Beyond Brownian motion and the Ornstein-Uhlenbeck process: Stochastic diffusion models for the evolution of quantitative characters

摘要: Gaussian processes such as Brownian motion and the Ornstein-Uhlenbeck process have been popular models for evolution of quantitative traits are widely used in phylogenetic comparative methods. However, they drawbacks which limit their utility. Here I describe new, non-Gaussian stochastic differential equation (diffusion) trait evolution. present general methods deriving new diffusion models, discuss possible schemes fitting evolutionary to data. The theory provides a mathematical framework understanding properties current, future Attention details diversification may help avoid some pitfalls when using model macroevolution.