Likelihood and Wi {RInSp}

Likelihood measure of niche breadth

Description

The procedure calculates the estimation of likelihood measures of niche breadth and overlap described in Petraitis (1979).

Usage

like.Wi(dataset)

Arguments

dataset

Object of class RInSp with data.

Details

The function returns the likelihood of the observed diet (\lambda_i) the associated probability , and the value of the Petraitirs' W. The likelihood of the observed diet of individual i is:

\lambda_i = \prod_j (\frac{q_j}{p_{ij}})^{n_{ij}}

where q_j is the population proportion of the resource j, p_{ij} is the proportion of the resource j in the diet of the individual i, and n_{ij} is the number of items for the individual i and the resource j.

This can be used to calculate a p-value to test the significance of the diet specialization, as -2ln(\lambda) is distributed as a chi-square with (r-1) degrees of freedom, where r is the number of resource categories.

The generalised likelihood ratio test rejects the null hypothesis for a unilateral alternative hypotesis using significance level \alpha if:

-2ln(\lambda) > \chi^2_{(r-1)}

Petraitis' W is computed following:

W_i = \lambda_i^{(1/D_i)}

where D_i is the number of diet items recorded in the diet of individual i. This index is a measure of niche width relative to a specified distribution. For a complete generalist individual, W_i = 1, and the value decreases with greater specialization.

Value

Return a list of class RInSp with:

MeanWi

the mean population value of Wi;

ResCat

the number of resource categories;

ind.vals

A matrix with three columns: “Likelihood” with value of the likelihood index for the individual i; “p-value” for the the probability associated to the likelihood value; “Wi” with the value of the Petraitis' W index for the individual i.

Author(s)

Dr. Nicola ZACCARELLI

References

Petraitis, P. S. 1979. Likelihood measures of niche breadth and overlap. Ecology 60(4): 703-710.

Bolnick, D.I., L.H. Yang, J.A. Fordyce, J.M. Davis, and Svanback, R. 2002. Measuring individual-level resource specialization. Ecology 83: 2936-2941.

Examples

# Likelihood and Wi example with stickleback data
# from Bolnick and Paull 2009
data(Stickleback)
# Select a single spatial sampling site (site D)
SiteD <- import.RInSp(Stickleback, row.names = 1,
info.cols = c(2:13), subset.rows = c("Site", "D"))
Wi <- like.Wi(SiteD)
rm(list=ls(all=TRUE))