Several Results Of Simpson Diversity Indices And Exploratory Data Analysis In The Pielou Model
Price
Free (open access)
Transaction
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.