PHYLOGENETIC TESTS FOR INTERVAL-SPECIFIC VARIATION IN RATES OF MORPHOLOGIC CHANGE

Concurrent shifts in rates of change might occur among distantly related lineages within a clade due to extrinsic influences such as ecological release following mass extinction or major climatic changes. Existing methods for inferring rate variation over branches are insufficient to test such hypotheses. In particular, these hypotheses predict “polyphyletic” rate shifts rather than shifts diagnosing clades (e.g., the result of intrinsic factors). Additional methodological concerns include the possibility of unsampled lineages persisting over multiple intervals. We propose a new approach to test competing models of rate variation among discrete time intervals over the branches a phylogenetic tree.

The absolute time spanned by a given phylogenetic tree is divided into temporal intervals. State changes of discrete characters are reconstructed on the phylogenetic tree using parsimony. Rates then are calculated from the total number of changes and the total duration of phylogenetic branches contained in the interval. The simplest models posit a single rate over all intervals whereas the most complex posit distinct rates for each interval. We then test rate variation models using information theory criteria accounting for both sample size and model complexity. Specifically, the AIC scores are compared for among optimal models 1-, 2-, …, n-rate models where n is the number of discrete time intervals.

We also propose a variation of this method using maximum likelihood (ML). Here, we calculate the joint likelihoods of trees given data and the aforementioned models of rate variation among intervals. This approach has the advantage of not requiring the use of inferred changes as input data, but rather calculates the likelihood of the tree, models of character evolution and models of temporal rate variation simultaneously, which can then be compared using AIC, as above. This approach has the added advantage of permitting variation among both time intervals and branches of the tree to be modeled simultaneously.

We demonstrate these methods using existing data sets, and offer R scripts for their implementation.