BAYESIAN STATE-SPACE MODELING OF EVOLUTIONARY PROCESSES

Time series analysis using state-space models is well established in electrical engineering and statistics and here we demonstrate the approach and its advantages using evolutionary processes. The approach has several advantages, which we describe. The state-space model comprises two equations; the first is an observation equation that models the variation associated with measurement. This assumes there is a latent process and we observe a noisy version of it. The second is a system equation that describes the evolution of the process, generally a random walk. This paradigm fits nicely into the likelihood framework developed in Hunt, 2006, where the observation equation models the sampling error.

Once expressed in the state-space framework, we can now estimate parameters using a Bayesian approach, and this brings a new set of diagnostics and flexibility in modeling. We use a standard R-like package, JAGS (Just Another Gibbs Sampler), to express this model. It comes with a plethora of distributions and a full programming language to describe complex models as desired.

Finally, many studies tie evolutionary processes to other processes, especially environmental proxies. The processes run in parallel and can be couple using a multidimensional state-space process. This allows one to capture their interactions as processes, e.g, two parallel random walks that evolve differently but nonetheless can be show to be statistically related. We will illustrate these concepts using a data set of phenotypic change in a conodont lineage through end-Devonian extinction interval.