Revisiting evolutionary rate-time relationships.

Rates of molecular, phenotypic, and lineage diversification typically scale negatively with time interval of measurement, raising longstanding questions about time-dependency of evolutionary processes. These patterns and their potential meaning have recently re-entered evolutionary discussions. In this Perspective we revisit the general challenges in interpreting rate-time relationships. Much apparent temporal scaling of evolutionary rate is an inescapable outcome of plotting a ratio against its denominator, either directly or indirectly. Highly unlikely relationships between timescale and accumulated evolutionary change are required to produce anything other than negative rate-time relationships. Simulations reveal that constant rate evolutionary processes readily generate negative rate-time scaling relationships under many conditions, and that a range of rate-time scaling exponents can be generated by different evolutionary processes. Reanalysis of six empirical datasets reveals unscaled magnitudes of evolution that are either unrelated to time and/or vary in their relationship with time. Over 99% of variation in rate-time relationships across six datasets explained by time variation alone. We further evaluated a recent hypothesis that evolutionary rate-time scaling reflects three modes of change, from micro- to macroevolutionary time scales using break-point regression, but we found no strong support for this hypothesis. Taken together, negative rate-time relationships are therefore largely inevitable and challenging to interpret. In contrast, it is more straightforward to assess how evolutionary change accumulates with time.