Rate-time scaling in phenotypic evolution: Limitations of current models in capturing temporal dynamics.

Evolutionary rates correlate negatively with time, which makes it complicated to compare rates across lineages that have diversified on different time intervals. The causes of this correlation are debated. Using simulations, we first show that rates of evolution estimated as a parameter in the unbiased random walk (Brownian motion) model lack a rate-time scaling when data has been generated using this model, even when time series are made incomplete and biased. This indicates that it is theoretically possible to estimate rates that are not time correlated from empirical data. We then analyze 643 empirical time series to assess whether accounting for model misspecification, sampling error, and model identifiability reduce the negative scaling, but none appear to have a significant impact. This suggests that the rate-time correlation requires an explanation grounded in evolutionary explanations, and that common models used in phylogenetic comparative studies and phenotypic time series analyses often fail to accurately describe trait evolution in empirical data. Making meaningful comparisons of estimated rates between clades and lineages covering different time intervals remains a challenge.