Automatic Discovery of Optimal Discrete Character Models

Abstract

Modeling discrete character evolution in a Markovian framework has become common practice in phylogenetic comparative methods. The increasing size and complexity of these models reflects a trend of analyses to include more taxa and more discrete characters. However, as complexity of the models increase, so do the number of potential model structures and number of estimable parameters, making it nearly impossible to consider all modeling options for a given dataset. To overcome this issue, I apply a combination of regularization and simulated annealing to models of discrete character evolution. This allows for the automatic searching and optimization across different model structures without user specification. I test this framework under several simulation scenarios including hidden rates and multiple discrete characters. The results indicate that regularized models significantly outperform traditional approaches, yielding a far lower variance and a nearly tenfold reduction in the overall error of parameter estimates in the most extreme scenarios. I illustrate the power of automatic model selection by revisiting the ancestral state estimation of concealed ovulation and mating systems in Old World monkeys. Using the dredge algorithm, I discover a previously unexamined model structure which has both better statistical performance and a differing ancestral state reconstruction when compared to default model sets. In general, these results highlight the dangers of an over-reliance on default model sets. The combination of automatic model selection and regularization help overcome problems of over-parameterization, and these results demonstrate that when inferences are drawn from a larger model space, they can be both more statistically robust and biologically realistic.