Game-theoretical evolution of seed mass in multi-species ecological models

Within plant communities seed mass often varies over 3 to 5 orders of magnitude, yet simple evolutionary models predict a single optimum seed mass. Here we explore a class of models where seed mass determines 1) the number of seeds produced via a size number trade-off and 2) competitive ability plants arising from large seeds are assumed to have a competitive advantage over those derived from small seeds. In this setting the existence of a single-species global ESS seed mass requires the competitive advantage of large seeds over small ones to be unbounded. If there is a limit on the competitive advantage that large seeds obtain then it is always possible to find a smaller seed mass that will successfully invade. In such circumstances there might be a multi-species coevolutionarily stable coalition of several species each with a different seed mass. In this way a wide range of seed masses could be promoted by evolution. In general the adaptive landscape generated by these models is extremely flat leading to slow evolutionary dynamics. The implications of these results for the interpretation of observational, comparative and experimental studies are discussed.