Modelling compositional and exchange rate changes over time

Abstract The process of evolution can change over time, and may result in compositional tree heterogeneity (CTH) and exchange rate tree heterogeneity (ERTH). Models that can accommodate CTH and ERTH in molecular evolution are described. Fit of these models was compared using a likelihood ratio test in maximum likelihood, and in Bayesian analysis using the conditional predictive ordinate (CPO)-based log pseudomarginal likelihood (LPML), also known as leave-one-out cross-validation (LOO-CV). To decrease overparameterization in these parameter-rich models, CTH and ERTH can be flexibly modelled in a Bayesian framework with models that tune themselves to the amount of heterogeneity in the data being analysed. Since model-based phylogenetic analysis is usually done using tree-homogeneous models, the effects of CTH and ERTH in simulated data on subsequent phylogenetic analysis using tree-homogeneous models were described. Compositional effects due to CTH were seen as expected, for example where unrelated taxa with similar compositions would group together in analyses assuming a homogeneous evolutionary process. Similar effects were demonstrated due to ERTH, showing a novel source of incongruence. Detection of CTH and ERTH by modelling was compared to detection using matched-pairs tests (MPTs) of homogeneity that have been used to test molecular sequences for stationarity, reversibility, and homogeneity (SRH). Comparison between modelling and MPTs on simulated datasets showed that the two approaches differed greatly. Modelling showed greater statistical power, especially in detection of ERTH, with some ERTH completely invisible to MPTs but decisively detected by modelling. Detection and modelling of CTH and ERTH is shown in two empirical datasets, where modelling affects topology, support, and branch length estimation.