Table of Contents...........................................................................1 List of Figures................................................................................................ 3 List of Tables ................................................................................................. 4 C h a p t e r 1 ................................................................................................ 6 I n t r o d u c t i o n........................................................................................................ 6 1.1 Motivation............................................................................................................. 7 1.2 Aim of the study.................................................................................................... 7 1.3 Objectives ............................................................................................................. 8 1.4 Project layout ........................................................................................................ 8 C h a p t e r 2 ................................................................................................ 9 L i t e r a t u r e R e v i e w .......................................................................................... 9 2.1 Definitions............................................................................................................. 9 2.2 Estimating animal abundance ............................................................................. 10 2.1.1 Line transect sampling ................................................................................. 10 2.1.2 Mark-recapture methods .............................................................................. 17 2.1.3 Brief review of State Space Models of population abundance.................... 21 2.3 Resampling ......................................................................................................... 22 2.3.1 Randomisation exact testing ........................................................................ 23 2.3.2 Cross validation ........................................................................................... 24 2.3.3 Jackknife ...................................................................................................... 26 2.3.4 The bootstrap method .................................................................................. 28 C h a p t e r 3 .............................................................................................. 51 M e t h o d o l o g y ...................................................................................................... 51 3.1 Source and nature of the data.............................................................................. 51 3.2 Proposed model................................................................................................... 51 3.2.1 Algorithm 3.1............................................................................................... 54 3.3 Bootstrap application .......................................................................................... 56 3.4 Confidence intervals ........................................................................................... 60 3.4.1 Standard confidence interval: ...................................................................... 60 3.4.2 Percentile confidence intervals: ................................................................... 61 3.5 Monte Carlo simulation ...................................................................................... 61 3.6 Jackknife application .......................................................................................... 62 3. 7 Software and package ........................................................................................ 63 C h a p t e r 4 .............................................................................................. 64 W h i t e R h i n o R e s u l t s ................................................................................... 64 4.1 Calculation of net losses ..................................................................................... 64 4.2 Model fitting algorithm 3.1................................................................................. 64 4.3 Bootstrapping...................................................................................................... 67 4.3.1 200 Replications........................................................................................... 67 4.3.2 1000 Replications......................................................................................... 71 4.4 Comparison of bootstrap estimates and the full sample estimates of the true.... 74 population sizes......................................................................................................... 74 4.5 Monte Carlo simulations..................................................................................... 75 4.5.1 Estimated coverage probability.................................................................... 76 1 4.5.2 Average length of confidence interval......................................................... 77 4.6 Jackknife ............................................................................................................. 79 4.6.1 Results obtained on removing each time point............................................ 80 4.6.2 Jackknife standard error for the sample estimates ....................................... 84 4.7 Comparison of the bootstrap and jackknife ........................................................ 85 4.7.1 Comparison of the bootstrap and jackknife estimates ................................. 85 4.7.2 Comparison of the bootstrap and jackknife standard errors ........................ 86 C h a p t e r 5 .............................................................................................. 88 B l a c k R h i no R e s u l t s..................................................................................... 88 5.1 Calculation of Net Losses ................................................................................... 88 5.2 Model fitting algorithm 3.1................................................................................. 88 5.3 Bootstrapping...................................................................................................... 90 5.3.1 200 Replications........................................................................................... 90 5.3.2 1000 Replications......................................................................................... 93 5.4 Comparison of bootstrap estimates and the full sample model of the true......... 96 population sizes.................................................................................................. 96 5.5 Monte Carlo Simulations .................................................................................... 98 5.5.1 Estimated coverage probability.................................................................... 98 5.5.2 Average length of confidence interval......................................................... 99 5.6 Jackknife ........................................................................................................... 101 5.6.1 Results obtained on removing each time point.......................................... 101 5.6.2 Jackknife standard error for the sample estimates ..................................... 105 5.7 Comparison of the bootstrap and jackknife ...................................................... 106 5.7.1 Comparison of the bootstrap and jackknife estimates ............................... 106 5.7.2 Comparison of the bootstrap and jackknife standard errors ...................... 107 C h a p t e r 6 ............................................................................................ 108 S u m m a r y a n d R e c o m m e n d a t i o n s.................................................. 108 6.1 White Rhino...................................................................................................... 108 6.2 Black Rhino ...................................................................................................... 109 6.3 Discussion......................................................................................................... 109 A p p e n d i c e s........................................................................................ 120 Appendix A: Datasets used..................................................................................... 120 Appendix B: Matlab program for fitting the model................................................ 121 Appendix C: Matlab program for bootstrap application......................................... 122 Appendix D: Matlab program for percentile confidence intervals ......................... 123 Appendix E: Matlab program for Monte Carlo simulation .................................... 124 Appendix E: Matlab program for the jackknife...................................................... 127 References.................................................................................................. 111 2 List of Figures Figure 2.1: Example of line transect sampling and measurement .................................... 13 Figure 4.1: Plot of the estimated true population sizes and the survey estimates at each of the eight surveys ....................................................................................................... 66 Figure 4.2: Plot of the bootstrap