Time dependency of foamy virus evolutionary rate estimates

Pakorn Aiewsakun, Aris Katzourakis

It appears that substitution rate estimates co-vary very strongly with their timescale of measurement; the shorter the timescale, the higher the estimated value. Foamy viruses have a long history of co-speciation with their hosts, and one of the lowest estimated rates of evolution among viruses. However, when their rate of evolution is estimated over short timescales, it is more reminiscent of the rapid rates seen in other RNA viruses. This discrepancy between their short-term and long-term rates could be explained by the time-dependency of substitution rate estimates. Several empirical models have been proposed and used to correct for the time-dependent rate phenomenon (TDRP), such as a vertically-translated exponential rate decay model and a power-law rate decay model. Nevertheless, at present, it is still unclear which model best describes the rate dynamics. Here, we use foamy viruses as a case study to empirically describe the phenomenon and to determine how to correct rate estimates for its effects. Four empirical models were investigated: (i) a vertically-translated exponential rate decay model, (ii) a simple exponential rate decay model, (iii) a vertically-translated power-law rate decay model, and (iv) a simple power-law rate decay model. Our results suggest that the TDRP is likely responsible for the large discrepancy observed in foamy virus short-term and long-term rate estimates, and the simple power-law rate decay model is the best model for inferring evolutionary timescales. Furthermore, we demonstrated that, within the Bayesian phylogenetic framework, currently available molecular clocks can severely bias evolutionary date estimates, indicating that they are inadequate for correcting for the TDRP. Our analyses also suggest that different viral lineages may have different TDRP dynamics, and this may bias date estimates if it is unaccounted for. As evolutionary rate estimates are dependent on their measurement timescales, their values must be used and interpreted under the context of the timescale of rate estimation. Extrapolating rate estimates across large timescales for evolutionary inferences can severely bias the outcomes. Given that the TDRP is widespread in nature but has been noted only recently the estimated timescales of many viruses may need to be reconsidered and re-estimated. Our models could be used as a guideline to further improve current phylogenetic inference tools.