Detection of evolutionary shifts in variance under an Ornsten-Uhlenbeck model

Abrupt environmental changes can lead to evolutionary shifts in not only the optimal trait value, but also the rate of adaptation and the diffusion variance in trait evolution. While several methods exist for detecting shifts in optimal values, few explicitly model shifts in both evolutionary variance and adaptation rates. We use a multi-optima and multi-variance Ornstein-Uhlenbeck (OU) process model to describe trait evolution with shifts in both optimal value and diffusion variance and analyze how covariance between species is affected when shifts in variance occur along the phylogeny. We propose a new method that simultaneously detects shifts in both variance and optimal values by formulating the problem as a variable selection task using an L1-penalized loss function. Our method is implemented in the R package ShiVa (Detection of evolutionary Shifts in Variance). Through simulations, we compare ShiVa with methods that only consider shifts in optimal values (l1ou; PhylogeneticEM), and PCMFit. Our method demonstrates improved predictive ability and significantly reduces false positives in detecting optimal value shifts when variance shifts are present. When only shifts in optimal value occur, our method performs comparably to existing approaches. Applying ShiVa to empirical data from cordylid lizards , we find that it outperforms l1ou and PhylogeneticEM, achieving the highest log-likelihood and lowest BIC.