Stochastic Abundance Models: With Emphasis on Biological Communities and Species Diversity

ISBN-13: 9789400957862 / Angielski / Miękka / 2012 / 126 str.

S. Engen

Opis

This monograph deals with the analysis of populations of elements. Each element is a member of one and only one class, and we shall mainly be concerned with populations with a large number of classes. No doubt the present theory has its outspring in ecology, where the elements symbolize the individual animals or plants, while the classes are the various species of the ecological community under consideration. Some basic ideas point back to a classical contribution by R.A. Fisher (1943, in collaboration with A.S. Corbet and c.B. Williams) representing a breakthrough for the theoretical analysis of diverse populations. Though most of the work in this field has been carried out by ecologists, statisticians and biometri- cians have, over the past 15 years, shown an ever increasing interest in the topic. Besides being directed towards biometricians and statisticians, this monograph may hopefully be of interest for any research worker dealing with the classification of units into a large number of classes, in particular ecologists, sociologists and linguists. However, some background in statistics and probability theory is required. It would be unless to read the present book without some knowledge of the continuous and discrete probability distributions summarized in section 1.1, and the use of generating functions. In particular, a clear intuitive and formal understanding of the concept of condi- tional probability and conditional distributions is required in order to interpret the various models correctly.

Spis treści

I: Theoretical Treatement.- 1. Introduction.- 1.1 Abundance models.- 1.2 Some distributions used in the statistical analysis of abundance and diversity.- 1.3 Description of fixed populations.- 1.4 Description of random populations.- 2. Sampling from a Population of Classes.- 2.1 Introduction.- 2.2 The limitation of inference drawn from one sample.- 2.3 Sampling from a finite population.- 2.4 Sampling from an infinite population.- 2.5 Quadrat sampling : presence absence data.- 2.6 Species-area curves.- 2.7 Good’s (empirical) Bayesian approach.- 3. Abundance Models.- 3.1 General introduction.- 3.2 Maximum liklihood theory applied to symmetric models.- 3.3 Fisher’s logarithmic series model.- 3.4 The negative binomial model.- 3.5 The geometric series model.- 3.6 The Poisson lognormal model.- 3.7 Zipf’s model.- 3.8 Some other models.- 3.9 Some concluding remarks.- 4. Sample Coverage.- 4.1 Introduction.- 4.2 Finite populations.- 4.3 Infinite populations.- 4.4 Some results for the negative binomial model.- 5. Indices of Diversity and Equitability.- 5.1 Introduction.- 5.2 Finite populations.- 5.3 Infinite populations.- 5.4 Parameter transformation.- II: Ecological Applications.- 6. Abundance Models in Ecology.- 6.1 Introduction.- 6.2 Some historical remarks.- 6.3 Interpretations of fixed and random models in ecology.- 6.4 The stability of population parameters.- 7. Abundance Models in Ecology—Examples.- 7.1 Discussion of assumptions.- 7.2 Judging goodness of fit.- 7.3 Quadrat sampling.- 7.4 Higher order classification.- 7.5 Species diversity of chironomid communities— an example.- References.- Appendix A: The Structural Distribution for the Model dealt with in Example 2.4.- Appendix B: Tables.- Author Index.