Discrete probability models to assess spatial distribution patterns in natural populations and an algorithm for likelihood ratio goodness of fit test

  • Gonzalo Durán Pacheco
Palabras clave: Spatial patterns, discrete probability distributions, likelihood ratio test, matlab


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.

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