surveys

followed the standard surface-survey method, with exception of the 2 days when a block net

was placed at the boundary between the shelf and deep pool. Shelf surveys occurred 14

concurrently with dive surveys and began ca. 10 min after divers started their descent. The shelf was divided into three sections on the north-south axis and three different observers counted fish in their section of the shelf. Shelf counts were not timed and ended when counters finished counting fish in their section. Typically, each shelf count lasted 2-3 min.

Shelf counters were allowed to communicate with one another to prevent double-counting fish that swam into multiple sections. Each shelf survey consisted of four counts; one practice count and three subsequent official counts. Each observer counted the same section of shelf for all four counts in a survey, but observers were randomly assigned to different sections of the shelf between surveys. Official counts were summed across sections and averaged for each shelf survey.

We conducted statistical analyses using SAS version 9.2 (SAS Institute, Inc., Cary,

North Carolina) and we set α = 0.05 for analyses. As a preliminary analysis, we examined historical records of estimates of size of population (1972-2009) to assess effects of diver

(three divers), order of diver (two orders; first and second), and time of day (two times of day; morning and midday). To help meet assumptions of normality and homogeneity of variances, estimates of abundance were ln-transformed prior to analysis. We used a mixed model (PROC MIXED) with time of day (morning and midday), diver (three divers), and order of diver (two orders) designated as fixed effects and date × time of day designated as a random effect to analyze sources of error from estimates in historical surveys. Designating date × time of day as a random effect accounted for variation across individual dives and allowed for assessment of time of day, diver, and order of diver. We neither assessed sources of error in shelf surveys in historical analysis, nor did we assess interactions between factors due to limited samples. 15

Due to differences in sizes of experimental units across factors, we used a split-split plot ANOVA to assess effects of net, time of day, diver, and order of diver on estimates from surveys in experimental dives for Devils Hole pupfish (Littell et al., 2002). In the split-split plot analysis, number of days represented whole plots, because block-net-present and no-net treatments were set up for the entire day (net, n = 4). Dives signified the first subplots, as time of day was constant for all four levels in each dive (time of day, n = 12). The second subplots were represented by each level, as diver and order of diver changed according to level (level, n = 96; diver, n = 96; order of diver, n = 96). Level was added as a fixed effect to account for differences in density of pupfish at different levels. Because there were differences in density among levels, excluding level from analysis would have hindered our ability to test effects of the other four factors. Counts were log(x+1) transformed to help equalize variances and to enable assessment of multiplicative effects.

Similarly, a split-plot ANOVA was used to assess effects of net and time of day in log(x+1) transformed shelf surveys with days representing the whole plot and dives signifying the first subplot. Due to the limited sample, only certain interactions were assessed in dive surveys. Interaction terms included in the model were those presumed to be important (i.e., a priori). For example, we assumed that the difference in abilities of divers to count fish was not influenced by time of day and excluded time of day × diver from the model.

Because official estimates have been attained from both dive and shelf surveys in the past, we conducted additional analyses to evaluate effects of time of day and net on combined estimates of dive and shelf surveys. For each dive, estimates of abundance in all four levels were summed and estimates from the two divers were then averaged and added to 16

the average of the three official shelf counts. A split-plot ANOVA was then used to assess

effects of time of day and net on the combined estimate from dive and shelf surveys. The

same combined estimates were used to compare variances between the net-present and no-net

treatments, because one of our goals was to determine how to increase precision in surveys.

We hypothesized that estimates from dives with net present would have lower variability

than estimates from dives with no net because we speculated that variability in estimates was

partly attributed to movement of fish. As such, we tested influence of the net on variability

by comparing residuals between treatments. Residuals were calculated by subtracting the

mean combined estimate from surveys with nets from each survey with nets, and the mean

combined estimate from surveys with no net from each survey with no net. Absolute values

of residuals were then used in Levene’s test to evaluate differences in variability between

treatments.

RESULTS—Inconsistencies in historical records limited our ability to detect sources of

error in dive surveys. Specifically, dives were excluded from historical analysis if dives

included only one diver counting fish or if records did not indicate which of two divers dove first and which dove second. As such, only 88 observations from 22 days were used in historical analysis. In the mixed-effects model, order of diver was the only factor that had a significant effect on estimates (F1,41 = 10.21; P < 0.01; Table 2.1), with the second diver seeing 16% fewer fish than the first diver.

Similarly, there was no effect of diver (F1,56 = 0.01; P = 0.92) in analysis of

experimental dive surveys; however, effect of order of diver was not significant (F1,56 = 0.83;

P = 0.37; Table 2.1). Statistically significant interactions between time of day × level (F6,56 =

7.11; P < 0.01) and net × level (F3,56 = 9.25; P < 0.01) complicated assessment of time of day 17

and net as main effects in analysis of experimental dives. We determined that time of day

could not be assessed as a main effect due to opposing directionality of time of day × level

interactions at levels III and IV. Specifically, there were more fish on level IV during dives

in morning and midday, and less fish on level IV during dives in afternoon; whereas, there

were more fish on level III during dives in afternoon and fewer fish on level III during dives

in morning and midday (Fig. 2.2a). Estimates for level IV, the uppermost level, were greater

for dives with net present than for dives with no net (t56 = -6.72; P < 0.01; Fig. 2.2b).

Because estimates of size of the population were reported as the sum of fish on all four levels, we assessed net as a main effect. Evaluation of net as a main effect averaged the effect of presence of net over all four levels; thus, allowing us to determine how the net affected the final estimate. As such, net was significant as a main effect (F1,2 = 24.10; P =

0.04); dives with a net produced higher estimates than dives without a net. The significance of net as a main effect was most influenced by greater abundance of pupfish on level IV during dives with nets present.

Analysis of experimental shelf surveys showed the effect of time of day was nearly significant (F2,4 = 6.60; P = 0.05) and effect of net was not significant (F1,2 = 0.00; P = 0.99;

Table 2.1). Summing average estimates from dive and shelf surveys helped determine the effect of these potential sources of error on a coarser scale. Effects of net (F1,2 = 4.24; P =

0.14) and time of day (F2,4 = 3.38; P = 0.18) were not significant after combining shelf

counts with dives. Levene’s test showed that residuals from net and no-net treatments were

not different for combined estimates (F1,10 = 0.18; P = 0.68). Because residuals between treatments were not significantly different, there was no evidence that precision differed 18

between net and no-net treatments; however, comparing estimates of the variance for net and no-net dives is tenuous due to the small sample.

DISCUSSION—Although there was no significant effect of diver on estimates of size of population in both the historical and experimental analyses of dives, both analyses included only a small subset of divers that had participated in past surveys. Thus, neither analysis tested effects of other divers in the historical records. In particular, experience of a

SCUBA diver can affect estimates (Williams et al., 2006) and was not assessed in this study.

In addition, effect of order of diver was significant in the historical analysis and not significant in analysis of experimental dives despite a similar estimate of precision in both tests. Whether these contradictory results can be attributed to divers switching orders between levels is unknown. The effect of order of diver can be further assessed during subsequent surveys of adult pupfish.

Laboratory and field studies have shown that different species of fish may select habitat based on temperature of water (Barlow, 1958; Podrabsky et al., 2008; Rydell et al.,

2010). Our results from assessment of time of day support the conclusion of James (1969) and Baugh and Deacon (1983) who observed that Devils Hole pupfish tend to move into deeper waters in afternoon during summer to avoid thermal stress in shallow water.

Discovering that the time of day × level interaction was significant in dive surveys and nearly significant in shelf surveys indicates that fish were more likely to be in deeper water during dives in afternoon compared to dives in morning and midday. However, temperature on the shelf is lower in autumn and spring, the two seasons when surveys of adults typically occur.

Accordingly, dive surveys conducted during autumn and spring may be a better test for assessing effect of time of day, because it is less likely that there will be a significant 19

interaction between time of day × level during these seasons. Because preference of fish for

shelf or deep-pool habitat may depend on time of day, combining the two surveys may

provide a more precise assessment of the effect of time of day on estimates.

One of the novel findings of the experimental dives is that fish may move non-

randomly during the dive survey. Greater density of fish at level IV during dives with a

block net suggests that fish may be avoiding divers, and as a consequence, they may escape

both dive and shelf surveys. Other studies have reported different responses of fish to

SCUBA divers. While some studies have shown that abundance decreases with presence of

SCUBA divers (Stanley and Wilson, 1995), others detected no effect of SCUBA divers (De

Girolamo and Mazzoldi, 2001), that abundance increases with presence of SCUBA divers

(Chapman et al., 1974; Cole, 2007), or that the effect of presence of SCUBA divers varies by species (Wilson and Harvey, 2007; Dearden et al., 2010). If Devils Hole pupfish avoid

SCUBA divers, timing of shelf and dive surveys is such that fish may be missed by both surveys. Specifically, fish could be present in the deep pool during the first 15 min of the dive while counters at the shelf are counting fish and divers are counting fish at lower levels.

These fish may then move onto the shelf later during the dive, after counters at the shelf have finished their counts and divers were in the process of counting fish in upper levels. Such trends in movement would cause historical surveys to underestimate abundance. There are at least two other possible explanations for the increased number of fish on level IV during dives with a net present. First, fish may have used the net as cover; however, lack of a significant interaction between time of day × net × level would indicate otherwise. Second, the white background of the net may make fish more visible to divers, but both divers indicated that they did not believe that the net increased detectability. 20

Although analysis of dive surveys indicates that presence or absence of a net had a significant effect on estimates, this effect disappeared after estimates from dive surveys were combined with shelf surveys. Assessment of combined surveys may provide valuable insight as to how dive and shelf surveys interact. Accordingly, more research is needed to determine the effect of net on combined estimates. If combined estimates from dives with nets present are statistically different from no-net dives, estimates from dives with nets present are not comparable to those of no-net dives. As a result, estimates from dives with nets present are not comparable to estimates from historical records. Moreover, if fish avoid divers, as is supported by our results, dives with nets present may produce more accurate estimates of abundance because it is less likely that fish can escape both dive and shelf surveys.

Based on our study, managers must decide whether to use the net on future surveys for adult Devils Hole pupfish. Importantly, because distribution of fish throughout the four levels in Devils Hole differs in spring and autumn compared to summer, the block net must be evaluated as an alternative method during September and April to determine how the net affects accuracy and precision of estimates during the times of year when surveys of adults occur. As such, we suggest that subsequent surveys include 2 days of dives, with at least two dives conducted with a net present and two dives conducted with no net. This will provide additional data as to whether dives with a net result in larger estimates and whether dives with a net improve precision of surveys occurring in September and April. If agencies decide to implement dives with a net as the standard sampling method, estimates from dives with a net and dives with no net could be calibrated, as calibration has been used in sampling fisheries to facilitate comparison of methods (Peterson, 1991; Peterson and Paukert, 2009).

However, calibration should proceed with caution because such efforts are, at best, rough 21

comparisons. Simulation of estimates from when a net is present and dives with no net also

may be a useful tool to compare the two sampling methods (Peterson and Paukert, 2009).

Nichols and Williams (2006) described differences between two types of

environmental monitoring; surveillance monitoring, a general monitoring used to assess

trend, and targeted monitoring, or monitoring designed to assess a priori hypotheses,

prioritize conservation needs, and evaluate management actions. We believe assessment of

sources of error in dive and shelf surveys for adult Devils Hole pupfish represents an

important first step toward targeted monitoring. Further, monitoring should be evaluated regularly for ability to assess trends, because routine assessment will help monitoring efforts avoid getting stuck with a poor design because it has years of historical precedence. The philosophy behind the monitoring protocol for Devils Hole pupfish has been to control observational error by maintaining the highest degree of consistency possible among surveys.

Unfortunately, maintaining consistency among surveys decreases the sample available to estimate mean and variability in estimates, while also limiting ability to detect sources of error. In particular, past estimates have been obtained exclusively from the estimate of the first diver on the morning survey; thereby, excluding estimates from the second diver and the survey in midday. The limited sample hinders differentiation of observational error from trends in populations, and as a result, there is little confidence in estimated trends. Managers recognize pitfalls of the current survey protocol, yet they are understandably reluctant to

change methods because comparisons between future estimates and 38 years of historical

records may become obscured. As such, future surveys of adult Devils Hole pupfish will

continue to evaluate sources of error; thereby, helping determine which estimates can serve

as replicate counts. Increasing replicate counts will improve the power of dive and shelf 22

surveys to assess trend, ultimately helping evaluate management actions and aiding conservation of this unique species.

We thank S. D. Hillyard and Z. L. Marshall for conducting SCUBA surveys as well as T. Jaskulski, M. Maloney, R. Perotti, and P. Garcia for serving as safety divers. In addition, thanks are extended to S. Harris and P. J. Barrett for helping with logistics and data.

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Table 2.1. Evaluation of sources of error in estimates of size of the population of Devils Hole pupfish (Cyprinodon diabolis) in Nye County, Nevada. Test statistics are shown for mixed- effects model assessing historical records of estimates, split-split plot ANOVA evaluating experimental dives, split-plot ANOVA examining experimental shelf surveys, and split-plot ANOVA analyzing combined estimates from experimental dives and shelf surveys. Numerator Denominator Probability Variable F-value df df > F Historical analysis Day 22 20 53.29 <0.01 Time of day 1 20 0.07 0.79 Order of diver 1 41 10.21 <0.01 Diver 2 41 0.73 0.49

Dive survey Net 1 2 24.1 0.04 Time of day 2 4 5.64 0.07 Level 3 56 213.14 <0.01 Order of diver 1 56 0.83 0.37 Diver 1 56 0.01 0.92 Net × time of day 2 4 1.84 0.27 Net × order of diver 1 56 0.43 0.51 Order of diver × diver 1 56 0.05 0.82 Net × level 3 56 9.25 <0.01 Net × time of day × level 6 56 1.73 0.13 Time of day × level 6 56 7.11 <0.01 Net × order of diver × level 6 56 0.51 0.80

Surface survey Net 1 2 0 0.99 Time of day 2 4 6.60 0.05 Time of day × net 2 4 0.03 0.97

Combined (Dive + shelf survey) Net 1 2 4.24 0.18 Time of day 2 4 3.38 0.14 Time of day × net 2 4 0.30 0.76

Figure 2.1. Side view of Devils Hole, Nye County, Nevada, illustrating the four levels used in SCUBA-dive surveys.. The entire geographic range of the Devils Hole pupfish (Cyprinodon diabolis) resides in this cavern system.

Figure 2.2. Mean number of Devils Hole pupfish (Cyprinodon diabolis) in Nye County, Nevada, by: a) time of day × level; and b) net × level. Error bars represent SE estimated from ln-transformed estimates of size of population. The interval of the ln-transformed mean ±1 SE was then back-transformed so that it could be applied to estimates of abundance. Different letters represent contrasts that were statistically different (P <0.05).

d Morning a Midday cd Afternoon c Time of day x level ce P < 0.01 e f

Number of pupfish of Number b b a a a b 0 20406080

c No net b Net cd d Net x level P < 0.01

Number of pupfish of Number a ab ab b 0 102030405060

I II III IV Level

CHAPTER 3. USING VARIANCE COMPONENTS TO ESTIMATE POWER IN A HIERARCHICALLY NESTED SAMPLING DESIGN: IMPROVING MONITORING OF LARVAL DEVILS HOLE PUPFISH

Modified from a paper submitted to Environmental Monitoring and Assessment

Maria C. Dzul1, Philip M. Dixon2, Michael C. Quist3, Stephen J. Dinsmore1, Michael R. Bower4, Kevin P. Wilson5, D. Bailey Gaines5

ABSTRACT

We used variance components to assess allocation of sampling effort in a hierarchically

nested sampling design for ongoing monitoring of early life history stages of the federally-

endangered Devils Hole pupfish (DHP) (Cyprinodon diabolis). Sampling design for larval

DHP included surveys (five days each spring 2007-2009), events, and plots. Each survey was comprised of three counting events, where DHP larvae on nine plots were counted plot- by-plot. Statistical analysis of larval abundance included three components: 1) evaluation of power from various sample size combinations, 2) comparison of power in fixed and random plot designs, and 3) assessment of yearly differences in the power of the survey. Results indicated that increasing the sample size at the lowest level of sampling represented the most realistic option to increase the survey’s power, fixed plot designs had greater power than random plot designs, and the power of the larval survey varied by year. This study provides

1 Graduate student and Associate Professor, respectively, Department of Natural Resource Ecology and Management, Iowa State University. 2 Professor, Department of Statistics, Iowa State University. 3 Assistant Unit Leader, U.S. Geological Survey - Idaho Cooperative Fish and Wildlife Research Unit, University of Idaho. 4 Fish biologist, U.S. Forest Service – Bighorn National Forest. 5 Fish biologist and aquatic ecologist, respectively, U.S. Park Service – Death Valley National Park. 31

an example of how monitoring efforts may benefit from coupling variance components

estimation with power analysis to assess sampling design.

INTRODUCTION

Diversity of freshwater fishes is at risk in North America (Ricciardi and Rasmussen

1999) with an estimated 39% of freshwater and diadromous fishes considered endangered,

threatened, or vulnerable (Jelks et al. 2008). The imperiled status of many freshwater fish

species makes understanding population trends imperative to successful conservation.

Monitoring populations can help prioritize management actions, thereby promoting efficient use of conservation funds (Nichols and Williams 2006). For monitoring to be useful in detecting population trends, the survey design must have high statistical power. Statistical power in population monitoring represents the probability of detecting a real change in population abundance. Survey designs with low statistical power have a high probability of failing to detect population change and are likely to mislead managers by falsely concluding a population is stable (Peterman 1990; Taylor and Gerrodette 1993; Legg and Nagy 2006).

Incorporating estimates of statistical power is therefore essential when choosing an appropriate sampling design structure (Legg and Nagy 2006; Field 2007), which in turn affects monitoring schemes.

Trends in fish populations are difficult to detect due to high spatial and temporal variability in population abundance (Silliman 1946; Gibbs 1998; Sammons and Bettoli

1998), so statistical power in surveys of fish populations tends to be low compared to power 32

in surveys for other organisms (Gibbs et al. 1998). For instance, Cyr et al. (1992) estimated

that about half of the surveys that focused sampling on the early life history stages of fish had

less than 80% power to detect a one order of magnitude change in the abundance of larvae.

Low power in surveys for larval fish is regrettable because mortality rate of larval fishes is often high in comparison to mortality at later life history stages, thus larval fish abundance may be an important indicator of year class strength (Diana 1995; Sammons and Bettoli

1998). One technique for increasing power is to conduct surveys at fixed locations if the spatial distribution of the population is predictable between surveys (e.g., Quist et al. 2006).

However, surveys with fixed sites are less capable of detecting spatial patterns than surveys with random sites located throughout the survey area.

The Devils Hole pupfish (DHP) (Cyprinodon diabolis) is thought to inhabit the smallest habitat of any vertebrate species (Moyle 1976). It is endemic to Devils Hole, a small limestone cavern located in southwestern Nevada. In the late 1990s, the adult DHP population declined for unknown reasons, reaching a low of just 38 individuals (April 2006 and April 2007). Although population records for adult DHP date back to 1972, very little is known about its early life history stages. Gustafson and Deacon (1997) and Lyons (2005) studied the relationship between microhabitat characteristics and abundance of DHP larvae.

Although both studies provided insight as to the distribution of larval DHP, neither was able to detect meaningful relationships between habitat characteristics and abundance.

Consequently, surveys for larval DHP began in 2005 to monitor long-term trends in the

abundance of larval fish with the hopes that the data would help elucidate mechanisms

associated with recruitment. 33

While estimating statistical power is fairly straightforward for simple survey designs,

estimating power in complex designs requires more sophisticated techniques (Urquhart and

Kincaid 1999; Larsen et al. 2001). Surveys for larval DHP are hierarchically nested and

include samples, sub-samples, and sub-sub-samples. Decomposing these sources of survey

variation into variance components can help determine the relative contribution of factors to

overall variation in the survey (Lewis 1978; Matthews 1990; Morrissey et al. 1992; Kincaid

et al. 2003). Increasing the sample size at levels of sampling with high variance will result in

a survey design focused on minimizing variation, thereby maximizing the survey’s power to

detect changes in the population (Morrissey et al. 1992; Larsen et al. 2001). As a general

rule, increasing the number of samples will result in a greater increase in power than

increasing the number of subsamples or sub-subsamples (Urquhart and Kincaid 1999).

However, increasing the number of samples is usually more cumbersome and costly than increasing subsamples. In this study, we estimated variance components for all levels of sampling in DHP larval surveys to determine how altering sample size in a hierarchically

nested design affected statistical power. Then, we discuss these findings as they relate to

modifications of the long-term monitoring scheme for the Devils Hole pupfish. Other studies

have combined variance components estimation with power analysis to quantitatively assess sampling designs.

METHODS

Study area

Devils Hole is located in an open fault zone adjacent to Ash Meadows National

Wildlife Refuge, an oasis in the Amargosa Desert in Nye County, Nevada. A fissure formed

by tectonic activity, Devils Hole is part of a network of subterranean carbonate formations

that transport water to springs in Ash Meadows. The depth of Devils Hole remains

unknown, though divers have explored down to a depth of 133 m without seeing the bottom

(Riggs and Deacon 2004). The Devils Hole pupfish is the only aquatic vertebrate species

living in Devils Hole. Pupfish habitat in Devils Hole can be divided into two separate strata:

the “shallow shelf,” a boulder face approximately 2 m × 5.5 m in area submersed under 0.2-

0.7 m of water, and the “deep pool,” or the deeper waters of the cavern where pupfish inhabit

the upper 25 m. Except for a few extremely rare occasions, pupfish larvae have been

observed exclusively on the shallow shelf (Gustafson and Deacon 1997), suggesting that

pupfish recruitment is highly dependent on habitat conditions associated with the shallow

shelf. In addition, primary production and invertebrate biomass are greatest on the shallow

shelf (Riggs and Deacon 2004). While water temperature, pH, and conductivity remain fairly

constant in the deep pool at 32-33°C, 7.1-7.5, and 820 µS/cm, respectively (Shepard et al.

2000), the shallow shelf is more dynamic and experiences greater fluctuations of temperature

(32-34.5°C) and dissolved oxygen (2 – 8 mg/L; Gustafson and Deacon 1997; Shepard et al.

2000; Lyons 2005). In addition, the Devils Hole spawning shelf experiences large

magnitude disturbances from earthquakes and flood events (Lyons 2005), though the

influence of disturbance events on the DHP population remains unknown. 35

Survey design

Sampling effort in surveys for larval DHP was nested and included surveys

(conducted every other week), counting events (conducted three times within a survey with

one hour in between each event), and plots (nine observational units in an event). Larval

surveys were conducted by biologists from the National Park Service, U.S. Fish and Wildlife

Service, and Nevada Department of Wildlife. Plots used in this study were 30 cm × 14.5 cm

quadrants constructed from 3 pieces of white polyvinylchloride (PVC) piping which had

been laterally bisected (Figure 3.1). The three pieces of PVC were lashed together by monofilament fishing line. Bead spacers were placed on the fishing line to maintain a 6 mm

gap between the PVC halves. Gaps allowed larvae to emerge from the sediment and settle on

the plot. The white background contrasted with the darker substrate, thereby making small

larvae more visible and easy to detect on plots. Nine plots were placed at fixed locations

(Lyons et al. 2005) on the floor of the shelf a few hours before dusk to avoid disturbing

larvae during the survey (Figure 3.1). Since DHP larvae typically emerge from the sediment

at night (Lyons 2005), surveys commenced three hours after sunset. Observers illuminated

each plot with a headlamp and counted all larvae present on the plot for one minute. After

observers finished counting larvae on the nine plots (i.e., after one counting event), observers

waited until one hour after the commencement of the first counting event, and once again

counted the number of larvae present on the nine plots. This process was repeated once more

for a total of three counting events, each with nine plots. Since the shallow shelf was small

in area (approximately 3 m × 6 m), the plots sampled 3% of the habitat available for DHP

larvae. 36

Previous studies assessing temporal trends in DHP larval populations have shown

larval abundance to be greatest in spring (Gustafson and Deacon 1997). Similarly, although

spawning occurred ten months out of the year, data from 2007-2009 surveys show larval

abundance was greatest in early April, after which larval abundance declined until early

autumn when another, albeit lesser, increase in larval abundance occurred. Five dates in

mid-March to mid-May were used in our analysis (Figure 3.2), because the large amount of

variation in larval abundance between different seasons would have obscured comparison of

population trends between years. We chose to analyze abundance data from spring sampling

dates only because variation in larval abundance was greatest and power was lowest during

this season. As such, estimates of statistical power from spring sampling dates would be

most conservative when larval abundance estimates were compared within the same season

across years.

Statistical analysis

All statistical analyses were conducted in SAS® version 9.2 ® (SAS Institute Inc.,

Cary, NC). Larval abundance was estimated from the mean number of larvae detected per

plot during each survey. We analyzed ln-transformed larval abundance because preliminary inspection of the data suggested that the variance among plots within an event was not constant, and that events and surveys had multiplicative effects on the larval count. Values of 0 were replaced by 0.5 before ln-transformation. Evaluation of residuals showed that the log-transformation was reasonable. The model describing ln-transformed abundance includes

year (Ө) and plot (β) as fixed effects; and surveys (b), events (c), and plots (e) as random effects: 37

      b  c  e (1) y p(v(s(a)))  a p s(a) v(s(a)) p(v(s(a)))

where parameters are distinguished based on year (a), survey (s), event (v), and plot (p).

The survey variance component represents short-term temporal variability, the event variance component is a larger-scale replicate of spatial variability, and the plot variance components represents small-scale spatial variability. Plots were treated in two different ways, corresponding to two different survey designs. If the same plot locations were used each survey (the fixed plot design), then plot effects were considered as fixed effects. The error variance was then the variance associated with each measurement. If new plot locations were used each survey (the random plot design), then plot effects (βp) were deleted from the

model; the error variance then included spatial variability.

Variance components associated with each random effect were estimated by equating

observed and expected mean squares using PROC MIXED in SAS 9.2 (Littell et al. 2002).

Equating observed and expected mean squares is a method of moments estimation procedure

and does not require assumption of normality (Searle et al. 1992). Estimated variance

components were then used to assess the effect of sample size on the variability in the mean

observation (Snedecor and Cochran 1980) in the following equation:

 2  2  2  2  s  v  p (2) y ns ns  nv ns  nv  n p

Here, y is the sample mean, n is the sample size, and σ2 is the variance component for the

level of sampling indicated by the subscript.

Estimating power requires four pieces of information: 1) an estimate of variance, 2)

the specified effect size, 3) the desired level of significance (α), and 4) the sample size.

Variance of the mean was estimated using the variance components equation (Equation 2).

Effect size was the hypothetical difference in ln-transformed larval abundance between two

years. For example, an effect size of ln(1.2) would estimate power to detect a 20% increase

in abundance while an effect size of ln(0.8) would be used to detect a 20% decrease. The

effect size and estimate of variance were used to calculate the noncentrality parameter from a

t-distribution with degrees of freedom equal to two times the number of surveys minus two.

Alpha was set to 0.05 for all analyses, and the sample size varied depending on the analysis.

It is important to note that this method assesses hypothetical changes in larval abundance from year to year; it is ill-advised to use this method to retrospectively estimate power with

observed trends (Thomas 1997). Furthermore, we used a linear model to describe larval

counts because of its relatively simple structure, which facilitates incorporation of multiple

levels of sampling. Variance components were estimated separately for all three years

(2007-2009) as well as for all years pooled together to compare annual variability. For each year, estimates of variance were used to calculate the power of the sampling design used from 2007–2009 (i.e., the power of five surveys, three events, and nine random plots). In addition, the number of plots, events, and surveys were manipulated to compare estimates of power resulting from various sampling design structures. Lastly, power from surveys with fixed plots and random plots were estimated by estimating variance components from models with (fixed plot) and without (random plot) “plot” as a fixed effect. Variance of the mean 39

observation was then estimated separately for fixed- and random-plot designs using their

respective estimates of the plot variance component (Equation 2).

RESULTS

Estimating power for different sample size combinations illustrated how increasing the number of samples (i.e., surveys) had the greatest influence on statistical power (Figure

3.3). This result was expected, because increasing the number of samples decreases the contribution from every variance component (Equation 2). A more surprising finding,

however, was that the subsample (i.e., event) contributed negligibly to the overall variation in the mean observation. In fact, the estimated variance component for events in 2008 and 2009 was negative. As such, increasing the number of events had virtually the same effect as increasing the number of plots. To test whether negative variance components estimates could be attributed to the estimation procedure, we re-estimated variance components in SAS

using restricted maximum likelihood and type I sums of squares (i.e., proc mixed method =

reml and proc varcomp method = type1 in SAS, respectively). Variance components for

event were negative using proc varcomp and proc mixed method=reml nobound, thus we feel

confident that the negative variance estimate was not a result of the estimation procedure.

For years when variance components were estimated to be negative (e.g., 2008, 2009,

grouped years), the restricted maximum likelihood method tended to provide lower estimates

of variance components for positive variance components relative to the equating observed

and expected mean squares. Nevertheless, power estimates from the from the two estimation 40

procedures differed by less than 0.001 for survey design consisting of five surveys, three

events, and nine random plots.

Surveys with fixed plots had slightly higher statistical power than surveys with

random plots, although the difference in power between the two designs decreased as the

total number of plots increased (Figure 3.4). The higher power of the fixed plot design was

due to fixed plot variance component being roughly 24% less than the random plot variance

component. Estimates of larval density varied each year, with the greatest densities of larval

DHP occurring in 2007 and the lowest in 2008. Likewise, statistical power in the larval

survey varied each year; the survey had its lowest power in 2007 and its highest power in

2008 (Table 3.1). The power to detect a decrease was always greater than the power to

detect an increase of the same magnitude because the effect size was ln-transformed.

Variance component estimates from all three years of data showed that the survey design

with 5 surveys, 3 events, and 9 random plots had low power to detect a 20% increase (1 – β =

0.30) or decrease (0.40) in population abundance, however, power to detect a 50% increase

(0.80) or decrease (0.99) was relatively high.

DISCUSSION

Other fish monitoring studies have assessed variance partitioning at spatial and temporal scales in hierarchically nested survey designs. Gray et al. (2009) found that variability in abundance of ten fish species in southeast Australian lakes was greatest at the lowest level of sampling (sites located 50-100 m apart) relative to larger spatial scales (1 -20 41

km apart). Similarly, variation in reef fish assemblages in northeastern New Zealand was

greatest between transects (tens of meters) compared to sites (hundreds to thousands of

meters), locations (hundreds of kilometers), and years (Anderson and Millar 2004). In a

literature review of thirty-nine studies of algal and macroinvertebrate abundance in coastal habitats, variability in biomass was typically greatest at small spatial scales (Fraschetti et al.

2005). However, the relative magnitude of variability in abundance of eight different taxa of benthic macrofauna in Botany Bay, Australia was variable across different spatial scales

(Morrissey et al. 1992).

The decision of whether to use fixed or random sites should depend on whether the

goal of monitoring is to assess spatial or temporal trends, as well as how much variation in the data can be explained by site location. If site location explains a substantial amount of variation, fixed sites will result in greater power than random sites (Urquhart and Kincaid

1999; Quist et al. 2006). Conversely, trends from fixed sites may not be representative of regional trends, even when great care is taken with site selection (Stoddard et al. 1998).

Urquhart and Kincaid (1999) assessed power in various sampling designs that used both

fixed and random plots, such as designs with random site revisits, and discussed the

advantages of various sampling design strategies. Other studies comparing fixed and random

sites in aquatic ecosystems have found either no difference in variation between fixed and

random sites (King et al. 1981), or lower variability for fixed sites (Van der Meer 1997). In

our study, although fixed plots had 24% less variation than random plots, the difference in power between fixed and random site designs was small. However, differences in power between fixed and random sites would be greater if plots represented samples, not sub- subsamples. Due to the small area of Devils Hole shallow shelf, detecting spatial patterns of 42

DHP larvae is of less interest than detecting temporal changes in the larval population.

Although the fixed plot design has greater power than the random plot design, the high power comes with the price of an added assumption that abundance patterns occurring on fixed plots are representative of the entire spawning shelf. Using combinations of fixed and random sites presents a practical solution if the goal of larval monitoring is to relate larval abundance to microhabitat characteristics such as water depth, substrate composition, dissolved oxygen concentration, or macroinvertebrate abundance.

Surveys conducted from 2007 to 2009 had different abundances as well as different estimates of power (Table 3.1). Estimates of power in surveys for larval Devils Hole pupfish were high compared to surveys for other species of larval fish (Cyr et al. 1992). The higher power for surveys of DHP larvae was likely attributed to a relatively large proportion of habitat on the Devils Hole shallow shelf being exposed to sampling. Although power was relatively high compared to surveys for other larval fishes, power to detect increases or decreases less than 30% magnitude was still low. One option to increase power in surveys is to increase the Type I error probability (α). Increasing α is wise if the population of interest is threatened by inaction (Gryska et al. 1997; Dauwalter et al. 2009) because a greater α improves the survey’s ability to detect population trends at the cost of increasing the probability of a false detection. Additionally, tests for negligible trend can be used as a complement to traditional hypothesis testing (Dixon and Pechmann 2005). With this method, the alternative hypothesis tests whether the 90% confidence interval falls within a specified

(by the researcher) interval around zero. As such, it is possible for poorly estimated trends to be not significantly different from zero and not significantly negligible with the same level of confidence for both tests (Dixon and Pechmann 2005). 43

The event variance component was estimated to be negative by the mixed model used

to estimate variance components for the three levels of sampling in surveys for DHP larvae.

However, because variance is a squared value, in theory it cannot be negative. Negative

variance components can occur if variation between samples is lower than variation between subsamples. Numerous interpretations of negative variance components exist, and, as a

consequence, there are multiple methods to solve the “problem” of a negative variance

component. One perspective is that negative variance components are impossible, therefore

they arise due to random variation around zero. According to this perspective, negative

variance components should be set to zero, effectively removing the source of variation from

the model (Thompson and Moore 1963; Fletcher and Underwood 2002). Alternatively, restricted maximum likelihood estimates of variance components, which by definition cannot be negative, can be used instead of observed and expected mean squares (Fletcher and

Underwood 2002). Yet another approach, which differs from the two above-mentioned

approaches because it allows negative variance components to remain in the model, is to

view parameters from analysis of variance as covariances rather than as variances (Smith and

Murray 1984). When all variance components are estimated positive and data are balanced,

restricted maximum likelihood method is equivalent to equating observed and expected mean

squares (Littell et al. 2002). When variance components are estimated negative, the restricted maximum likelihood method produces biased estimates of other positive variance components (Searle et al. 1992). We thought it was reasonable to retain the negative

variance component in the model, because it realistically depicted patterns of variation in

larval abundance and allowed estimates of variance components to remain non-biased.

Specifically, if larvae were found on a certain plot, they might be less likely to be found on 44

other plots because of limited space on the Devils Hole spawning shelf. Under such a circumstance, the variation in the sum of larvae on all plots (i.e., the variation of events) would be less than the variation in the number of larvae on separate plots.

CONCLUSION

Although the results of the power analysis are easy to interpret mathematically, using the findings of this study to recommend an “optimal” sampling design is more complex due to obstacles such as limited staff time, financial constraints, and concerns with disturbance due to sampling. Year-to-year differences in power due to dissimilarities in larval abundance further complicate construction of the “optimal” survey design for DHP larvae. Thus, developing a sampling design to consistently yield a certain level of statistical power was an unrealistic goal. Instead, we used the results of our study to compare relative differences in power from different combinations of sample sizes at each level of sampling. While increasing the number of surveys presented the best method to increase power, surveys are more demanding on resources and time. In contrast, the finding that event contributed negligibly and plot substantially to variation illustrates that increasing the number of plots per event is a relatively easy way to increase power in the sampling design without increasing sampling effort considerably. However, since surveys for larval DHP sample a fairly large proportion of larval DHP habitat, there is an upper limit to the number of plots which can be placed on the shallow shelf. If too many plots are placed on the shelf, larvae could swim onto multiple plots during one counting event, thus violating the assumption of 45

independence between plots. Hence, because the results showed that the difference in power was minimal between surveys with three events and surveys with two events, a sampling design that includes two events, each with thirty plots is a practical alternative to the previous design because there is little difference in power and it requires less effort while still allowing for plots to maintain independence (Figure 3.5). Specifically, a survey design with

30 plots and 2 events lasts ca. 1 hour and 15 minutes whereas a survey design with 3 events and 9 plots lasts ca. 2 hours and 5 minutes. Importantly, increasing the number of plots and(or) events will not substantially affect power to detect 30% (or lower) increases or decreases in larval abundance. Hence, if detecting fine-scale changes in larval abundance is of interest (e.g., hypothesis testing), the number of surveys must be increased to attain reasonable power. Because the sampling design of surveys for larval DHP is still in an experimental phase, its structure has been altered multiple times since 2005. Maximizing statistical power to detect year to year differences in larval density will help managers assess the influence of earthquakes and flood events on survival of DHP larvae. Furthermore, as data accumulate, year-to-year variability can be estimated as a random effect, thus allowing estimation of the survey’s power to detect long-term trends. Hopefully, monitoring of DHP larvae will continue far into the future and become a long-term record of larval abundance that will accompany surveys of adult DHP as well as current habitat monitoring surveys.

This holistic monitoring approach will provide valuable insight as to the life history and habitat requirements of the Devils Hole pupfish, thus aiding managers make decisions on where to focus future management actions. Although the results of this study are specific to

Devils Hole, many other monitoring efforts may benefit from coupling variance components

estimation with power analysis. 46

Acknowledgements

We thank the National Park Service (NPS) and the U.S. Fish and Wildlife Service

(USFWS) for providing funding for the study. In addition, we thank P. Barrett (USFWS), S.

Harris (Nevada Department of Wildlife (NDOW)), J. Sjoberg (NDOW), and J. Wullschleger

(NPS) for collecting larval abundance data and for helping attain financial support for this study. 47

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Table 3.1. Variance components and their associated estimates of statistical power in hierarchically nested surveys of Devils Hole pupfish (DHP) larvae, Cyprinodon diabolis, in Devils Hole, Nye County, NV. Values were attained from ln-transformed abundance estimates of DHP larvae from mid-March to mid-May. Power was estimated from sampling designs with five surveys, three events, and nine plots. Plots were treated either as fixed (F) or random (R) effects.

Power Power Plot Total Survey Event Plot CV 50% 50% Effect Variance Variance Variance Variance Decrease Increase 2007 R 0.571 0.8780.084 0.005 0.482 0.927 0.570 2008 R 0.241 0.522 0.001 -0.015 0.255 1.000a 1.000a 2009 R 0.335 0.631 0.059 -0.004 0.280 0.985 0.726 All Years R 0.380 0.680 0.048 -0.007 0.339 0.993 0.781 2007 F 0.357 0.6550.084 0.005 0.268 0.943 0.600 2008 F 0.182 0.447 0.001 -0.015 0.196 1.000 1.000 2009 F 0.299 0.590 0.059 -0.004 0.244 0.987 0.734 All Years F 0.301 0.593 0.048 -0.007 0.260 0.995 0.800

aThe estimated variance component estimates in 2008 were very low and thus caused problems in estimating power for some sample size combinations in 2008 (not shown). Power estimates calculated from variance components estimated using restricted maximum likelihood (a method which constrains variance components to be greater than or equal to zero) did not differ from power estimates from the ANOVA method by more than 0.001 (not shown).

Figure 3.1. Sampling design structure for surveys of larval Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. The left photograph shows the Devils Hole spawning shelf with placement of fixed plots represented by numbers. In the upper left corner, there is a photograph of the sampling apparatus. The right diagram depicts the hierarchically nested structure of the sampling design.

Figure 3.2. Estimates of larval abundance per plot from mid-March to mid-May for the Devils Hole pupfish, Cyprinodon diabolis, in Devils Hole, Nye County, NV. Average larval abundance per plot from 2007-2009 was estimated as the average number of larvae occurring on plots during each survey

1.5 2007 2008 1.0 2009

0.5

0.0

-0.5

-1.0 Natural log of average number of larvae per plot per larvae of number average of log Natural

-1.5 15-Mar 1-Apr 15-Apr 1-May 15-May

Date

Figure 3.3. Statistical power to detect increases in the abundance of Devils Hole pupfish larvae, Cyprinodon diabolis, in Devils Hole, Nye County, NV. Power was estimated for different sample size combinations in a hierarchically nested sampling design. Estimates of variance components and power were attained from pooling abundance data from five surveys days each year in mid-March thru mid-May in 2007 –2009. In each panel, the sample sizes of two levels of sampling were held constant to show how increasing sample size at a specific level of sampling influenced statistical power. Power was estimated from sampling designs with (a) 3 events and 9 random plots, (b) 5 surveys and 9 random plots, and (c) 5 surveys and 3 events

_ 1.0 30% increase 25% increase 20% increase _ 0.5 Power

_ 0.0

024681012 Number of surveys _ 0.6 _ 0.5 _ 0.4 Power _ 0.3 _ 0.2 024681012 Number of events _ 0.6 _ 0.5 _ 0.4 Power _ 0.3 _ 0.2 0 10203040 Number of plots 56

Figure 3.4. Comparison of power from sampling designs with fixed plots and random plots in surveys of larval Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV . Power was calculated from pooled estimates of variance in spring 2007-2009 from sampling designs with 5 surveys and 3 events.

1.0

30% Decrease 0.8

0.6 30% Increase Power

0.4

0.2

Fixed Random 0.0 0 10203040

Number of plots

Figure 3.5. Statistical power of different sampling design structures to detect a 30% increase population abundance in Devils Hole pupfish larvae, Cyprinodon diabolis, in Nye County, NV. Symbols on the graph represent the number of events in each survey. The dotted line represents a constant sampling effort of thirty plots partitioned differently among events (i.e., for 5 plots and 6 events versus 30 plots and 1 event). The line slopes gently upwards, indicating that maximizing the number of plots per event will result in a survey design with higher power. The number of surveys was held constant at five. Power of the previous (3 events, 9 plots) and proposed (2 events, 30 plots) sampling designs are designated by circles.

0.55 6 6 6 6 6 3 23 6 6 3 3 2 6 3 2 2 1 6 3 2 O 1 3 1 6 2 0.50 3 2 1 3 1 6 2 1 3 2 O 1 0.45 2 1 3

1 0.40 2

Statistical power 1

0.35 1

0.30 0 10203040

Number of plots

CHAPTER 4. DEVELOPING A SIMULATION MODEL OF THE DEVILS HOLE PUPFISH POPULATION USING MONTHLY LENGTH FREQUENCY DISTRIBUTIONS

A paper to be submitted to Population Ecology

Maria C. Dzul1, Stephen J. Dinsmore1, Michael C. Quist2, D. Bailey Gaines3, Kevin P. Wilson3, Michael R. Bower4, Philip M. Dixon5

ABSTRACT

The Devils Hole pupfish, Cyprinodon diabolis, is a federally-endangered fish that is endemic

to Devils Hole, Nye County, NV. Due to its status, Devils Hole pupfish monitoring must be

non-obtrusive and thereby exclude techniques that require handling fish. While certain

aspects of Devils Hole pupfish ecology have been studied extensively, knowledge of Devils

Hole pupfish life history remains limited. Accordingly, Devils Hole pupfish managers have

expressed a need for a population model describing population dynamics, which can be used

to identify vulnerable life history stage(s) and inform management actions. In early 2009, the

National Park Service acquired a SCUBA-diver-operated stereovideo system which can be

used to obtain fish lengths from video images. Beginning in March 2009, the National Park

Service initiated monthly SCUBA dives in Devils Hole to generate estimates of length-

frequency distributions of the Devils Hole pupfish population. Because it is difficult to

1 Graduate student and Associate Professor, respectively, Department of Natural Resource Ecology and Management, Iowa State University. 2 Assistant Unit Leader, U.S. Geological Survey - Idaho Cooperative Fish and Wildlife Research Unit, University of Idaho. 3 Fish biologist and aquatic ecologist, respectively, U.S. Park Service – Death Valley National Park. 4 Fish biologist, U.S. Forest Service – Bighorn National Forest. 5 Professor, Department of Statistics, Iowa State University. 59

differentiate population processes (e.g., recruitment, survival, growth) without individual

histories, we constructed a set of individual-based simulation models designed to explore

effects of population processes and evaluate assumptions. We developed a baseline model,

whose output best resembled both observed length-frequency data and predicted intra-annual

abundance patterns. We then ran simulations with 5% increases in larval, juvenile, and adult

survival rates to better understand Devils Hole pupfish life history, thereby helping identify

vulnerable life history stages that should become the target of management actions.

Simulation models with temporally constant adult, juvenile, and larval survival rates were

able to reproduce observed length-frequency distributions and predicted intra-annual

population patterns. In particular, models with monthly adult and juvenile survival rates of

80% and a larval survival rate of 4.7% resulted in good fit. Whereas intra-annual patterns

were affected by adult survival rates, larval survival rates had no noticeable effect on intra-

annual trends. Population growth was most affected by 5% increases in larval survival,

whereas adult and juvenile survival rates had similar effects on population growth. Outputs from our model were used to assess factors suspected of influencing Devils Hole pupfish population decline.

INTRODUCTION

Conservation efforts directed by vague biological data about targeted species are often unlikely to be successful (Tear et al. 1995; Foin et al. 1998; Boersma et al. 2001; Clark

et al. 2002; Gerber and Hatch 2002). In their review of 180 recovery plans, Gerber and

Hatch (2002) found that endangered species with recovery plans exhibiting clearly-defined,

biologically-based recovery criteria are more likely to exhibit an improved status. In

particular, developing quantitative recovery criteria can help assess successes and failures of 60

management actions, which can lead to improved management (Gerber and Hatch 2002).

Understanding population processes is therefore vital for conservation efforts, as basic knowledge about population dynamics can help biologists focus monitoring efforts on evaluating factors likely related to population decline (Campbell et al. 2002). Key to successful recovery of imperiled species is identification of vulnerable life history stages and subsequent evaluation of environmental factors influencing variability in those stages

(Schemske et al. 1994). For example, Crouse et al. (1987) developed a stage-class population matrix model for the threatened loggerhead sea turtle, Caretta caretta, from

which they calculated sensitivity values for population parameters at different life stages.

Results of the sensitivity analysis illustrated that the loggerhead turtle population was most

sensitive to juvenile survival; thus, Crouse et al. (1987) recommended that management

actions switch their focus from protecting nests on beaches to encouraging commercial

fishermen to use a Trawl Efficiency Device (TED) that reduces bycatch of juvenile turtles.

The Crouse et al. (1987) study illustrates how improving understanding of biological

processes can lead to the development of targeted conservation strategies.

Statistical models describing population dynamics are extensively used in wildlife

and fisheries management to identify vulnerable life stages of imperiled populations (Crouse

et al. 1987; Doak et al. 1994; Crooks et al. 1998), evaluate mechanisms suspected of

influencing species’ declines (Lamberson et al. 1992; Fahrig 1997; Huxel 1999; Doubledee

et al. 2003), and assess the impact of management alternatives on population dynamics

(Heppell et al. 1994). Simulation can provide insight into which population processes

influence model behavior (Caswell 1988; Van Nes and Scheffer 2005). Because the modeler

knows “truth” about processes (i.e., the modeler can control population processes by 61

changing parameters and equations that comprise the model) but not about effects, simulation can be thought of as reverse experimentation. Simulation models are often evaluated by their ability to match observed data and are deemed validated if they closely match observed data.

However, even if a simulation model is validated, it indicates that the model structure and parameter estimates are merely possible, not actual (Lewontin 1968). Simulation models can often identify processes which influence model behavior, and these influential processes can be further tested through empirical studies (Van Nes and Scheffer 2005). Furthermore, the usefulness of simulation modeling does not rest solely on the model’s ability to mimic reality. One benefit of simulation is that it can help explain which assumptions lead to aberrant model behavior (Van Nes and Scheffer 2005).

The Devils Hole pupfish, Cyprinodon diabolis, is a federally-endangered species endemic to Devils Hole, Nye County, Nevada. Their small population size, coupled with a limited geographic range, requires that all sampling of Devils Hole pupfish be non-obtrusive.

Developing a population model for the Devils Hole pupfish is of interest because this species’ experienced a dramatic decline in abundance from the late 1990s to mid-2000s. As such, updated information about Devils Hole pupfish population processes is needed to evaluate management alternatives. Two previous models have described population fluctuations in the Devils Hole pupfish; these models include a population model developed by Chernoff (1985) and a system dynamics model developed by Graves (2004). The premise of Chernoff’s (1985) model was to partition pupfish mortality into three separate categories: mortality due to a drop in water level, mortality due to a decrease in primary production, and residual mortality (or the average "natural" mortality according to Chernoff). Chernoff

(1985) accounted for the first two parameters by using established linear relationships of 62

pupfish abundance with water level (Deacon 1976) and production (Deacon and Deacon

1979). He then used observed trends in the pupfish population to deduce natural mortality,

from which he estimated average life expectancy of an adult pupfish to be 10 months.

Alternatively, the Graves’ (2004) model described ecosystem processes and predicted the effects of management alternatives on survival of Devils Hole pupfish larvae. While useful, the Chernoff (1985) and Graves (2004) models rely almost solely on assumptions because direct measurements of wild Devils Hole pupfish are difficult to obtain. In contrast, our simulation model used additional sources of data from wild Devils Hole pupfish to help guide parameterization of model inputs.

The goal of our simulation model was to increase understanding of Devils Hole pupfish population dynamics while also providing a tool to evaluate alternative management strategies. We compared simulation models with growth curves estimated from length- frequency distributions attained from SV dives to simulations using growth curves estimated from in situ caged Devils Hole pupfish (James 1969). Furthermore, we compared discrete population growth rates (λ) from simulations with changes in larval, juvenile, and adult

survival rates to determine vulnerable life history stages. Lastly, we assessed feasibility of

winter recruitment by comparing simulation models with and without winter recruitment.

METHODS

Study site

Devils Hole is a small limestone cavern located in a discontiguous portion of Death

Valley National Park adjacent to Ash Meadows National Wildlife Refuge (Nye County, NV).

For practical purposes, Devils Hole is often divided into two strata: the shallow shelf and the 63

deep pool. The shallow shelf is a 5.5 × 2.0 m boulder face submerged under 0.2-0.7 m of water. The depth of the deep pool is unknown, but is greater than 133 m. Devils Hole pupfish population size fluctuates seasonally, historically reaching a maximum of 400 -500 in early autumn and a minimum of 200-300 in mid-spring (Andersen and Deacon 1991).

However, population abundance declined in the mid-1990s to mid-2000s, reaching a low of

38 individuals in April 2006 and April 2007.

Estimation of length-frequency distributions

In the past, researchers have attempted to make inference about the size structure of the Devils Hole pupfish population by either dip-netting fish near or on the shelf (James

1969) or from visual assessment by SCUBA divers and surface observers (Threloff 2004).

Length estimates by SCUBA divers can be imprecise and biased (Harvey et al. 2002; Bower et al. 2011) and dip-netting at the surface may preferentially sample a certain size class of individuals due to habitat associations or catchability (Ream and Ream 1966). In contrast, stereovideo (SV) technology presents a powerful tool for non-obtrusively collecting accurate and precise length measurements (Harvey et al. 2002; Harvey et al. 2004). Bower et al.

(2011) compared length measurements of Saratoga Springs pupfish, C. nevadensis nevadensis, generated from a SV system to visual estimates from SCUBA divers. Results showed that length measurements from the SV system had negligible bias and greater precision compared to length estimates from SCUBA divers. We used SV technology to obtain monthly length-frequency distributions of the Devils Hole pupfish population.

Stereovideo dives in Devils Hole were conducted every month from March 2010 to

February 2011 to assess the annual dynamics of population size structure. Time intervals 64

between successive stereovideo dives were not uniform and varied from 3-6 weeks.

Stereovideo dives were conducted by two SCUBA divers; one diver operated the SV system while the other served as the safety diver. The SV system consisted of a SeaGIS underwater stereovideo camera system (SeaGIS Pty. Ltd., Bacchus Marsh, Victoria, Australia) equipped with a pair of Canon Vixia HV30 high-definition cameras (Canon USA, Inc., Lake Success,

New York). Cameras settings were zero zoom, infinity focus, and an F-stop of 4.8. Detailed information about the SV system is described in Bower et al. (2011). Because biologists hypothesize small fish are more active during night hours, two SV dives were conducted for each sampling date. The night SV dive occurred one hour after sunset and the day SV dive occurred the following morning around 9 a.m. Divers first descended approximately 26 m in

Devils Hole, waited 5 minutes, and then began to slowly ascend Devils Hole and videotape fish. Divers followed the same route for each dive and attempted to videotape a random sample of fish from the Devils Hole pupfish population (e.g., divers were instructed avoid preferentially videotape larger, more visible fish or large schools of fish). To obtain clear frames of fish images, divers videotaped encountered fish for ~10 seconds or until a desirable profile shot was obtained. Video processing was completed using the computer program

PhotoMeasure, which accompanies the SV equipment (SeaGIS 2009). Processing video requires manual marking of four points on a pair of simultaneous video images. Total length was measured for each fish by manually marking the tip of its snout and the end of its caudal fin. For each fish, three measurements from three different pairs of video frames were measured in PhotoMeasure and the length of each fish was estimated as the mean of the three measurements. If the video-processor was not confident in length measurements for a 65

particular fish (e.g., image was blurry), the fish was excluded from length-frequency distributions.

Evaluating length-frequency distributions using mixture models

Due to logistical constraints, we were unable to process videotape from night SV dives. Thus, only length-frequency distributions from SV dives conducted during daylight hours were used to construct the simulation model. To determine the number of cohorts in each length-frequency distribution, normal and lognormal mixture models were fit to length- frequency distributions from stereovideo dives using the package MCLUST in R (Fraley and

Raftery 2009). Although normal distributions are commonly fit to length-frequency distributions (MacDonald and Pitcher 1979; Fournier et al. 1990; Fournier et al. 1998), we also assessed mixture models fitting lognormal distributions due to the observation that

Devils Hole pupfish population exhibit continuous recruitment (Gustafson and Deacon 1997;

Lyons 2005). Lognormal distributions have higher probability density in the upper tails of the distribution relative to normal distributions. As such, lognormal distributions may be better suited for describing pupfish length-frequency distributions. For lognormal mixture models, lengths were loge transformed and subsequently fit to normal mixtures. MCLUST fits one to nine normal distributions (i.e., mixtures) with equal and unequal variances, generating a total of seventeen models. The most parsimonious model was selected using the

Bayesian Information Criterion (BIC; Schwartz 1978). Because BIC values from normal and log-normal distributions are not directly comparable, BIC values were corrected for the lognormal distribution by adding a constant term (Lindsey 1974). 66

Model construction

Our model uses a simulation approach which assigns specific functions to population

processes and generates monthly length-frequency distributions. Simulation models required

three inputs: number of larvae per female, survival rates, and a growth model. When

possible, we used current data to describe population processes. For example, we were able

to use best-fit mixture models fit to observed length-frequency distributions of adult Devils

Hole pupfish to help construct growth models. Similarly, we were able use larval abundance

estimates from 2010 biweekly early life stage (ELS) monitoring of Devils Hole pupfish to

estimate timing and magnitude of recruitment.

Simulation modeling

In populations that exhibit pulse-recruitment, cohorts may be identifiable in length- frequency distributions by the appearance of separate modes (Petersen 1891; MacDonald and

Pitcher 1979). Assuming length distributions within a cohort follow a specified parametric

distribution, cohorts can be identified and separated using maximum likelihood (MacDonald

and Pitcher 1979; Fournier et al. 1990; Roa-Ureta 2009). For instance, a procedure that can

simultaneously estimate age composition (i.e., number of cohorts) and growth has been

developed by Schnute and Fournier (1980). Such methods are popular when organisms are

difficult to age (e.g., tropical fish, crustaceans, turtles), the status of the species precludes removal of structures for age and growth analysis, or when costs of performing age and growth studies are prohibitive. Unfortunately, the above-mentioned methods are ill-suited for modeling the Devils Hole pupfish population because following sequential estimates of mean cohort length will result in underestimation of growth in populations which exhibit 67

continuous recruitment (Wang and Somers 1996). Low detectability of small fish further complicates model construction and evaluation because size selectivity can bias growth parameters (Fournier et al. 1990). Our choice to use simulation instead of the above- mentioned methods stems from the difficulty of simultaneously estimating survival, recruitment, and growth from a continuously-reproducing population with only one year of length-frequency data. Consequently, we used an individual-based simulation model to describe Devils Hole pupfish dynamics because this approach allowed us to use a wide variety of data sources to estimate population parameters.

Estimating reproduction

We predicted monthly adult abundance using a linear additive model, which will hereafter be referred to as the adult abundance model. The adult abundance model included two fixed effects, month and year, and was fit to abundance estimates from 1972-2010 adult surveys. We assumed that historic intra-annual patterns in adult abundance reflected current patterns. Adult abundances were loge transformed prior to analysis because we wanted to predict geometric means. Although our intentions were to use the adult abundance model to predict monthly estimates of adult population abundance in 2010, we were unable to do so because adult abundance estimates for April and October dive surveys in 2010 were similar

(120 and 118, respectively). Thus, we used estimates of adult abundance from 2009 to predict adult abundance in 2010. Abundance estimates of prolarvae (3-5 mm larvae) from

ELS surveys in 2010 were used to fit a generalized linear model to predict larval abundance

(henceforth referred to as the larval abundance model). Specifically, the sum of the number of prolarvae observed per event was a Poisson-distributed response variable that was 68

predicted by a polynomial equation with time as the predictor variable (Wood 2006). We fit models with 3-6 degree polynomial terms and selected the best model using BIC.

Abundance of prolarvae was estimated from the larval abundance model by integrating between two specified time intervals in the function and multiplying this number by the proportion of shelf area sampled by ELS surveys.

Spawning behavior in Devils Hole pupfish occurs year-round, with peak spawning occurring from mid-February to mid-May (Lyons 2005). Captive female Devils Hole pupfish collected in October began spawning in January and produced 1 egg per day with ~4 days between spawning events (Deacon et al. 1995). In contrast, females collected in May spawned immediately and produced 0-2 eggs per day, with one female producing 25 eggs in an 8-day period (Deacon et al. 1995). We attempted to establish a relationship between female size and fecundity from Minckley and Deacon (1973), which includes egg counts for

26 wild female Devils Hole pupfish collected during different times of year. Unfortunately, we could not establish a relationship between female length and fecundity from their data, likely due to the small sample size. We therefore assumed all females greater than 13 mm

(the minimum length of a reproductive female [Minckley and Deacon 1973]) were reproductive and produced equivalent numbers of larvae. The minimum length of reproduction will be referred to as reproductive length. While this assumption may seem overly simplistic, Mire and Millet (1994) could not establish a relationship between female length and fecundity, length of spawned larvae, or survival of spawned larvae in an experiment involving 39 female Owens pupfish, C. radiosus. Similarly, no correlation was observed between female size and fecundity in captive Saratoga Springs pupfish (Shrode and

Gerking 1977). We estimated the number of larvae produced per female by dividing the 69

predicted number of larvae by the predicted number of female pupfish for each interval.

Abundances of 3-5 mm larvae (or prolarvae) were predicted by integrating the function

describing the larval abundance model. Specifically, for each interval, we integrated the larval abundance function from the present interval to the next interval. We then extrapolated this value to the entire larval population by multiplying by the inverse of the proportion of the area covered by ELS surveys. Abundances were estimated assuming prolarvae required one week to grow to lengths greater than 6 mm. We assumed that detectability in the adult abundance surveys was equivalent to detectability of SV surveys; this assumption is reasonable because both surveys are conducted by SCUBA divers. For each interval, the proportion of spawning females was estimated by multiplying the probability of a fish being over 13 mm in length (estimated by integrating the best fit mixture models for each month) by the probability of being female (assumed to be 50%). Although there is some evidence that the sex ratio may differ during certain months (James 1969), we chose a sex ratio of 1:1 because we were uncertain whether sex could be correctly determined, particularly for small fish. Estimated proportions of spawning females were then multiplied by predicted abundance estimates from the adult abundance model for each interval. Numbers of spawning females were estimated by taking the mean of the predicted numbers of spawning females from the present interval and one interval into the future.

Importantly, because detection is low for fish with lengths from 13-18 mm, this method may overestimate the number of larvae per female. 70

Fitting a growth model

We used two different growth models, a fast-slow model and a mode model, to

portray Devils Hole pupfish growth (see descriptions below). Both growth models assume von Bertalanffy growth (von Bertalanffy 1938) and were fit using the Fabens parameterization, which is well-suited for fitting growth curves to mark-recapture of tagged individuals (Haddon 2011). Preliminary analyses showed that growth data from individual

Devils Hole pupfish (James 1969) were well described by a von Bertalanffy growth model.

The Fabens parameterization of the von Bertalanffy model estimates two parameters, the mean maximum asymptotic size (L∞) and the growth coefficient (K; Haddon 2011), using

three pieces of information (i.e., time interval, growth increment, original length). To portray

variability in growth among individuals, a random number was selected from a standard

normal distribution and added to the predicted growth increment for every individual.

Individual fish lengths could not decrease with time; if the length of a fish was smaller in a

future interval (i.e., the random term was negative and its absolute value was greater than the

predicted growth increment), the fish’s length remained equal to its length during the

previous month.

The fast-slow model included two growth curves, a fast and a slow growth curve

(Figure 4.1). The fast growth curve was used to model all fish from the larval stage until

they reached 15 mm . In addition, fish born between March and June also followed the fast

growth curve from March to June. Fish greater than 15 mm that were born July through

February followed the slow growth curve. The basis for two growth curves stems from the

results of an in situ caged experiment study of Devils Hole pupfish where biologists observed

vastly different growth rates for fish with different hatch dates (James 1969). While it is 71

possible to estimate growth curves from length-frequency distributions of populations exhibiting continuous recruitment, Wang and Somers’ (1996) method is not useful for estimating a growth curve for the Devils Hole pupfish due to low detectability of small fish.

Consequently, the fast growth curve was estimated from growth of caged individuals born in spring (James 1969), whereas the slow growth curve was estimated by following estimates of mean length from best-fit normal mixture models in months without substantial recruitment

(i.e., October through March) as well as the means of the older cohort from April to June.

When estimating the slow growth curve, we assumed neither recruitment nor size-selective mortality occurred between November and March. In addition, for months where the best fit mixture models included two cohorts (i.e., April, May, June), we assumed that neither recruitment nor size-selective mortality occurred into the older cohort.

The mode model was estimated by following temporal modes of length bins observed in SV dives and ELS surveys. Although growth of larval fish often differs from growth of adult fish, we grouped larval and adult growth estimates together due to a sparse dataset.

One important assumption of estimating a growth curve by following modes is that all modes

represent the same individuals. For each month, we multiplied adult abundance estimates

from the adult abundance model by probability distributions of best-fit normal mixture

models describing length-probability from SV dives to attain the predicted number of fish in

each 0.1 mm length bin. We then grouped length bins by the month during which the

predicted mode occurred and calculated the mean of modes. For example, if the maximum

number of fish with length bins 13.1- 13.5 mm were predicted to occur in March, the mean

length in March was estimated as 13.3 mm. Additionally, we followed length modes for

larval fish in ELS surveys to estimate growth of larval fish. Because measurement of larval 72

fish in ELS surveys was less precise than the SV method, we grouped larval fish into length

categories (i.e., prolarvae, early postlarvae, late postlarvae, and prejuvenile) determined by

morphological characteristics (Lyons 2005). For each length category, we used the same

method used to fit the larval abundance model to determine the appropriate polynomial term

in generalized linear models describing temporal abundance patterns. We subsequently calculated roots of the derivative of polynomial equations to determine the date during which maximum abundance occurred for each length group.

Survival

Egg, larval, juvenile, and adult survival rates were assigned different parameter values. We assumed egg survival was 100%, because we had no information to inform this

parameter. Individuals transitioned between larval and juvenile survival rates when they

reached juvenile length (set to 12 mm), and between juvenile and adult survival rates when

they reached adult length (18 mm). Adult and juvenile lengths were determined based on

their association with notable behavioral changes. We assumed mortality of larvae occurred

within the first month after birth. High mortality at early life history stages indicates a Type I

survival curve, which is common among fishes. Larval mortality was set to zero after the

first month post-birth up until simulated fish reached juvenile length. Juvenile and adult

survival rates were described by a Type II survival curve, which is commonly assumed in

fisheries when estimating mortality from catch curves (Haddon 2011). Monthly juvenile and

adult survival rates were converted to daily survival rates to adjust for unequal time intervals.

Simulated individuals would first grow and subsequently attain a survival probability based

on the individual’s length during the current period and the next period. For example, if an 73

individual was a juvenile during the current period and an adult during the next period, we

used the following equation to estimate that individual’s survival probability:

, , , , ,

Where rj and ra are the respective instantaneous survival rates for juveniles and adults, and li,t and li,t+1 are the respective current and future lengths of individual i. The parameter la represents adult length. This equation was also used to estimate the survival probability of individuals transitioning from the larval to juvenile stage, with instantaneous larval and juvenile survival rates replacing instantaneous juvenile and adult survival rates, and juvenile length replacing adult length. Although we assumed juvenile and adult survival rates were equal for our baseline model, other models included unequal juvenile and adult survival rates.

All simulated fish greater than 30 mm in length had their survival set to 0 in July to reflect senescence of the older cohort. Likewise, we added a term for senescence in April through July in simulations with a monthly adult survival rate of 75%. Specifically, all simulated fish greater than 20 mm in length in March were given a monthly survival rate of

75% from April to June. Senescence of the older cohort was supported by observed length- frequency distributions from SV dives. Additionally, we assumed adult, juvenile, and larval survival rates were constant for all months. While constant survival may be not perfectly reflect population dynamics, assuming constant survival will help interpret deviations of simulated data from observed monthly abundance patterns. 74

Simulation runs

For the first iteration of each simulation, the initial population was comprised of 108 fish with lengths equal to those observed in the March SV dive. These 108 fish were randomly assigned a sex (“male” or “female”) with equal probability. Fish then grew according to the appropriate growth curve. To determine survivorship, simulated fish received a random number drawn from a uniform distribution between 0 and 1. Only individuals that received a random number less than their survival probability survived to the next interval. Upon surviving, individuals would grow according to the specified growth curve. Recruitment was calculated by taking the mean of the numbers of females greater than 13 mm in length for the current interval and the subsequent future interval, then multiplying it by the fecundity estimate for the particular month. The number of larvae was then multiplied by the larval survival rate to obtain the number of larvae which survived the first month post-birth. Upon surviving the first month, larvae were assigned a sex (“male” or

“female”) with equal probability. They were then randomly assigned a hatch date from a multinomial distribution, with probabilities of hatch dates obtained from the larval abundance function. Hatch dates were entered into the growth function for each larva to determine its length during the sampling period. Assigning larvae a random hatch date allowed us to use discrete time to realistically depict continuous spawning. Namely, because the initial length of each larva was a function of its hatch date, lengths of larvae entering the population were not uniform. We ran simulation models out 120 months and used the first 24 values as burn- in values. We selected 24 months because it was short enough that starting points (i.e., year

3) between iterations were sufficiently similar but long enough to stabilize length-probability and abundance trends. 75

Simulation Models

Choosing a baseline model

Our first task was to select a baseline simulation model that realistically portrayed the

Devils Hole pupfish population. Based on its resemblance to observations, this model would

help determine realistic values for survival probabilities of Devils Hole pupfish. Regrettably,

size selectivity of Devils Hole pupfish SCUBA survey methods hindered direct quantitative

comparison of simulations to observations. Consequently, simulation runs were evaluated

qualitatively using visualization methods. Simulations were run with monthly adult survival

probabilities of 70%, 80%, and 86%. We chose 86% instead of 90% because the adult

abundance model predicts the Devils Hole pupfish population declines by 14% each month

from October to April. As such, a 90% survival probability is unrealistic if monthly survival rates are constant. Through trial and error, we selected a larval survival rate for each adult

survival probability that resulted in population growth parameter (λ) near 1. We ran 2000,

120-month simulations to evaluate model performance, after which we used two different assessments to evaluate fit of simulations. First, we visually compared intra-annual

(monthly) abundance patterns from simulations to estimates predicted by the adult abundance

model. All abundance values were scaled to the maximum number of fish in a given year.

Due to low detectability of small fish in SCUBA surveys, abundances of simulated

populations were calculated as numbers of individuals greater than detection length to

facilitate comparison between simulations and predictions. Detection length was set at 18

mm and refers to the minimum length of maximum detectability. Importantly, expressing

detection as a function of length would likely be more appropriate, as small fish are still 76

partially detected by SCUBA surveys. However, because we had no data to inform this

function, we chose 18 mm as a cut-off because this number seemed reasonable to SCUBA

divers. Second, we plotted monthly length-frequency probability distributions from one

randomly-chosen year from 100 different 120-month simulations against probability

distributions of observed length-frequency from SV dives. Similar to assessment of intra-

annual patterns, we excluded fish with lengths less than 18 mm in length-probability

distributions due their low detectability in stereovideo dives. We used these two criteria to

select a baseline model, which was used in subsequent analyses to assess the effects of model

parameters on population growth rates.

Assessing elasticity of model inputs

For each simulation, we ran 2000 iterations of population growth for 120 months.

The first 24 months of each 120-month iteration were considered burn-in months, and they

were not included in summary statistics. Simulations were summarized by calculating the

geometric mean ( ˆ ) and standard error of population growth rates from 2000 iterations, as

well as the probability of extinction. Geometric means were included in summary statistics in lieu of arithmetic means because discrete population growth rates are multiplicative.

ˆ ˆ Calculation of  required first calculating the geometric mean within iterations (  I ), then

ˆ ˆ calculating the geometric mean of all 2000  I values. We estimated  I by calculating the

arithmetic mean abundance for each year within an iteration, converting mean abundances to

finite population growth rates by dividing estimates from consecutive years, and then taking

the geometric mean of mean population growth rates within each iteration. We then

calculated the geometric mean from all 2000 iterations to estimate the geometric mean of the 77

simulation model. In cases where an iteration resulted in population extinction, we excluded

all years post-extinction from the average lambda calculation. The probability of extinction

was estimated as the proportion of simulations which resulted in a population comprised of

less than 10 individuals after 8 years. Notably, estimates of extinction probability and

population growth are reported to help illustrate differences between simulation models and

not for their (weak) predictive capability. In particular, estimating quasi-extinction rates is

tenuous, especially with a limited dataset (Fieber and Ellner 2001).

We conducted an elasticity analysis to assess the influence of model inputs on

population growth (de Kroon et al. 1986). Elasticity is the proportional change in λ divided

by the proportional change in vital rates (e.g., survival, fecundity) evaluated at a specific value of the vital rate. Results of elasticity analyses can be used to help evaluate alternative management strategies and determine how uncertainty in parameter estimates will affect estimates of population growth (Morris and Doak 2002). For example, if increasing larval survival by 5% has a substantially larger effect on population growth compared to increasing

adult survival by 5%, then managers may want to focus recovery efforts on increasing larval

survival rates. Yet, if there is uncertainty in a parameter’s value (e.g., in this case there is

uncertainty about reproductive length), high elasticity values signify that population growth

rates are greatly affected by the parameter estimate. As such, attaining a better estimate of

the parameter is warranted to make accurate assessments about population growth.

Specifically, we ran simulations with 5% increases in annual larval, juvenile, and adult

survival rates, as well as 5% increases in juvenile length and reproductive length.

Furthermore, we ran one simulation with decreased fecundity values (Table 4.1). We will 78

refer to the geometric mean population growth rate of the baseline model as ˆ.and of altered

ˆ simulations as a , where the difference between the baseline model and altered simulation a

is one parameter (referred to as x. in the baseline model and xa in the altered model). We

calculated elasticity using the following formula (Morris and Doak 2002):

ˆ / ˆ a . xa / x.

Whereas adult and larval survival rates may be affected by various management practices,

reproductive length and juvenile length are biological characteristics that would likely be

unaffected by management alternatives. As such, elasticity values of juvenile length and

reproductive length help evaluate how uncertainty in these parameters affects simulation

model performance. In addition to increasing aforementioned parameters, we ran one simulation which included a fourfold decrease in fecundity coupled with a fourfold increase in larval survival. We included this simulation because we suspected that the baseline model over-estimated fecundity. Importantly, this coupling of larval survival and fecundity parameters did not represent a change in larval abundance values. Rather, we hypothesized differences in pairings of fecundity and larval survival parameters may affect demographic stochasticity, which could in turn affect population growth. Because elasticities are calculated at specific parameter estimates (Caswell 1996), we also calculated elasticity values for 2000 iterations of simulation models with 5% increases in adult, juvenile, and larval survival for models with initial adult survival rates of 70% and 86%. We calculated

elasticities for models with adult survival rates of 70% and 86% to determine if the relative 79

effects of larval, juvenile, adult survival were similar for various adult and juvenile survival

probabilities.

Because there is some debate as to whether recruitment occurs into the Devils Hole

pupfish population in winter months, we ran one simulation where no recruitment occurred

into the Devils Hole pupfish population in winter months. The debate about over-winter

recruitment arises from low detection of 8-18 mm fish in adult and larval surveys coupled

with lower larval abundances in winter months. As such, rarity of 8-18 mm fish in winter

could be attributed to low detection coupled with low abundances, or simply just absence.

We compared a simulation model without recruitment to the baseline model. The simulation

model without winter recruitment assumed 100% mortality of all fish with lengths less than

18 mm in December. Furthermore, recruitment during November, December, and January

was set to zero.

RESULTS

Best-fit normal mixture models for April, May, June, and October length-probability distributions were comprised of two mixtures. For all other months, best-fit normal mixture

models consisted of a single mixture (Figure 4.1). Similarly, best-fit lognormal mixture models included two mixtures for April, May, and October; however, unlike normal mixture models, the best-fit June lognormal mixture model consisted of a single distribution and the best-fit November lognormal mixture model consisted of two mixtures. Lognormal mixture models exhibited superior fit to normal mixture models after correction of BIC values (Table

4.2). Unfortunately, means from lognormal distributions used to fit the slow growth curve did not exhibit good fit to the von Bertalanffy model. As such, we used means estimated 80

from normal mixtures, which better conformed to von Bertalanffy model, to estimate the slow growth curve (Figure 4.2). The larval abundance model which included a fifth degree polynomial resulted in the best fit (Figure 4.3) and was used to estimate timing and magnitude of recruitment (Figure 4.4).

Interestingly, the fast-slow model generated more realistic length probability distributions compared to the mode model, because the mode model under-estimated relative abundance of large fish in August-September (Figures 4.5, 4.6, and 4.7). As such, all subsequent simulations used the fast-slow model to depict pupfish growth. Whereas the choice of adult survival rate had a large effect on intra-annual abundance patterns, larval survival rates primarily affected inter-annual abundance and population growth. When assessing intra-annual patterns, simulations with a monthly adult survival rate of 86% tended to over-estimate abundance in winter, whereas simulations with a monthly adult survival rate of 70% tended to result in greater magnitude population fluctuations when compared with the adult abundance model (Figure 4.8). The simulation model with a monthly adult survival rate of 80% produced highly variable estimates in March and April, some of which greatly overestimated abundance. Nevertheless, simulations a monthly adult survival rate of 80% exhibited good fit to the adult abundance model. Furthermore, length-probability distributions from simulations with a monthly adult survival rate of 80% resembled observed length-probability distributions from SV dives from March to February. However, the simulation model underestimated the proportion of large fish in April and May, suggesting that the model underestimated growth and(or) overestimated mortality of large fish during these months (Figure 4.6). Length-probability models from simulations with a monthly adult survival rate of 86% likewise exhibited good fit to observed length-frequency probabilities. 81

In contrast, length-probability distributions from simulations with a monthly adult survival

rate of 70% tended to under-estimate relative abundance of large fish in July through

December. We selected a monthly adult survival rate of 80% for our baseline model because

survival values exhibited the best overall resemblance to the adult abundance model and to

length-frequency distributions from SV dives. Corresponding monthly survival probabilities

for larvae and juveniles were set to 4.7% and 80%, respectively.

Iterations within simulations exhibited high variability (Figure 4.9). Regardless of whether the monthly adult survival rate was set to 70%, 80%, or 86%, results of the elasticity

analysis indicated that growth of the simulated population was most affected by larval survival. Increasing juvenile and adult survival rates had more similar effects on population growth (Table 4.1; Figure 4.10), though increasing juvenile survival usually had a greater effect on population growth than increasing adult survival. Furthermore, elasticity values for juvenile length and (to a lesser extent) reproductive length were also relatively high (1.02 and

0.87, respectively). In contrast, assuming larval abundance estimates were similar to those of the baseline model (see Figure 4.4), uncertainty in larvae per female had a negligible effect on population growth rates nor on the probability of extinction. For models without winter

recruitment, juvenile survival had to be increased from 4.7% to 7.0% to avoid extinction.

Simulation models without winter recruitment overestimated abundance in November and underestimated abundance from May to August and January to February (Figures 4.11). In addition, simulations without winter recruitment exhibited poor fit to observed length- probability distributions from SV dives in May and June, and underestimated the relative abundance of large fish in June to September (Figures 4.12, 4.13). 82

DISCUSSION

Conducting monthly SCUBA dives in Devils Hole was difficult due to the endangered status of the Devils Hole pupfish. Nonetheless, length-frequency distributions from SV dives provided useful information about the population structure in Devils Hole.

Moreover, observed length-frequency distributions from SV dives served as a diagnostic tool to evaluate competing models, which thereby provided a basis on which to evaluate competing biological models. The ability to make comparisons to observed data allowed us to use the simulation model to improve understanding of Devils Hole pupfish life history.

Specifically, simulations with parameterizations which resulted in poor fit were considered to be biologically unlikely, whereas simulations with good fit were regarded as plausible. Once we had identified a model which best resembled observed data, we altered survival rates at larval, juvenile, and adult life stages to assess effects of management alternatives.

Mixture models were used to identify cohorts of the Devils Hole pupfish population.

Results of best-fit mixture models confirm that the Devils Hole pupfish population seems to experience a pulse of new recruits from March to June. While the spring pulse in recruitment is well recognized (Gustafson and Deacon 1997; Lyons 2005), a curious finding resulting from SV dives is that the best-fit model describing the October length-frequency distribution included two mixtures. Unfortunately, it is impossible to determine whether the selection of two cohorts can be attributed to sampling error, increased spawning, or increased larval survival with only one year’s worth of data. Early life history surveys from 2007 observed an increase in larval abundance in September (though the increase could arguably be due to a run-off event). Other years (2008-2010) show a very slight or absent increase in larval abundance during early fall. Best-fit normal mixture models fit to length-frequency 83

estimates of Devils Hole pupfish from James (1969) also selected two mixtures in April,

May, and June. Interestingly, mean lengths for cohorts estimated from SV dives were

consistently about 50% greater than means from James (1969). Differences in mean lengths

may be attributed to different sampling methods; as James (1969) sampled fish from the

shallow shelf using a dip net and SV dives primarily sampled fish in the deep pool habitat.

Results of the population model provided some insight as to the mathematical nature

of Devils Hole pupfish population fluctuation. Interestingly, for each estimate of adult

survival, there was only a small range of values for larval survival which resulted in stable population growth. Surprisingly, simulation models with constant adult and larval survival rates do resemble observed length-frequency distributions as well as intra-annual abundance patterns. While this result does not directly contradict previous studies, constant survival

seems incongruent with past findings. For example, Deacon and Deacon (1979) observed a

correlation between monthly estimates of Devils Hole pupfish population size and primary

production. Similarly, Wilson and Blinn (2007) observed an 80-96% reduction in carbon

sources in Devils Hole during winter months. Both studies suggest Devils Hole pupfish

experience a decline in energy availability during winter months, which could plausibly

result in lower overwinter survival rates. However, decreases in reproductive activity and(or)

slower growth would lower energetic demands of pupfish, which would at least partially

counteract the effect of reduced energy availability. Although we are not claiming that the

constant survival model is the “true” model, we do believe that it may have some credibility.

Furthermore, the simplicity of a constant-survival model facilitates interpretation of model

output. 84

Our simulation differed from observations and predictions in previous studies.

Compared to Devils Hole pupfish biologists’ opinions about pupfish population parameters

(Barrett 2009), the current model used lower estimates of larval survival and greater

estimates of fecundity. James (1969) observed a caged population of Devils Hole pupfish

grow from an initial size of four males and two females to a final size of 36 from March to

July. While this corresponds to 15 individuals per female, our baseline simulation model

predicts 5.1 individuals per female. However, in James’ (1969) study, many larvae in the

caged population grew to lengths greater than 13 mm and could have spawned during the course of the experiment. Furthermore, larval survival rates are suspected of causing the

recent decline in the Devils Hole pupfish population (Graves 2004); as such, historic and

current larval survival rates may differ. In addition, we obtained a lower estimate of adult

survival than Chernoff (1985) who also assumed a Type II survival curve described adult

survival. Chernoff (1985) obtained a monthly adult survival rate of 91%, from which he

estimated the average age of an adult Devils Hole pupfish to be 10 months. In contrast, the

adult survival rate used in the current model (80%) predicts an average age of 4.5 months

after fish have reached 18 mm (5.8 months from the larval stage). Importantly, Chernoff

(1985) assumed that no recruitment occurs from October to January. Furthermore, one

caveat of Chernoff’s (1985) model is that adult mortality was partitioned into mortality due

to declining primary production (which exhibits a predictable seasonal pattern) and “natural

mortality.” As such, interpreting Chernoff’s (1985) estimate as an “average age” is

misleading because it does not incorporate mortality of fish due to seasonal effects. An

alternative simulation that assumes constant adult survival is 86% per month closely

resembles the observed length-probability distributions from SV dives but has poorer fit to 85

the adult abundance model and produces an average age estimate of 7.9 months, which is

more similar to Chernoff’s estimate.

Length-probability distributions from simulation models with no overwinter

recruitment more closely resembled length-probability distributions from the SV dives than

the baseline model when fish of all lengths (i.e., including fish with lengths less than 18 mm)

were incorporated into length-probability distributions. Specifically, SV dives in December,

January, and February did not detect any fish less than 17 mm in length. As such, it is not

surprising that simulation models without winter recruitment exhibited good fit to SV dives.

After accounting for differences in detection by excluding fish with lengths less than 18 mm

from length-probability distributions, the baseline model exhibited better fit. Interestingly,

intra-annual abundance patterns for simulations without winter recruitment exhibited poorer

fit compared to the baseline model. However, such results may arise due to a violation of the

assumption of the temporally-constant survival estimates. To compensate for the lack of

winter recruitment, larval survival rates had to be increased by 49% to result in stable

population growth. Accordingly, further investigation is needed to understand the role of

recruitment during winter months.

According to Scheffer et al. (1995), individual-based models are a promising method to unite modelers and empiricists because they are constructed from knowledge about the behavior of individuals, which tend to be better understood than properties of populations.

Compared to population models which attempt to identify patterns at the population-level,

individual-based models depict population dynamics as the collective effect of processes

acting upon individuals. Furthermore, individual-based models retain some degree of

randomness because they incorporate demographic stochasticity (Huston et al. 1988; 86

DeAngelis and Mooij 2005). Simulation runs from our population model exhibited high

variability in population growth rates, showing that demographic stochasticity can greatly influence growth rates in small populations. Despite incorporation of demographically stochastic processes, the current model is partly deterministic because it ignores the effects of environmental variability on population processes. Although the environment in Devils Hole is relatively stable, slight deviances in water temperature, sunlight, or dissolved oxygen concentrations on the shallow shelf may influence pupfish survival and recruitment.

Likewise, disturbance events such as earthquakes and rain events may have far-reaching effects. Positive correlation between vital rates can further increase stochasticity (Feiburg and Ellner 2001). Clearly, there are many uncertainties when using the current simulation model as a predictor of future population trends. Notwithstanding these short-comings, the simulation model can still be used for exploratory analysis to help evaluate mathematical plausibility of various biological scenarios and to compare various management alternatives.

Accordingly, we conducted elasticity analysis for 5% increases in larval, juvenile, and adult survival rates in models with monthly adult survival rates of 70%, 80%, and 86% and found that elasticity values for larval survival rates were greater than elasticity values of adult and juvenile survival rates. On a practical note, elasticity values should be put into a realistic context to attain meaningful results (Morris and Doak 2002). For instance, in this case doubling the annual adult survival rate causes intra-annual population dynamics to deviate from past patterns. However, if current adult survival rates are lower than past rates, restoring the population to past conditions may have indirect positive effects (i.e., positive feedback) on larval survival, which may increase population growth. Elasticity values for juvenile length and reproductive length were 1.02 and 0.87, respectively (Table 4.1), thus 87

showing that the baseline model was more sensitive to uncertainty in juvenile length than

reproductive length. However, altering the larval survival rate in models with 5% increases

in juvenile length did result in intra-annual patterns and length-probability distributions that

closely resembled those of the baseline model. As such, the simulation model’s structure

realistically describes observations if larval survival rates are altered to produce reasonable

population growth rates.

Biologists have identified water temperature, dissolved oxygen, sulfide and ammonia

concentrations, proportion of fine sediments on the shallow shelf, food availability,

inbreeding depression, and disease as factors potentially influencing pupfish abundance

(Wilson et al. 2009). Of these factors, those influencing the shallow shelf environment (e.g.,

water temperature, dissolved oxygen) are hypothesized to exclusively influence egg and

larval stages. Although the general trend in fishes is that early life history stages are more

sensitive to environmental stressors compared to later stages (Pollock et al. 2007), relative

sensitivities of various early life history stages (e.g., eggs, early postlarvae, late postlarvae) to

environmental stressors are species-specific (Dahlburg 1979). A rough calculation from ELS survey data indicates the greatest decline in larval abundance occurs between the prolarval and early postlarval stages (83%), followed by early postlarval to late postlarval stages

(53%), and late postlarval to prejuvenile stages (14%). Whether decreased abundances are due to high mortality rates or lower detectability is unknown.

Although the water temperature in the deep pool of Devils Hole is fairly constant, the shallow shelf environment is more thermally dynamic (Lyons 2005). Water temperature of shallow portions of the shelf can exceed 36°C (Lyons 2005), a temperature which corresponded to a precipitous decrease in egg survival in captive pupfishes (Echelle et al. 88

1972; Shrode 1975). An experimental study comparing temperature tolerance of Saratoga

Springs pupfish showed oogensis and egg survival were most affected by high temperatures compared to later life history stages (Shrode 1975; Shrode and Gerking 1997). One potential

mechanism explaining lower survivorship of eggs incubated at high temperatures is the

observation that females produce eggs with smaller yolks in high temperature environments

(Echelle et al. 1972; Shrode and Gerking 1977). If pupfish eggs are incubated under

fluctuating temperatures, however, their thermal tolerance increases (Shrode and Gerking

1977).

Similarly, dissolved oxygen concentrations greatly influence survivorship of fishes

(Moyle and Cech 2000). Whereas low dissolved oxygen levels often increase egg mortality

(Dahlberg 1979), high dissolved oxygen concentrations can counteract the effects of high temperature on egg survival. For instance, desert pupfish, C. macularis, in freshwater tanks

exhibited 100% egg mortality in treatments with dissolved oxygen levels set to70% air

saturation but not at 100% air saturation at 31°C (Kinne and Kinne 1962). The Devils Hole

pupfish likely exhibits increased tolerance to oxygen and temperature combinations, as the

average water temperature and oxygen concentrations on the Devils Hole shallow shelf are

32°C and 40% air saturation, respectively (Deacon et al. 1995). However, the Devils Hole

spawning shelf exhibits a gradient of environmental conditions, with shallow areas

experiencing more extreme temperatures and higher dissolved oxygen levels than deeper areas (Deacon et al. 1995; Lyons 2005). Interestingly, larval pupfish abundance tends to be greatest in shallow portions of the shallow shelf (Deacon et al. 1995), suggesting that egg survival or habitat selection by larvae may favor higher dissolved oxygen concentrations.

Similarly, dissolved oxygen levels are influenced by substrate characteristics as well as by 89

hydrogen sulfide and ammonia concentrations. Siltation is a source of egg mortality in many fishes (Dahlburg 1979). Accordingly, high proportions of fine sediments may decrease oxygen availability to developing pupfish eggs and larvae. Whereas small-scale rain events deposit fine sediments on the shallow shelf in Devils Hole, earthquakes and large storms scour the shelf and remove fine sediments (Lyons 2005).

Because Devils Hole pupfish fecundity is lower compared to that of other pupfishes

(Minckley and Deacon 1973; Gerking et al. 1979; Jester and Suminski 1982), it is conceivable that Devils Hole pupfish life history may have evolved to be more “K-selective” relative to other pupfishes. Populations of Atlantic molly, Poecilia mexicana, inhabiting a

light-limited and sulfide-rich environment exhibited reduced fecundity and increased larval

survival relative to populations in less stressful environments, suggesting that high egg and

larval survival rates were an adaptation to stressful conditions (Riesch et al. 2010).

Accordingly, environmental conditions decreasing larval survival may counteract years of

evolutionary forces which have selected for high egg and larval survival rates.

Whereas dissolved oxygen concentrations and temperature were hypothesized to primarily affect larval stages, suspected factors contributing to the decline of the Devils Hole pupfish such as decreased food availability, inbreeding depression, and disease are hypothesized to affect all life stages (Wilson et al. 2009). Negative effects of inbreeding depression on population growth are difficult to quantify. Not surprisingly, there is little genetic diversity in Devils Hole pupfish population due to its small population size and high inbreeding (Duvernell and Turner 1999). Yet, there are no studies assessing the relationship between genetic diversity and fitness in pupfishes. In contrast, numerous studies provide 90

evidence for energy-limitation in Devils Hole, particularly in winter months (Deacon and

Deacon 1979; Lema and Nevitt 2006; Wilson and Blinn 2007). Furthermore, there has been

an increase in primary production coupled with compositional shift in algal community

structure during the past ten years, which may affect pupfish food availability. Cannibalism

of larval fish by adult Devils Hole pupfish has been observed by James (1969) and Deacon et

al. (1995). Cannibalism of larvae in other fishes has been observed to be negatively related

to food availability (Dionne 1985; Dou et al. 2000). As such, increased cannibalism of

Devils Hole pupfish larvae due to low food availability may act as a positive feedback on

population growth.

CONCLUSION

Results of our simulation model challenge many beliefs about the Devils Hole

pupfish population; namely, the current simulation model produced lower estimates of larval survival and lower estimates of pupfish age. Furthermore, although this study provided some support that increasing larval survival rates would be most effective at increasing population

growth, it raises some interesting questions that may be addressed with future studies.

Attaining estimates of monthly adult abundance would greatly facilitate comparisons of

historic and current conditions in Devils Hole. Because adult abundance surveys represent

the most detailed and extensive historic records of biological conditions in Devils Hole,

current monthly abundance estimates may help biologists identify changes in population

dynamics which may provide insight as to causes of the recent population decline. Likewise,

there is some preliminary evidence that Devils Hole pupfish growth may differ from past

growth patterns. If the Devils Hole pupfish population reaches an appropriate size to allow 91

biologists to use wild fish for empirical studies, duplicating James (1969) caged experiment

may provide useful information about current growth patterns. Experiments assessing

detectability as a function of fish length, perhaps conducted with the captive population of

hybridized Devils Hole pupfish and Ash Meadows pupfish, C. diabolis × C. nevadensis

mionectes, would further improve future studies. However, the best method to assess

population dynamics would be to attain individual capture histories. Future enhancements in

DNA and photo-recognition technologies may hold promise as non-obtrusive sampling

methods which can be used to attain individual capture histories.

We believe the limitations imposed by non-obtrusive sampling make our simulation

model a particularly useful tool for modeling the Devils Hole pupfish population.

Specifically, the simulation approach allows incorporation of data from a wide variety of

sources (e.g., ELS surveys, past Devils Hole pupfish studies, studies of other pupfishes). In addition, our simulation model allows comparison between biological opinions and observed

data. To enable our model to address future questions of interest to Devils Hole pupfish

biologists, we have built flexibility into the model‘s framework by allowing specification of

monthly survival and fecundity estimates as data become available. As such, we hope our simulation model will continue to aid biologists’ pursuit of identifying causes of population decline of the Devils Hole pupfish.

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Table 4.1. Summary of parameterizations used in simulation models describing population dynamics of Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, Nye County, NV. Specifically, annual survival probabilities for adult, juvenile, and larval pupfish were increased by 5% to determine the effect of survival probabilities on the finite population growth rate (λ). Likewise, reproductive length and juvenile length were increased by 5% in the baseline model to evaluate the response of λ to uncertainty in these parameter estimates. One additional simulation which includes decreased estimates of the number of larvae per female and increased estimates of larval survival probabilities was run to determine response of λ to uncertainty in fecundity estimates. Importantly, because survival of juveniles and adults was modeled as a Type 2 survival curve, 5% annual increases in adult and juvenile survival rates corresponds to a 0.4% (or 1.051/12) increase in monthly survival probabilities.

Monthly Monthly Monthly Reproductive Juvenile Average Extinction adult juvenile larval Elasticity length length λ probability survival survival survival Monthly adult survival rate of 80% Baseline model 0.800 0.800 0.047 13.00 12.00 1.041 0.015 NA 101 5% increase in annual larval survival 0.800 0.800 0.049 13.00 12.00 1.172 0.003 1.073 5% increase in annual juvenile survival 0.800 0.803 0.047 13.00 12.00 1.061 0.010 0.971 5% increase in annual adult survival 0.803 0.800 0.047 13.00 12.00 1.065 0.017 0.975 5% increase in reproductive length 0.800 0.800 0.047 13.65 12.00 0.941 0.075 0.861 5% increase in juvenile length 0.800 0.800 0.047 13.00 12.60 1.115 0.004 1.021 75% decrease in larvae per female & 0.800 0.800 0.192 13.00 12.00 1.033 0.022 NA 400% increase in larval survival

Table 1. Continued (see page 101 for description).

Monthly Monthly Monthly Reproductive Juvenile Average Extinction adult juvenile larval Elasticity length length λ probability survival survival survival Monthly adult survival rate of 70% Reference model 0.700 0.700 0.076 13.00 12.00 1.013 0.062 NA 5% increase in annual larval survival 0.700 0.700 0.080 13.00 12.00 1.210 0.005 1.137 5% increase in annual juvenile survival 0.700 0.702 0.076 13.00 12.00 1.055 0.022 0.992 5% increase in annual adult survival 0.702 0.700 0.076 13.00 12.00 1.034 0.029 0.972 Monthly adult survival rate of 86% Reference model 0.860 0.860 0.034 13.00 12.00 1.049 0.021 NA 5% increase in annual larval survival 0.860 0.860 0.036 13.00 12.00 1.172 0.003 1.064 5% increase in annual juvenile survival 0.860 0.864 0.034 13.00 12.00 1.075 0.007 0.976 102 5% increase in annual adult survival 0.864 0.860 0.034 13.00 12.00 1.033 0.020 0.938

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Table 2. Summary of mixture model parameters describing monthly length-frequency of the Devils Hole pupfish population, Cyprinodon diabolis, Devils Hole, Nye County, NV. For each month, mixture models with normal and lognormal distributions were compared and the top model was selected using the Bayesian Information Criterion (BIC). Sums of BIC values from mixture models fit to lognormal distributions were lower than the sum of BIC values fit to a normal distribution (∆BIC = -6.1).

Means (mm) Variance (mm2) Proportion Month Lognormal Normal LognormalNormal Lognormal Normal Mar 27.2 27.5 20.2 19.3 1.00 1.00 Apr 10.9 11.2 3.7 6.3 0.20 0.20 30.6 31.0 29.1 24.1 0.80 0.80 May 15.5 14.6 32.7 21.4 0.32 0.26 29.2 29.1 19.1 21.4 0.68 0.74 Jun 21.0 18.4 44.3 16.8 1.00 0.70 NA 30.7 NA 16.8 NA 0.30 Jul 21.4 21.9 23.2 23.1 1.00 1.00 Aug 22.2 22.6 19.2 19.1 1.00 1.00 Sep 22.0 22.7 31.2 29.2 1.00 1.00 Oct 13.3 13.3 0.7 0.5 0.15 0.13 22.8 22.9 15.9 18.4 0.85 0.87 Nov 19.9 23.7 22.2 29.8 0.57 1.00 27.8 NA 7.9 NA 0.43 NA Dec 24.2 24.4 12.9 13.3 1.00 1.00 Jan 25.5 25.7 13.4 13.7 1.00 1.00 Feb 25.9 26.1 11.1 11.5 1.00 1.00

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Figure 4.1. Mixture models fit to monthly length-probability distributions of the Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, Nye County, NV. Observed length-probability distributions from stereovideo dives (solid line) are plotted against best-fit normal mixture models (dotted line) for March-February.

March April May 0.12 n = 108 n = 88 n = 75 0.10 0.08 0.06 0.04 0.02 0.00 ------June July August 0.12 n = 114 n = 115 n = 127 0.10 0.08 0.06 0.04 0.02 0.00 ------September October November 0.12 n = 88 n = 94 n = 88

Probability 0.10 0.08 0.06 0.04 0.02 0.00 ------December January February 0.12 n = 73 n = 50 n = 94 0.10 0.08 0.06 0.04 0.02 0.00

10 20 30 40 10 20 30 40 10 20 30 40

Length(mm) 105

Figure 4.2. Von Bertalanffy growth models describing individual growth of Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, Nye County, NV. The fast-slow simulation model uses two growth curves to describe pupfish growth; individuals born in spring following a fast trajectory and individuals born during other times of year following a slow trajectory. In contrast, the mode model estimated growth from observed length-frequency distributions from stereovideo dives and early life stage surveys of Devils Hole pupfish.

20 Length (mm) Length

Fast/slow model (1-Mar hatch date) Fast/slow model (1-Sep hatch date) 0 Mode model

0 50 100 150 200 250 300 350

Age (days) 106

Figure 4.3. Seasonal abundance of Devils Hole pupfish larvae, Cyprinodon diabolis, Devils Hole, Nye County, NV. Points on the figure represent the sum of 3-5 mm larvae observed on twenty-seven 30 cm × 14 cm plots on the Devils Hole spawning shelf. The line on the figure is the best-fit generalized linear model with a Poisson response. The best-fit model includes a fifth degree polynomial equation with time as the predictor variable.

10 Number of prolarvae of Number

0 || | | | | 15-Jan 15-Mar 15-May 15-Jul 15-Sep 15-Nov

Month 107

Figure 4.4. Monthly estimates of the number of larvae per reproductive female for the Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, Nye County, NV. Numbers of larvae per female were estimated by dividing larval abundance estimates by predicted adult abundance estimates. Note that numbers of larvae per female were corrected to account for unequal sampling intervals.

15 Larvae per female per Larvae

| ||||| Feb Apr Jun Aug Oct Dec

Month

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Figure 4.5. Simulated and observed length-frequency distributions of the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). The simulation model used a monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 4.7%, and the fast-slow model to describe pupfish growth.

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Figure 4.6. Simulated and observed length-frequency distributions of the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). To facilitate comparison between stereovideo dives and the simulation model output, length probability distributions only include fish with lengths greater than 18mm. The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 4.7%, and the fast-slow model to describe pupfish growth.

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Figure 4.7. Simulated and observed length-frequency distributions of the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). To facilitate comparison between stereovideo dives and the simulation model output, length probability distributions only include fish with lengths greater than 18mm. The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 4.7%, and the mode model to describe pupfish growth.

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Figure 4.8. Intra-annual abundance patterns of Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, in Nye County, NV. Simulation models were run with three different monthly adult and juvenile survival probabilities: 70% (top), 80% (middle), and 86% (bottom). Larval survival rates were 7.6% (top), 4.7% (middle), and 3.4% (bottom). All abundance values were scaled by dividing by maximum observed annual abundance. Lines represent scaled monthly abundance estimates of Devils Hole pupfish predicted by the adult abundance model. Points represent scaled abundance (for fish greater than 18 mm total length) of from five random iterations of simulation models with different adult survival probabilities.

1.0

0.8

0.6

0.4

0.2  = 1.00 S(a,j) = 0.70; S(l) = 0.076 0.0

1.0

0.8

0.6

0.4

0.2  = 1.04 S(a,j) = 0.80; S(l) = 0.047 0.0

1.0

0.8

0.6

Relative pupfish abundance scaled to yearly maximum yearly scaledRelative abundance to pupfish 0.4

0.2  = 1.04 S(a,j) = 0.86; S(l) = 0.034 0.0 ------Mar May Jul Sep Nov Jan Month

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Figure 4.9. Summary of simulated population trends of the Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, in Nye County, NV. Median (dark line) and 2.5% and 97.5% quantiles (dotted lines) of population abundance trajectories of 2,000 iterations of the baseline simulation model. The baseline simulation model included constant monthly adult and juvenile survival rates of 80% and a larval survival rate of 4.7%.

400

300

200

100

0 ||||||||||

400

300

200 Pupfish abundance (individuals > 18mm TL) (individuals18mm abundance Pupfish > 100

12345678910

Year

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Figure 4.10. Mean discrete population growth rates (λ) for simulation model parameters describing population dynamics of Devils Hole pupfish, Cyprinodon diabolis, Devils Hole, in Nye County, NV. Summary of population growth rates from simulation models with 5% increases in annual larval, juvenile, and adult survival probabilities. Due to uncertainty in the current adult survival rate, we estimated finite annual population growth rates from simulation models with monthly adult survival rates of 70%, 80%, and 86%. Error bars represent 2.5% and 97.5% quantiles of population growth rates from 2,000 iterations.

Reference 5% increase in larval survival 5% increase in juvenile survival 5% increase in adult survival Lambda 0.60.81.01.21.4 |||

Sa  0.70 Sa  0.80 Sa  0.86 Sj  0.70 Sj  0.80 Sj  0.86 Sl  0.076 Sl  0.047 Sl  0.034 Reference model parameterization

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Figure 4.11. Intra-annual abundance patterns of a simulation model with zero over-winter survival of larvae and juvenile Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Monthly adult and juvenile survival rates were set to 80% and larval survival was set to 7.0%. All abundance values were scaled by dividing by maximum observed annual abundance. Lines represent scaled monthly abundance estimates of Devils Hole pupfish predicted by the adult abundance model. Points represent scaled abundance (for fish greater than 18 mm total length) of from five random iterations of simulation models with different adult survival probabilities.

1.0

0.8

0.6

0.4

0.2

Relative pupfish abundance scaled to yearly maximum yearly scaled to abundance Relative pupfish 0.0 ------Mar May Jul Sep Nov Jan

Month

115

Figure 4.12. Simulated and observed length-frequency distributions of the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 7.0%, and the fast-slow model to describe pupfish growth. Furthermore, survival probabilities of juvenile and larval fish were set to 0 from November to January.

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Figure 4.13. Simulated and observed length-frequency distributions of the Devils Hole pupfish, Cyprinodon diabolis, in Nye County, NV. Length-probability distributions from stereovideo dives (dark line) compared to length-probability distributions from 100 randomly-chosen iterations of a simulation model (light lines). To facilitate comparison between stereovideo dives and the simulation model output, length probability distributions only include fish with lengths greater than 18mm. The simulation model used monthly adult and juvenile survival probabilities of 80%, a larval survival rate of 7.0%, and the fast-slow model to describe pupfish growth. Furthermore, survival probabilities of juvenile and larval fish were set to 0 from November to January.

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CHAPTER 5. GENERAL CONCLUSIONS

Importantly, all three chapters are motivated by the belief that monitoring efforts need to be routinely evaluated for their ability to detect biologically meaningful changes in ecological processes. Evaluation of Devils Hole pupfish monitoring efforts is especially crucial because management agencies must limit the frequency and duration of sampling occasions to reduce disturbance to Devils Hole. As such, ensuring that survey methods are efficient is an important goal.

Although monitoring of adult Devils Hole pupfish was initiated in 1972, we present results from the first formal attempt to identify factors influencing accuracy and precision of

SCUBA dive surveys for adult Devils Hole pupfish (Chapter 2). Results showed that there was no measurable difference between individual SCUBA divers’ estimates of Devils Hole pupfish abundance. Furthermore, this study provided preliminary evidence that pupfish avoid SCUBA divers because SCUBA dives that hindered pupfish movement (i.e., dives with a block net placed in between the shallow shelf and the deep pool) resulted in greater abundance estimates than surveys conducted without a block net. Consequently, past adult surveys (which did not use a block net) may be less accurate than surveys with a block net.

Future dive surveys will continue to evaluate use of the block net as alternate survey method for adult Devils Hole pupfish.

We also assessed statistical power of larval Devils Hole pupfish monitoring using a method that combined variance components estimation with power analyses (Chapter 3).

Specifically, combining these analyses allowed assessment of sampling effort in a hierarchically nested sampling design. Increasing the number of plots per event (i.e.,

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increasing the number of sub-subsamples per subsample) was an efficient way to increase statistical power. This study identified a new survey design that requires less time and results in greater power than the previous designs. Furthermore, results indicated that the new and previous survey designs resulted in >80% power to detect 50% increases and decreases in larval abundance.

Lastly, we used simulation modeling to describe population dynamics of the Devils

Hole pupfish and evaluate a suite of management alternatives and biological assumptions

(Chapter 4). Our simulation model with constant larval, juvenile, and adult survival rates produced realistic length-frequency and abundance estimates. We provided preliminary evidence that larval survival and average adult lifespan may be over-estimated by previous models. Furthermore, population growth in our simulation model was most affected by increasing larval survival, suggesting that management agencies should focus recovery efforts on larval fish survival. Suspected sources of mortality to larval Devils Hole pupfish include low dissolved oxygen concentrations and high water temperatures.

We hope that improved survey methods will help assess future hypotheses concerning the timing and magnitude of Devils Hole pupfish population processes, as well as their relationships to environmental variables. For example, increasing statistical power of larval surveys may enable future researchers to study the effects of earthquakes and run-off events on the larval Devils Hole pupfish population. Likewise, stereovideo methods may be coupled with adult survey dives to help identify vulnerable months and life stages affecting

Devils Hole pupfish population growth. It is our belief that the results presented in this thesis will ultimately benefit the long-term management of the Devils Hole pupfish.