Abstract

DURAN PACHECO, Gonzalo. Discrete probability models to assess spatial distribution patterns in natural populations and an algorithm for likelihood ratio goodness of fit test. RevActaNova. [online]. 2006, vol.3, n.3, pp.543-563. ISSN 1683-0789.

Population spatial distribution analysis allow environmental researchers to describe, and understand how individuals (study subjects) grow and interact in a given study site, this information might be used in numberless applications from classical ecology, pest management, sample design optimization, particles dispersion patterns, so forth, to epidemiology and public health. Probability discrete models (Poisson, Binomial and Negative Binomial) are used to asses the three principal spatial patterns (random, uniform and aggregated distributions respectively). In this paper a matlab algorithm is presented to perform spatial patterns analysis through the evaluation of probability models. Likelihood Ratio Goodness of Fit Test (G-test) was used to test for agreement between observed vs expected density data for the three probability distributions, and two sets of random count data (m = 100 and 2229) were simulated for the three probability distributions in order to test the algorithm. Results showed that the algorithm was sensitive in assessing for agreement random generated counts for the three discrete probability models but in less measure for contagious distribution when m = 2229 (p > 0.05 for poisson and binomial models, and p < 0.05 for negative binomial model in both cases). Likelihood Ratio test reported significant difference from negative binomial when in fact it was the population distribution for m = 2229, although graphical distribution analysis showed agreement between observed and expected negative binomial counts.

Keywords : Spatial patterns; discrete probability distributions; likelihood ratio test; matlab.

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