Degree Type

Dissertation

Date of Award

1989

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Glen D. Meeden

Abstract

The problem of estimating the total number T of distinct species in some specified region based on a random sample from the region is discussed. Two sampling procedures are of interest, sampling by elements and quadrat sampling;In the case of sampling by elements, we assume that the investigator has available a list containing a total of M known species that he believes could be found in that particular region, M 0 and known, to the relative abundances of the species in group two. Admissible estimators are also presented for the case where [beta] → 0 and [beta] → [infinity];In the case of quadrat sampling, two models are discussed. The first is basically a version of the Efron and Thisted (1976) model adapted to the case of quadrat sampling. Some Empirical Bayes estimators for T are derived. It is seen that these estimators are easy to apply in practical situations, they give very good point estimates, they take into account how much the sample represents the whole region and they give more reasonable estimates than the jackknife and the bootstrap estimators proposed by Heltshe and Forrester (1983), and Smith and Belle (1984). Some discussion about the effect of quadrat area and sampled area is given. The second model discusses the case where the species in the region have exactly two replicas. Admissible stepwise Bayes estimators are derived for T in this case and an application in archaeology is presented;References. (1) Efron, B. and Thisted, R. 1976. Estimating the number of unseen species: How many words did Shakespeare know? Biometrika 63:435-447. (2) Heltshe, J. F. and Forrester, N. E. 1983. Estimating species richness using the jackknife procedure. Biometrics 39:1-11. (3) Smith, E. P. and Belle, G. V. 1984. Nonparametric estimation of species richness. Biometrics 40:119-129.

DOI

https://doi.org/10.31274/rtd-180813-12380

Publisher

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

Copyright Owner

Sueli Aparecida Mingoti

Language

en

Proquest ID

AAI8920170

File Format

application/pdf

File Size

310 pages

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