Models for analysing species' presence/absence data at two time points

Species' presence/absence at two time points is a very common form of ecological data. It is the simplest type of longitudinal study and has fundamental applications in ecological succession, environmental monitoring, and climate change scenarios. Despite its widespread commonality the use of statistical regression to analyse such data has been wanting. We propose the use of the bivariate odds-ratio model to analyse these data. Seldomly used in ecology, it is argued as being suitable, especially within a constrained ordination framework. In particular, this paper presents the constrained ordination-odds ratio framework as a potentially important key in understanding the underlying processes of niche theory dynamics, e.g., local extinction and colonization probabilities can be described in terms of it. Some of the mathematical and statistical challenges associated with more ambitious extensions are highlighted. As examples, with an underlying Poisson abundance model, a complementary log-log link for the marginal probabilities is shown to be more appropriate. We then develop this model based on the zero-inflated Poisson distribution since excess absences relative to a Poisson distribution is frequent in practice. Two vegetation data sets are used for illustrative purposes.