Constrained ordination analysis in the presence of zero inflation
Constrained ordination analysis, with canonical correspondence analysis (CCA) as its best known method, is a class of popular techniques for analyzing species abundance studies in ecology. These methods rely on distributional assumptions on the conditional abundance distributions. For abundance observations, the Poisson and the negative binomial distributions are the most frequently considered distributions. However, many large abundance studies result in many zero abundances. This may happen because of several reasons. To name one, in microbial community ecology the abundances of a very large number of species are nowadays often obtained by means of sequencing the pooled DNA sample. Due to the small sensitivity for rare species, too many observed zeroes are to be expected. Moreover, more zeroes are expected with increasing number of species. We propose a constrained ordination method based on zero-altered count distributions (e.g., zero-inflated Poisson, hurdle models). We show how the parameters and the environmental gradients can be estimated. In simulation studies we examine the behaviour of the estimators, and we apply the method to a real data set. We conclude that in the presence of zero inflation our methods give better results than the Poisson-based approaches.