A HIDDEN-MARKOV MODEL FOR EVALUATING MACROEVOLUTIONARY TRENDS

Recently, there has been much interest in re-evaluating patterns historically interpreted as macroevolutionary trends. In particular, workers are concerned with categorizing trends by their causal mechanisms, usually focusing on two end-member processes: passive and active. Most will agree that these terms are umbrellas, each encompassing a broad suite of evolutionary processes. For example, it has been argued that passive trends may be as likely the result of movement away from unstable or toward stable regions in morphospace as they are a consequence of passive diffusion constrained by morphological boundaries (Alroy 2000). Recognition of such point equilibria requires understanding of the rate and magnitude of transitions from ancestral (A) to descendent (D) morphologies; however, such data are rare. Here a method for evaluating equilibrium points in the absence of a robust phylogenetic context is presented.

Morphological evolution is often modeled as a Markov process or system in which the future state (descendent morphology) is dependent only on the current one (ancestral morphology). The transition matrix defining the probabilities of moving from one region of morphospace to another is a measure of the expected rate at which specific A-D transitions occur. A-D transitions occurring with greater or lesser frequency than predicted given the overall behavior of the system are potential point equilibria.

In the absence of known A-D transitions, a Monte Carlo simulation is used to select random paths through morphospace over the sampled time interval within observed and simulated datasets. A hidden-Markov model is then use to estimate and evaluate the likelihood of transition matrices given the paths; the estimated matrix approaching the true set of probabilities with increasing numbers of sampled paths. This approach not only successfully matches trends generated via the underlying end-member processes (passive, bounded-passive, and active) with the appropriate causal mechanism, but also serves to elucidate more complex morphospace structure in both real and simulated data.