Statistical methods for assessing and managing wild populations Simon David Hoyle, BSc, MSc (Hons.) A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School of Mathematical Sciences Faculty of Science Queensland University of Technology December 2005 Key Words Anguilla reinhardtii, fishery management, population modelling, bootstrap, recreational catch, confidence intervals, Scomberomorus commerson, genetic mark-recapture, shadow effect, individual-based modelling, protected species, Bayesian, integrated analysis, management strategy evaluation, fisheries, Queensland, Stenella attenuata. Abstract This thesis is presented as a collection of five papers and one report, each of which has been either published after peer review or submitted for publication. It covers a broad range of applied statistical methods, from deterministic modelling to integrated Bayesian modelling using MCMC, via bootstrapping and stochastic simulation. It also covers a broad range of subjects, from analysis of recreational fishing diaries, to genetic mark recapture for wombats. However, it focuses on practical applications of statistics to the management of wild populations. The first chapter (Hoyle and Jellyman 2002, published in Marine and Freshwater Research) applies a simple deterministic yield per recruit model to a fishery management problem: possible overexploitation of the New Zealand longfin eel. The chapter has significant implications for longfin eel fishery management. The second chapter (Hoyle and Cameron 2003, published in Fisheries Management and Ecology) focuses on uncertainty in the classical paradigm, by investigating the best way to estimate bootstrap confidence limits on recreational harvest and catch rate using catch diary data. The third chapter (Hoyle et al., in press with Molecular Ecology Notes) takes a different path by looking at genetic mark-recapture in a fisheries management context. Genetic mark-recapture was developed for wildlife abundance estimation but has not previously been applied to fish harvest rate estimation. The fourth chapter (Hoyle and Banks, submitted) addresses genetic mark-recapture, but in the wildlife context for estimates of abundance rather than harvest rate. Our approach uses individual-based modeling and Bayesian analysis to investigate the effect of shadows on abundance estimates and confidence intervals, and to provide guidelines for developing sets of loci for populations of different sizes and levels of relatedness. ii The fifth chapter (Hoyle and Maunder 2004, Animal Biodiversity and Conservation) applies integrated analysis techniques developed in fisheries to the modeling of protected species population dynamics – specifically the north-eastern spotted dolphin, Stenella attenuata. It combines data from a number of different sources in a single statistical model, and estimates parameters using both maximum likelihood and Bayesian MCMC. The sixth chapter (Hoyle 2002, peer reviewed and published as Queensland Department of Primary Industries Information Series) results directly from a pressing management issue: developing new management procedures for the Queensland east coast Spanish mackerel fishery. It uses an existing stock assessment as a starting point for an integrated Bayesian management strategy evaluation. Possibilities for further research have been identified within the subject areas of each chapter, both within the chapters and in the final discussion chapter. iii Contents Key words.....................................................................................................................................ii Abstract.........................................................................................................................................ii Contents .......................................................................................................................................iv List of figures................................................................................................................................v List of tables................................................................................................................................vii List of publications and manuscripts ...........................................................................................xi Statement of original authorship.................................................................................................xii Dedication and acknowledgements............................................................................................xiii Chapter 1: Introduction.................................................................................................................1 Chapter 2. Longfin eels need reserves: modeling the effects of commercial harvest on stocks of New Zealand eels........................................................................................................................10 Chapter 3. Confidence Intervals on Catch Estimates From a Recreational Fishing Survey: a Comparison of Bootstrap Methods .............................................................................................35 Chapter 4 LocusEater and ShadowBoxer: programs to optimise experimental design and multiplexing strategies for genetic mark-recapture.....................................................................62 Chapter 5. Better estimates of animal abundance from DNA profiling: overcoming underestimates caused by individuals with the same genotype ..................................................70 Chapter 6. A Bayesian integrated population dynamics model to analyze data for protected species.........................................................................................................................................89 Chapter 7. Management Strategy Evaluation for the Queensland East Coast Spanish Mackerel ..................................................................................................................................................124 Chapter 8. Discussion and Further Research ............................................................................184 iv List of Figures Chapter 2 Figure 1: Female shortfin eels at equilibrium: Relative spawning per recruit and yield per recruit at a range of exploitation rates and minimum legal weights. a) Relative spawning per recruit. The decline in relative spawning per recruit of female shortfins with increasing fishing pressure is moderated by the current minimum legal weight of 220 g. b) Relative yield-per-recruit increases with exploitation rate for all minimum legal weights. Minimum legal weight has a relatively small effect on yield-per-recruit except at high fishing pressures. c) Relative yield- per-recruit at a range of minimum legal weights and exploitation rates. ...................................32 Figure 2: Female longfin eels at equilibrium: Relative spawning per recruit and yield per recruit at a range of minimum legal weights and exploitation rates for female longfin eels. a) Relative spawning per recruit. b) Relative yield-per-recruit. Maxima for each exploitation rate are marked with drop-down lines. ..................................................................................................33 Figure 3: Female longfin eels at equilibrium: relative spawning per recruit and yield per recruit by exploitation rate and maximum legal weight: a) Relative spawning per recruit . Maximum legal weight does little to increase relative spawning per recruit until it is 2 kilogram or less. b) Relative yield-per-recruit. All curves tend towards 1: the yield-per-recruit without a maximum legal weight for the indicated exploitation rate...........................................................................34 Chapter 3 Figure 1: Flow diagram showing the structure of the bootstrap simulation process. .................60 Figure 2: Coverage of the upper and lower confidence limits of catch rate and total catch for a range of resample sizes, using the bootstrap-t method. The ideal level is marked with a dotted line. ............................................................................................................................................61 Chapter 5 Figure 1. Average of the ratio of number of genotypes (G) to population size (N) at a range of population sizes, and for two combinations of average family size (F) and cluster size (C). The sampling distribution of family size is described in the text. .....................................................86 v Chapter 6 Figure 1: Diagrammatic representation of the two dimensions on which individuals flow through the model: through color phases (I = Neonate, II = Two-tone, III = Speckled, IV = Mottled, and V = Fused) and through age classes (0 to A, with sexual maturity at age 11). Rt is recruitment at time t, zt,a is total mortality [1-z = (1-M)*(1- u)], ψs,a is stage transition probability, and tr is the proportion of recruitment to the Two-tone stage. ......................................................................97 Figure 2: Observed and estimated proportions of dolphins captured by color phase (Neonate-I, Two-Tone-II, Speckled-III, Mottled-IV, and Fused-V) for five of the years for which data were available. Sample sizes for each year are given in the text. .....................................................121 Figure 3: Observed and estimated proportions of dolphins captured at age from 1973 to 1978. Data are pooled across color phase. Sample