Diffusion Theory

Abstract

In the previous chapter we encountered some difficulty in deriving explicit formulas for several quantities of evolutionary interest, particularly when the population behavior was described by the Wright-Fisher model (1.48) or any of its generalizations. Even for models such as (3.30), where explicit formulas can often be found, the effects of the genetic parameters are sometimes obscured by the complexities of the expressions that arise. For both these reasons, it would be most useful to us if we could find approximate formulae for these quantities by reasonably accurate expressions which are not only comparatively simple, but which also display explicitly the effects of the various genetic parameters involved. Fortunately there exists a general approach which very often does all this for us, namely in approximating the discrete process by a continuous-time continuous-space diffusion process.