OPTIMAL DISPERSAL RANGE AND SEED SIZE IN A STABLE ENVIRONMENT

The evolutionarily stable (ESS) dispersal range for annual plants is s tudied in a stable environment when there is a trade-off between seed survivability and dispersal range via seed size. Larger seed size is m ore beneficial in the competition for safe sites, but likely to be dis persed a shorter distance and to suffer competition among siblings. Pr eviously Hamilton & May found that dispersal can be adaptive in a stab le environment to reduce competition among sibs, but they assumed that dispersers were likely to enter all the patches equally-this is not s uitable for many terrestrial plants with limited dispersal range. In t his article I discuss the evolution of dispersal range for wind disper sed seeds when dispersal range is tightly coupled with seed size. I as sume that the density of dispersed seed follows a two-dimensional norm al distribution function, with variance decreasing with seed size. Due to the trade-off between the seed number and the survivability of a s eedling 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 t he size-dependent dispersal w is also calculated by neglecting the ef fect of spatial clumping of relatives. Under the environment unfavorab le for seed dispersal, the ESS seed size w can be much smaller than t he optimal seed size (w) over tilde, but there is a lower limit for th e ESS dispersal range even in the extremely sticky environment. Even i f the dependency of seed survivability on the seed size is so weak tha t the cost of long-range dispersal is small, the ESS seed dispersal ra nge cannot become very large. These results are confirmed by individua l-based computer simulations with more realistic assumptions consideri ng spatial clumping of non-sib relatives. (C) 1998 Academic Press Limi ted.