Beyond Brownian motion and the Ornstein-Uhlenbeck process: Stochastic diffusion models for the evolution of quantitative characters
نویسنده
چکیده
—Gaussian processes such as Brownian motion and the Ornstein-Uhlenbeck process have been popular 1 models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. How2 ever, they have drawbacks which limit their utility. Here I describe new, non-Gaussian stochastic differential 3 equation (diffusion) models of quantitative trait evolution. I present general methods for deriving new diffusion 4 models, and discuss possible schemes for fitting non-Gaussian evolutionary models to trait data. The theory of 5 stochastic processes provides a mathematical framework for understanding the properties of current, new and 6 future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution 7 and diversification may help avoid some pitfalls when using stochastic processes to model macroevolution. 8 (
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