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Testing Co-Evolution of Discrete Traits with Markov Evolutionary Reward Processes

Detecting co-evolution of two discrete morphological or behavioral traits is a longstanding problem in evolutionary biology. In such studies, researchers collect data from multiple closely related species and then analyze concordance between two traits of interest. Such comparative methods increasingly gain popularity among anthropologists who study co-evolution of cultural diversity traits in human societies. In both evolutionary and anthropological applications, the null hypothesis states that two traits under consideration evolve independently. Posterior predictive model diagnostics have been proposed to test such independence. This hypothesis testing framework allows for integration over nuisance parameters, including species and cultural evolutionary histories. We use Markov evolutionary reward process to construct discrepancy measures needed for posterior predictive p-value calculations. In contrast to previous applications of such discrepancy measures, we design an efficient, simulation free algorithm to compute properties of the Markov evolutionary reward process. To illustrate the utility of our method, we analyze primate mating behavior and evolution of wealth transfer mechanisms in human societies.