Donald's ideotype and growth redundancy: a game theoretical analysis

In a crop monoculture, the most competitive individuals will gain a disproportionate share of the limiting resource in the environment, and are thus favored by natural selection. However, a partitioning of limited assimilates to organs for competition requires a reduced partition to grain production. Re ̄ecting on this problem, Donald proposed that natural selection through competition would generally result in `over-growth' of some resource-foraging organs, which may be termed `growth redundancy'. According to Donald, an important way to increase the yield potential in annual seed crops would be to develop a `communal' ideotype that minimizes growth redundancy. Selection through competition within a crop seems to be an ideal topic for analysis using game theory, because the optimal strategy for each plant depends on what the other plants do. As a consequence, there are con ̄icts of interest between the individuals in a crop population and the optimizing process is actually a noncooperative game in which each individual is a player which optimizes its strategy, given other player's strategies. A game theoretical model of this kind is presented in this paper, and corroborates the Donald's view. It is shown that the optimal resource partition maximizing a crop's yield is never evolutionarily stable, implying a high incidence of growth redundancy in modern crop plants. Growth redundancy represents a particular version of the famous `tragedy of the commons'. # 1999 Elsevier Science B.V. All rights reserved.