Degree Type

Dissertation

Date of Award

1990

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Kenneth J. Koehler

Abstract

Many measures have been proposed and used to quantify the diversity of an ecological community. The evaluation of such measures generally requires information obtained by sampling a community. Often it is impractical to randomly sample individual members of a community, and, commonly, estimates are based on what is observed in a random sample of quadrats (plots of land, volumes of water, etc.). More complex schemes are also used involving stratification or subsampling from quadrats. It is generally straightforward to compute point estimates of measures of diversity, but formulas for variances and confidence intervals are often unavailable;This dissertation explores the application of resampling procedures for making inferences about measures of diversity from sample data. In particular, bootstrap and jackknife resampling procedures are used to obtain numerical values for variance estimates and confidence intervals without requiring the development of explicit mathematical formulas. The chapters of this dissertation are presented as individual articles, with the exception of the first chapter which provides a general introduction. Chapter 2 examines the behavior of bootstrap and jackknife estimators of species richness for data obtained from a random sample of quadrats. An improved estimator for the variance of the jackknife estimator is developed. A simulation study shows that both the jackknife and bootstrap estimators of species richness tend to underestimate the number of species when many species are not observed. Confidence intervals based on the percentiles of bootstrap sample tend to be superior to those based on the jackknife procedure when the samples are large enough for these procedures to provide reliable results. It is also shown that a recently developed empirical Bayes estimator of species richness tends to overestimate the number of species and is more variable than the resampling estimators. Chapter 3 focuses on the estimation of measures of diversity, including the popular Simpson and Shannon indices. Bootstrap estimators are developed as a special case of the more general problem of bootstrap estimation of functions of means or proportions for complex sample surveys. In particular, one and two stage cluster sampling are considered. The accuracy of bootstrap estimators for the Simpson and Shannon indices are examined with a simulation study. Point estimates and coverage levels of confidence intervals are substantially improved with the introduction of a bias correction. The bootstrap procedures are used to compare species richness and diversity among habitats in a study of birds in Ames, Iowa. Comparisons with corresponding results for the Wilcoxon test suggest that the bootstrap procedure can have much greater power for detecting differences than nonparametric procedures previously used in such studies.

DOI

https://doi.org/10.31274/rtd-180813-9169

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Clarice Azevedo de Luna Freire

Language

en

Proquest ID

AAI9101350

File Format

application/pdf

File Size

160 pages

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