Continuous-time Markov models for species interactions

Discrete-time Markov chains are widely used to study communities of competing sessile species. Their parameters are transition probabilities between states (species found at points in space), estimated from repeated observations. The proportion of nonzero entries in the transition matrix has been suggested as a measure of the complexity of interspecific interactions. This is not accurate if more than one transition can occur per time interval. In such cases, continuous-time Markov chains may be better, and discrete-time models may overestimate the complexity of species interactions. We reanalyze data from a marine community. A continuous-time model with homogeneous rates is not significantly worse than the maximum-likelihood discrete-time model. Compared to the continuous-time model, the discrete-time model overestimates the complexity of interspecific interactions. We also discuss the entropy of a continuous-time Markov chain, another measure of complexity.