The evolution of dispersal and seed size in plant communities

Uniting frameworks used by Hamilton and May (1977), Levin et al. (1984) and Ezoe (1998), we show that the problem of the evolution of seed size - or of any other single dispersal-determining trait - can, under certain conditions, be understood as a constrained optimization problem. We find a function, F, whose maxima represent convergence stable strategies -evolutionary attractors towards which selection will drive populations (given sufficient diversity of types either initially or generated through mutation). This function has a nice interpretation as the product of competitive ability and fecundity (both squared) and a functional describing the spread of the dispersal kernel. Using ideas pioneered by Dan Cohen and the theory of adaptive dynamics, we explore the consequences for the evolution of dispersal and seed size in populations, focusing on examples in metapopulations, with some comments on more general spatial models.