A note on investigating co-occurrence patterns and dynamics for many species, with imperfect detection and a log-linear modeling parameterization.

Patterns in, and the underlying dynamics of, species co-occurrence is of interest in many ecological applications. Unaccounted for, imperfect detection of the species can lead to misleading inferences about the nature and magnitude of any interaction. A range of different parameterizations have been published that could be used with the same fundamental modeling framework that accounts for imperfect detection, although each parameterization has different advantages and disadvantages.We propose a parameterization based on log-linear modeling that does not require a species hierarchy to be defined (in terms of dominance) and enables a numerically robust approach for estimating covariate effects.Conceptually, the parameterization is equivalent to using the presence of species in the current, or a previous, time period as predictor variables for the current occurrence of other species. This leads to natural, "symmetric," interpretations of parameter estimates.The parameterization can be applied to many species, in either a maximum likelihood or Bayesian estimation framework. We illustrate the method using camera-trapping data collected on three mesocarnivore species in South Texas.