The evolutionary implications and frequency of hybridization and introgression are increasingly being recognized across the tree of life. To detect hybridization from multi-locus and genome-wide sequence data, a popular class of methods are based on summary statistics from subsets of 3 or 4 taxa. However, these methods often carry the assumption of a constant substitution rate across lineages and genes, which is commonly violated in many groups. In this work, we quantify the effects of rate variation on the D test (also known as ABBA-BABA test), the D3 test, and HyDe. All three tests are used widely across a range of taxonomic groups, in part because they are very fast to compute. We consider rate variation across species lineages, across genes, their lineage-by-gene interaction, and rate variation across gene-tree edges. We simulated species networks according to a birth-death-hybridization process so as to capture a range of realistic species phylogenies. For all three methods tested, we found a marked increase in the false discovery of reticulation (type-1 error rate) when there is rate variation across species lineages. The D3 test was the most sensitive, with around 80% type-1 error, such that D3 appears to more sensitive to a departure from the clock than to the presence of reticulation. For all three tests, the power to detect hybridization events decreased as the number of hybridization events increased, indicating that multiple hybridization events can obscure one another if they occur within a small subset of taxa. Our study highlights the need to consider rate variation when using site-based summary statistics, and points to the advantages of methods that do not require assumptions on evolutionary rates across lineages or across genes.

The popularity of relaxed clock Bayesian inference of clade origin timings has generated several recent publications with focal results considerably older than the fossils of the clades in question. Here we critically examine two such clades: the animals (with focus on the bilaterians); and the mammals (with focus on the placentals). Each example displays a set of characteristic pathologies which, although much commented on, are rarely corrected for. We conclude that in neither case does the molecular clock analysis provide any evidence for an origin of the clade deeper than what is suggested by the fossil record. In addition, both these clades have other features (including, in the case of the placental mammals, proximity to a large mass extinction) that allow us to generate precise expectations of the timings of their origins. Thus, in these instances the fossil record can provide a powerful test of molecular clock methodology, and why it goes astray; and we have every reason to think these problems are general.

Determining the link between genomic and phenotypic change is a fundamental goal in evolutionary biology. Insights into this link can be gained by using a phylogenetic approach to test for correlations between rates of molecular and morphological evolution. However, there has been persistent uncertainty about the relationship between these rates, partly because conflicting results have been obtained using various methods that have not been examined in detail. We carried out a simulation study to evaluate the performance of five statistical methods for detecting correlated rates of evolution. Our simulations explored the evolution of molecular sequences and morphological characters under a range of conditions. Of the methods tested, Bayesian relaxed-clock estimation of branch rates was able to detect correlated rates of evolution correctly in the largest number of cases. This was followed by correlations of root-to-tip distances, Bayesian model selection, independent sister-pairs contrasts, and likelihood-based model selection. As expected, the power to detect correlated rates increased with the amount of data, both in terms of tree size and number of morphological characters. Likewise, greater among-lineage rate variation in the data led to improved performance of all five methods, particularly for Bayesian relaxed-clock analysis when the rate model was mismatched. We then applied these methods to a data set from flowering plants and did not find evidence of a correlation in evolutionary rates between genomic data and morphological characters. The results of our study have practical implications for phylogenetic analyses of combined molecular and morphological data sets, and highlight the conditions under which the links between genomic and phenotypic rates of evolution can be evaluated quantitatively.