Information Criteria for Comparing Partition Schemes.

When inferring phylogenies, one important decision is whether and how nucleotide substitution parameters should be shared across different subsets or partitions of the data. One sort of partitioning error occurs when heterogeneous subsets are mistakenly lumped together and treated as if they share parameter values. The opposite kind of error is mistakenly treating homogeneous subsets as if they result from distinct sets of parameters. Lumping and splitting errors are not equally bad. Lumping errors can yield parameter estimates that do not accurately reflect any of the subsets that were combined whereas splitting errors yield estimates that did not benefit from sharing information across partitions. Phylogenetic partitioning decisions are often made by applying information criteria such as the Akaike information criterion (AIC). As with other information criteria, the AIC evaluates a model or partition scheme by combining the maximum log-likelihood value with a penalty that depends on the number of parameters being estimated. For the purpose of selecting an optimal partitioning scheme, we derive an adjustment to the AIC that we refer to as the AIC$^{(p)}$ and that is motivated by the idea that splitting errors are less serious than lumping errors. We also introduce a similar adjustment to the Bayesian information criterion (BIC) that we refer to as the BIC$^{(p)}$. Via simulation and empirical data analysis, we contrast AIC and BIC behavior to our suggested adjustments. We discuss these results and also emphasize why we expect the probability of lumping errors with the AIC$^{(p)}$ and the BIC$^{(p)}$ to be relatively robust to model parameterization.