Evolutionarily stable stalk to spore ratio in cellular slime molds and the law of equalization in net incomes

The evolutionarily stable stalk ratio (ESSR) in the cellular slime molds is studied when the fruiting body is formed by multiple clones of various size. The survival probability of a spore cell is assumed to depend on the stalk ratio and the fruiting body size. ESSR is obtained as the non-co-operative equilibrium (Nash solution) that maximizes the fitness of each clone. The following two predictions are obtained: (1) the number of spore cells produced by each clone forming a fruiting body tends to be equalized, even if a variation in clone size exists. As a result, the larger clones do not necessarily enjoy higher fitness than the smaller ones. (2) The stalk ratio and the overall fitness of the fruiting body decrease as the genetic diversity in the fruiting body increases. A condition for the stalk to spore ratio to be invariant of overall fruiting body size is also investigated. Finally, "the law of equalization in net incomes" is proposed, extending result (1) into the broader range of resource allocation problems.