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

Sudden changes in environmental conditions can lead to evolutionary shifts not only in the optimal trait value (θ), but also in the diffusion variance (σ2) under the Ornstein-Uhlenbeck (OU) model. While several methods have been developed to detect shifts in optimal values, few explicitly account for concurrent shifts in both evolutionary variance and diffusion variance. We use a multi-optima and multi-variance OU model to describe trait evolution with shifts in both θ and σ2 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 existing methods that can automatically detect evolutionary shifts under the OU model (ℓ1ou, PhylogeneticEM, and PCMFit). Our method achieves lower mean integrated squared error (MISE) for the diffusion variance 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. We apply ShiVa to empirical data on floral diameter in Rafflesiaceae (with Euphorbiaceae outgroups) and buccal morphology in Centrarchidae sunfishes.