Dictyostelium discoideum is a eukaryotic amoeba, which, when starvation is imminent, aggregates to form fruiting bodies consisting of a stalk of reproductively dead cells that supports spores. Because different clones may be involved in such aggregations, cheater strategies may emerge that allocate a smaller fraction of cells to stalk formation, thus gaining a reproductive advantage. In this paper, we model the evolutionary dynamics of allocation strategies in Dictyostelium under the realistic assumption that the number of clones involved in aggregations follows a random distribution. By determining the full course of evolutionary dynamics, we show that evolutionary branching in allocation strategies may occur, resulting in dimorphic populations that produce stalkless and stalked fruiting bodies. We also demonstrate that such dimorphisms are more likely to emerge when the variation in the number of clones involved in aggregations is large
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