Extending null scenarios with Faddy distributions in a probabilistic randomization protocol for presence-absence data

1. The analysis of species occurrences at discrete locations makes use of statistical methods intended to elucidate whether a random process can explain a particular observed pattern of presences-absences (1-0). Various statistical methods have contributed to the development of null model analysis of (1-0) data in community ecology using randomization tests. Frequentist techniques assuming probability distributions under the null scenarios have been proposed, as in the work by Navarro and Manly (2009) (NM), a protocol that has been applied in the analysis of plant and microbial communities, and chemical hazards.

2. The NM method assumes that presences-absences are governed by independent Bernoulli random variables, and that a non-observable non-negative random variable (“quasi-abundance”) is associated to each species on each location. The quasi-abundance is presumed to follow any of three possible distributions (Poisson, Binomial and Negative Binomial) and to be log-linearly related...