Generalized linear models with Poisson family: applications in ecology

Ecological data are often discrete and do not follow the assumptions of the General linear model and its variants (linear regressions, ANOVA, etc.). Discrete response variables, such as count data, often contain many zero observations and are unlikely to have a normally distributed error structure even if transformed. To solve these problems, Generalized Linear Models (GLM) have been more recently developed. The basic GLM for count data is the Poisson model with log link. Frequently, count data are often overdispersed (variance of the response variable greater than the mean) and invalidating the use of the Poisson distribution. In these conditions, some extensions of Poisson model are usually used to deal with overdispersion, including the Negative binomial, Quasi-Poisson, zero-inflated Poisson (ZIP) models and Zero Inflated Negative Binomial (ZINB). The main objective of this study was to empirically assess the robustness of Poisson model and its extensions to overdispersion situations in ecological count data. The simulation plan considered took into account the overdispersion k (k=2, 4, 8, 10, 12 and 20), the sample size, n (n=25, 50, 100, 500 and 1000) and the proportion of zeros in the sample p (p=0.20, 0.40, 0.60 and 0.80). Two models have been considered: simple model (one explanatory variable) and 2-variables model. The comparison criteria were the mean bias (B), the mean relative error (RE) and the root mean-squared error (RMSE) of the slopes, Akaike Information Criterion (AIC) and Vuong statistic. Results obtained showed that no model perform better in all situations but Negative binomial and Zero Inflated Poisson models recorded overall good performances. Applications of these results in ecology revealed that the number of wilted plants is overdispersed because of the preponderance of zeros in the data set. The results proved that zero inflated models performed better on the number of wilted plants within pineapple cultivars in Benin.