Evolutionarily stable resource allocation for production of wind-dispersed seeds

We developed a game-theoretic model for wind-dispersed seed production to examine the seed mass-dispersal ability relationship and the evolutionarily stable distance of seed dispersal in terms of exploitation of safe sites. We assumed trade-offs between masses of the embryo (including albumen) and the wind-dispersal structures per seed, and also between seed mass and number of seeds per parent. We showed that ESS wing-loading is independent of embryo mass; that is, heavy seeds are not poor dispensers if the cost of producing wind-dispersal structures per unit area is constant. The ESS embryo mass per seed depends only on the factors which determine the probability of a seedling being established from a seed. However, wing-loading was found to increase with embryo mass when the change in length was isometric and there was a negative correlation between seed mass and dispersal ability. Thus, the area-mass relationship in wind-dispersal structures may have large effects on the ESS production of wind-dispersed seeds. On the other hand, given that only a limited number of adults can be established at a safe site, the ESS seed dispersal distance depends on the relative degree of sib to non-sib competition. A parent disperses its seeds over a wide area to exploit many safe sites if sib competition is strong. However, it disperses its seeds within a narrow area if the mean number of parents per unit area is large, or if non-sib competition is strong. Thus, in addition to an upper limit on the number of adults per safe site, the degree of sib and non-sib competition may be important for the ESS dispersal distance in wind-dispersed seeds.