Unveiling the molecular clock in the presence of recombination.

In a recent letter in Molecular Biology and Evolution, Schierup and Hein (2000a) showed that the likelihood ratio test (LRT) of the molecular clock (Felsenstein 1981) ‘‘wrongly’’ rejects the clock hypothesis when recombination has occurred. However, this result should not be taken as a failure of the LRT. Because in the presence of recombination often there is not one single tree describing the history of the sequences, but several, the LRT is correctly rejecting the actual null hypothesis tested, that is, that the data are evolving under a clock on one single tree. To appropriately test the clock hypothesis in the presence of recombination, we need to use a test independent of tree topology. Muse and Weir (1992) proposed a triplet likelihood ratio test to test for equality of evolutionary of rates for two species at a time using a third species as an outgroup (to avoid confusion, I will call this test the relative-rate test [RRT]). The RRT is therefore independent of topology and might be used for potentially recombinant sequences if an outgroup is selected which did not recombine with the ingroup. Here, the performance of the RRT with recombinant data is presented. Recombinant alignments were simulated using the coalescent with recombination (Hudson 1983). A program written in C for this purpose is available from the author. Alignments of 11 sequences (10 recombining ingroup and one nonrecombining outgroup) with 1,000 nt were evolved with a molecular clock under the JukesCantor (JC) model of evolution (Jukes and Cantor 1969). For each level of recombination and diversity, 1,000 replicates were generated. A maximum-likelihood (ML) tree was estimated for each simulated data set under the JC1G model of evolution in PAUP* (Swofford 1998) without assuming a clock. The G distribution for rate variation among sites (Yang 1993) was included because it is known that recombination introduces such rate heterogeneity (Schierup and Hein 2000b), and the likelihood increases significantly when this variation is accounted for. For the ML tree, the likelihood under the unconstrained model, where each lineage is allowed to have its own rate (alternative hypothesis), was compared with the likelihood obtained when the molecular clock was enforced (null hypothesis). If the data are evolving under a clock, the difference in likelihood between these two models should be close to zero. To establish statis-