The history of a trait within a lineage may influence its future evolutionary trajectory, but macroevolutionary theory of this process is not well developed. For example, consider the simplified binary trait of living in cave versus surface habitat. The longer a species has been cave dwelling, the more accumulated loss of vision, pigmentation, and defense may restrict future adaptation if the species encounters the surface environment. However, the Markov model of discrete trait evolution that is widely adopted in phylogenetics does not allow the rate of cave-to-surface transition to decrease with longer duration as a cave dweller. Here we describe three models of evolution that remove this memoryless constraint, using a renewal process to generalize beyond the typical Poisson process of discrete trait macroevolution. We then show how the two-state renewal process can be used for inference, and we investigate the potential of phylogenetic comparative data to reveal different influences of trait duration, or memory in trait evolution. We hope that such approaches may open new avenues for modeling trait evolution and for broad comparative tests of hypotheses that some traits become entrenched.
Biological Evolution Markov Chains