Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2001 Modern applied statistics and animal populations in geographically complex landscapes: data visualization and modeling Márcia Maria Almeida de Macedo Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Biostatistics Commons, and the Ecology and Evolutionary Biology Commons Recommended Citation Almeida de Macedo, Márcia Maria, "Modern applied statistics and animal populations in geographically complex landscapes: data visualization and modeling " (2001). Retrospective Theses and Dissertations. 909. https://lib.dr.iastate.edu/rtd/909 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. 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UMl" Modem applied statistics and animal populations in geographically complex landscapes: data visualization and modeling by M.ircia Maria Almeida tie Macedo A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY ( 'o-majors: Statistics: Ecology and Evolutionary Biology Major Professors: Dianne Cook and Brent Danielsou Iowa State University Ames. Iowa •2001 Copyright 0 Mârcia Maria Almeida tie Macedo. 2001. All rights reserved. UMl Number: 3003222 Copyright 2001 by Almeida de Macedo, Marcia Maria All rights reserved. UMl UMl Microform 3003222 Copyright 2001 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Il Graduate College Iowa State University This is to certify that the Doctoral dissertation of Marcia Maria Almeida de Macedo has met the dissertation requirements of [owa State University Signature was redacted for privacy. ( omlllittee Moillbe Signature was redacted for privacy. Committe^fember Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. For the Major Program Signature was redacted for privacy. iii I'o my mother. D. Severina Almeida de Macedo. IV TABLE OF CONTENTS LIST OF TABLES xi LIST OF FIGURES xxvii 1 OVERVIEW I 2 USING EDA TO UNCOVER POPULATIONAL CHARACTERISTICS OF THREE SPECIES OF SMALL MAMMALS IN A GEOGRAPHICALLY COMPLEX EN­ VIRONMENT I lut roiliict ion I Savannah Hiver Site Landscape Description 7 Data Collection at the SRS 1) Considerations About Data Collection 10 Descriptives of the Small Mammals Data Set llj Empirical Distributions 19 Data Descriptives by Age ( 'hiss "Jit Age Classes' Extreme Values 2ti Envelopes of Observed Extreme Values '27 Variables Affecting Species Densities ii'2 Species' Density and Age of Patch :!'2 Effect of Area Size on Species' Density liô Species Interactions XT Visualization of Spatial Dependence -Mi V Variograni Analysis 50 Data Transformation to Stabilize Variances .10 Decomposing Large-Scale Variation of the Data 51 Interpretation of Large-Scale Variation of Transformed Data (il Discussion (i;S Summary (il 3 MODELING POPULATIONS OF TWO COMPETING SPECIES OF SMALL MAMMALS IN A GEOGRAPHICALLY COMPLEX LANDSCAPE (kx Introduction (»{S The Model 71 Migration 7X Model Simulation 7(i Initial Conditions 7(i Parameters of the Model ts:{ Model Assessment ,S8 Assessment of Migration Procedure <)I Ktfect of Distance among Patches in Number of Immigrants 1)2 F.lfect of Landscape ( imposition on Migration Procedure 1)2 Hias of Migration Procedure 1)1 Comparison between Models DII and DDI 1)7 Differences Between Simulation Results According to Models DII and DDI 1)7 I!fFeet of Patch Age on Simulation Results 100 Spatial Dependence in Results of Models DII and DDI 102 Effect of Competition on Spatial Distributions 105 Comparison Between Simulated Results and Data on Small Mammals Surveyed at the SRS 109 VI Discussion 1 Hi 4 THE ROLE OF SPECIES' AVERAGE MIGRATION DISTANCE IN A METAPOP- ULATION PERSISTENCE: A SENSITIVITY ANALYSIS 120 Introduction 120 Sourcs of Variation in I he Model 121 Sensitivity Mensure 12:1 Sensitivity Results 121 Ecological Implications of the Sensitivity Analysis: the Role of the Spatial Component in a Metapopulation Persistence 1X2 Discussion lit 1 5 CONCLUSIONS i:Ls Contributions of this work for the joint field of Statistics and Ecology US* Challenges for the Eut lire 1:10 APPENDIX A CORRELATION ANALYSES AND VEGETATION VARIABLES 1 12 APPENDIX B COMPLETE DATA SET COLLECTED AT THE SAVANNAH RIVER SITE 1.11 APPENDIX C SPLUS CODE FOR COMPUTATION OF THE MEAN POLISH . 102 APPENDIX D FORTRAN CODE OF SIMULATION MODEL HS-I BIBLIOGRAPHY 177 Vtl LIST OF TABLES Table 2.1 Xumber of patches available for sampling and relative frequency of selection by age class. n,s is number of patches with age equal to a - 1 ft; n,,/n is the proportion of patches of age a with respect to the total number of patches available for sampling on each landscape (n - Kit in 199:i. n = 177 in 1994). l.'i Table 2.2 ii', represents a chosen number of patches to be trapped according to proportional allocation by age class: ri,, represents the number of patches by age class actually trapped m I lie field work to survey populations of small mammals at the SRS. These numbers are given by year since the field work was done in two different years 11 '['able 2.:\ Statistical summaries of densities of pohonotus. S. Iu>pidu* and I', yoxstipi- mi.s. for the data collected in 199:1 (where 102 patches were sampled), the data collected in 1991 (where 91 patches were sampled), and both sets together. ... 19 Table 2,1 Statistical summaries of densities of P. (xAionotus stratified by age classes. P. ftolianotus has zero as minimum values in each age class 21 Table 2. j Statistical summaries of densities of Iits/itdus. stratified by age classes. hispultis has zero as minimum values, in each age class 21 Table 2.(S Statistical summaries of densities of P. i/nssi/piniif,, stratified by age classes. P. ijos.si/pniu.s has zero as minimum values in each age class 25 Table 2.7 Statistical summaries of areas of patches trapped in 199:» and 199 1. I'nits of areas are in knv lit) VIII Table 2.8 .Joint occurrence/non-occurrence of zeros in densities of P. pohonotus. S. htspulus. and P. yossypirius 14 Table 2.9 Variances of raw j) with respective transformed ( '/.[} I densities. Transfor­ mation is such that Z\} — 'I* Z,j/0,. where 0: is the estimation of age-classes density means (here I am using estimation of standard deviations which are given in tables 2.4, 2 ">. and '2.15). Largest value of P. gossi/pintis age-class ;i years is dismissed for this analysis !1 Table 2.10 Empirical variogram estimates of mean-polish (with trimmed factor=0.2ô) resid­ uals of a transformation of species densities surveyed at the SRS (see text for details on data transformation mean polish residuals 19 Table :i.l Number of patches in each age class of the first landscape used in t he simulation model. Among patches, age-class 1 year-old amounts to :t">.(5 of the total number of patches 78 Table :(.2 Estimation of the function <1,(11, ,) to which carrying capacity /V, , f is propor­ tional to. s = P. S. where P stands for P. pohonotus and S stands for >'. Iiispulus. M Table Fitted model parameters considering the constraints that >'. Iiispulus are a stronger species than P. pohonotus. and both species metapopulations should coexist in 1994 (after 42 runs of the simulation). Units of instantaneous growth rate r, are individuals/individuals.(150 days): competitive effects of one species over another are unit less. Estimations of reproductive rates are inside the expected range of animals with body sizes similar to P. pohonotus and X. htsptdtis (Clark and Danielson (in press). Saner and Slade [198(5j. Saner and Slide [1987]) 88 "Table :î. 1 Statistical summaries of successful and unsuccessful migration distances </. A successful emigrant is the one which randomly locates a patch inside the ring (/ if. e = 0.0(5: otherwise, an emigrant is considered unsuccessful and dies. 9(5 IX Table X.5 Age-class percent of carrying capacity of maximum densities simulated according to models DII and DDI.