Several Results Of Simpson Diversity Indices And Exploratory Data Analysis In The Pielou Model
Free (open access)
D. Almorza Gomar & M. H. García Nieto
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.
Pielou model, probability distribution, diversity, Simpson index, exploratory data analysis.