Phenotypic evolution as an Ornstein-Uhlenbeck process: The effect of environmental variation and phenotypic...

Here we investigate phenotypic evolution from the perspective of the Ornstein-Uhlenbeck (OU) process. Evolutionarily speaking, the model assumes the existence of stabilizing selection toward a phenotypic optimum. The standard (OU) model is modified to include environmental variation by taking a moving phenotypic optimum and endowing organisms with phenotypic plasticity. These two processes lead to an effective fitness landscape, which deforms the original. We observe that the simultaneous occurrence of environmental variation and phenotypic plasticity leads to skewed phenotypic distributions. The skewness of the resulting phenotypic distributions strongly depends on the rate of environmental variation and strength of selection. When generalized to more than one trait, the phenotypic distributions are not only affected by the magnitude of the rate of environmental variation but also by its direction. A remarkable feature of our predictions is the existence of an upper bound for the critical rate of environmental variation to allow population persistence, even if there is no cost associated with phenotypic plasticity.