Statistical Ecology PDF
Preview Statistical Ecology
baut ECOSTAT The software ECOSTAT was developed to perform computations for the statistical methods not readily available in standard statistical packages. It may be downloaded free from the University of Nebraska website (http://vvww.ianr.unl,edu/ianr/biometry/ faculty/linda/lyoung.html). The zip file should be placed in a temporary folder. Then the individual files should be extracted (unzipped) from this zip file. The temporary folder(s) used for the zip file and the extracted files should NOT be ca lied ECOSTAT. Once the files have been extracted, ECOSTAT must be installed on the machine before it can be run. To do so, run SETUP.EXE. The downloaded zip file and the files that were extracted from the zip file may then be deleted from the temporary folder(s). ECOSTAT was developed for IBM-compatibles and a Windows95 environ ment. At least 16 megabytes of RAM are needed to run the full program, although some portions require less memory. The program is written in Microsoft's Visual Basic. ECOSTAT has seven parts. Probability Distributions has the set of programs that complement the first three chapters of the book. Sequential Sampling contains the programs for both the fixed and sequential methods in Chapters 4-6. Spatial Statistics is the portion relating to Chapters 7 and 8. Capture-Recapture is the program correspond ing to Chapters 9 and 10. Transect Sampling may be used for the material covered in Chapter 11. The temperature data of Chapter 12 can be analyzed using Temperature Models. The portion. of the program relating to Chapter 13 is in Life Stage. An eighth program, DISCRETE (Gates 1989), has been induded with ECOSTAT for use in Chapter 2. ECOSTAT is able to help the user identify some problems in running the program. However, at the present time, it is not designed to detect errors in the input file. These indude the errors that arise because the wrong format was used for the data. Care should be taken at this point. Should you encounter an error, please contact us at the following e-mail address: [email protected] Linda J. Young Biometry Department University of Nebraska-Lincoln Jerry H. Young Entomology Department (Emeritus) Oklahoma State University .... " Springer Science+Business Media, LLC tt E1ectronic Services < http://www.wkap.nl > Library of Congress Cataloging-in-Publication Young. Linda J. Statistical ecology : a population perspective / Linda J. Yo ung. J erry H. Yo ung p. cm. Includes bibliographical references and index. ISBN 978-1-4757-2831-6 ISBN 978-1-4757-2829-3 (eBook) DOI 10.1007/978-1-4757-2829-3 1. Ecology--Statistical methods. 2. Population biology--Statistical methods I. Young. Jerry H. 11. Tide. QH541.l5.S72Y68 1998 577' .01 '5195--dc21 97-25603 CIP British Library Cataloguing in Publication Data available Copyright c 1998 by Springer Science+Business Media New York. Third Printing 2002. Originally published by Kluwer Academic Publishers in 1998. Softcover reprint of the hardcover 1s t edition 1998 Cover design: Curtis Tow Graphics This printing is a digital duplication of the original edition. All rights reserved. No part of this publication may be reproduced. stored in a retrieval system or transmitted in any form or by any means. mechanical. photo-copying. recording. or otherwise. without the prior written permission of the publisher. Springer Science+ Business Media, LLC Printed on acid-free paper. To lohn, Shamar, and RaQwin Table of Contents Preface xiii Acknowledgments xv Chapter 1: Probability Distributions Introduetion 1 Diserete Distributions 2 Negative Binomial Distribution 7 Expected Frequencies 8 Geometrie Distribution 13 Expected Frequencies 14 Binomial Distribution 17 Expected Frequencies 18 Poisson Distribution 22 Expected Frequencies 23 Confidenee Intervals 24 Continuous Distributions 26 Normal Distribution 27 Lognormal Distribution 33 Exponential Distribution 34 Gamma Distribution 35 Weibull Distribution 37 Summary 38 Exereises 39 Chapter 2: Goodness-of-Fit Tests 42 Introduetion 42 Pearson's Chi-Squared Test 44 vii viii / Statistical Ecology Likelihood Ratio Test 50 Freeman-Tukey Chi-Squared Test 52 Power Divergence Statistic 54 Nass Test 55 Kolmogrov-Smimov Test 58 Summary 65 Exercises 66 Appendix 70 Chapter 3: Models and Sampling 75 Introduction 75 Binomial Models 75 Poisson Models 76 Negative Binomial Models 76 Bose-Einstein Versus Maxwell-Boltzmann Statistics 78 Stochastic Immigration Model 82 Modeling Within Field Movement 84 Restrietions on Carrying Capacity 85 Sampling Concepts 87 Simple Random Sampling 92 Stratified Random Sampling 93 Systematic Sampling 96 Ratio Estimation 97 Summary 97 Chapter 4: Sequential Estimation 99 Introduction 99 Sampie Sizes Required to Control CV(X) 100 Sampie Sizes Required to Set Confidence Intervals 105 Length Proportional to the Parameter o/Interest 106 Length Fixed 108 Sequential Estimation 110 Sequential Estimation for the Negative Binomial 112 Parameter k Unknown 112 Estimating Parameter k 114 Parameter k Known 123 Sequential Estimation for the Geometrie 129 Sequential Estimation for the Poisson 131 Sequential Estimation for the Binomial 133 Sequential Estimation Based on Iwao's Patchiness Regression 136 Sequential Sampling Based on Taylor's Power Law 144 Summary 148 Exercises 149 Table of Contents / ix Chapter 5: Sequential Hypothesis Testing 153 Introduction 153 Wald's Sequential Probability Ratio Test 153 SPRT for the Negative Binomial Distribution 159 SPRT for the Poisson Distribution 162 SPRT for the Binomial Distribution 165 Operating Characteristic and Average SampIe Number Functions 167 The 2-SPRT 173 Summary 186 Exercises 188 Chapter 6: Sequentially Testing Three Hypotheses 191 Introduction 191 Ecologists' Sequential Test 192 Sobel and Wald's Method 199 Armitage's Method 204 Testing Composite Hypotheses 209 Iwao's Method 209 Armitage's Methods 212 Summary 213 Exercises 213 Chapter 7: Aggregation and Spatial Correlation 215 Introduction 215 Measures of Aggregation 216 Variance-to-Mean Ratio and Index of Dispersion 217 Index of Clumping 217 Mean Crowding and Mean Patchiness 218 Comparison of Indices 219 Spatial Correlation 222 Moran's land Geary's c 224 Geostatistics 231 Intrinsic Stationarity 243 Median Polishing 244 The Semivariogram 250 Summary 268 Exercises 269 Chapter 8: Spatial Point Patterns 272 Introduction 272 Complete Spatial Randomness 273 K(h) amd L(h) Functions 276 Monte Carlo Tests 284 x / Statistical Ecology Nearest Neighbor Techniques 288 Summary 292 Exercises 293 Appendix 295 Chapter 9: Capture-Recapture: Closed Populations 297 Introduction 297 Lincoln-Petersen Model 298 Confidence Intervals 300 Sampie Size Considerations 303 Assumptions 305 Multiple Recapture Models 310 Model Mo: Constant Capture Probabilities 314 Model M,: Capture Probabilities Val}' With Time 315 Tests for the Model 317 Model Mb: Behavioral Response to Capture 318 Tests for the Model 320 Model M Heterogeneity of Capture Probabilities 322 h: Tests for the Model 324 Model Mbh: Heterogeneity of Capture Probabilities and Trap Response 325 Tests for the Model 326 Models Mb,' Mh,. Mbh, 327 Model Selection 330 Confidence Intervals 331 Removal and Catch Effort Models 335 Change-in-Ratio or Selective Removal Models 338 Density Estimation 347 Summary 347 Exercises 348 Chapter 10: Capture-Recapture: Open Populations 357 Introduction 357 Jolly-Seber Model 358 Adult Band and Tag Recovery Models 375 Summary 383 Exercises 384 Chapter 11: Transect Sampling 390 Introduction 390 Strip Transects and Circular Plots 391 Line and Point Transects 397 Ungrouped Data 407
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