Optimal dispersal range and seed size in a stable environment

The evolutionarily stable (ESS) dispersal range for annual plants is studied in a stable environment when there is a trade-off between seed survivability and dispersal range via seed size. Larger seed size is more beneficial in the competition for safe sites, but likely to be dispersed a shorter distance and to suffer competition among siblings. Previously Hamilton & May found that dispersal can be adaptive in a stable environment to reduce competition among sibs, but they assumed that dispersers were likely to enter all the patches equally-this is not suitable for many terrestrial plants with limited dispersal range. In this article I discuss the evolution of dispersal range for wind dispersed seeds when dispersal range is tightly coupled with seed size. I assume that the density of dispersed seed follows a two-dimensional normal distribution function, with variance decreasing with seed size. Due to the trade-off between the seed number and the survivability of a seedling offspring, there is a seed size (w) over tilde that maximizes the product of the two quantities. This is the optimal seed size when size-dependent dispersal is neglected. The ESS seed size considering the size-dependent dispersal w* is also calculated by neglecting the effect of spatial clumping of relatives. Under the environment unfavorable for seed dispersal, the ESS seed size w* can be much smaller than the optimal seed size (w) over tilde, but there is a lower limit for the ESS dispersal range even in the extremely sticky environment. Even if the dependency of seed survivability on the seed size is so weak that the cost of long-range dispersal is small, the ESS seed dispersal range cannot become very large. These results are confirmed by individual-based computer simulations with more realistic assumptions considering spatial clumping of non-sib relatives. (C) 1998 Academic Press Limited.