Model misspecification confounds the estimation of rates and exaggerates their time dependency

While welcoming the comment of Ho et al. (2015), we find little that undermines the strength of our criticism, and it would appear they have misunderstood our central argument. Here we respond with the purpose of reiterating that we are (i) generally critical of much of the evidence presented in support of the time-dependent molecular rate (TDMR) hypothesis and (ii) specifically critical of estimates of μ derived from tip-dated sequences that exaggerate the importance of purifying selection as an explanation for TDMR over extended timescales. In response to assertions put forward by Ho et al. (2015), we use panmictic coalescent simulations of temporal data to explore a fundamental assumption for tip-dated tree shape and associated mutation rate estimates, and the appropriateness and utility of the date randomization test. The results reveal problems for the joint estimation of tree topology, effective population size and μ with tip-dated sequences using BEAST. Given the simulations, BEAST consistently obtains incorrect topological tree structures that are consistent with the substantial overestimation of μ and underestimation of effective population size. Data generated from lower effective population sizes were less likely to fail the date randomization test yet still resulted in substantially upwardly biased estimates of rates, bringing previous estimates of μ from temporally sampled DNA sequences into question. We find that our general criticisms of both the hypothesis of time-dependent molecular evolution and Bayesian methods to estimate μ from temporally sampled DNA sequences are further reinforced.