WIT Press


Several Results Of Simpson Diversity Indices And Exploratory Data Analysis In The Pielou Model

Price

Free (open access)

Volume

81

Pages

10

Published

2005

Size

459 kb

Paper DOI

10.2495/ECO050161

Copyright

WIT Press

Author(s)

D. Almorza Gomar & M. H. García Nieto

Abstract

The Pielou model is a model of the abundance of species in a habitat. In this paper, we apply Simpson diversity indices to the Pielou model and obtain a result that may be useful for testing the goodness of fit of the Pielou model. To obtain our results, we describe the broken stick model as a probability distribution and we present some results from exploratory data analysis of this model. The inequalities we present are useful in ecological studies that apply the Pielou model. Keywords: Pielou model, probability distribution, diversity, Simpson index, exploratory data analysis. 1 Introduction In the Pielou model the probability of finding an individual of the specie i in the habitat is ∑ −= −i S i k S p k=0S 1 1 where 0 ≤pi ≤1, ∀i = 1, 2,...., S and ∑ s i= i p 1 = 1, pi ≥pj ,∀i ≤j , with i, j =1,…, S. 1.1 Pielou model as a probability distribution The probability density function (pdf) given by  ++ −+= i S S S pi 1 ... 1 1 1 1 with S >1, provides a probability distribution that arises from the Pielou model. Proof The pdf is consistent with 0 ≤pi ≤1, ∀i = 1,2,...., S and pi ≥pj , ∀i ≤j, with i, j =1, 2,…, S. Therefore, it is sufficient to prove that ∑ = s i i p 1 = 1.

Keywords

Pielou model, probability distribution, diversity, Simpson index, exploratory data analysis.