A seasonal hybrid model for the evolution of flowering onset. (21st August 2021) - Morris, Patricia; Lutscher, Frithjof
Highlights: Plants face a trade-off between growing large and flowering early. Model tracks the distribution of the time of flowering onset in a plant population. We show that an intermediate flowering onset is an ESS in a simple case. We develop moment generating functions for the hybrid system. This method confirms that intermediate flowering time is a convergent stable state. Abstract: In strongly seasonal environments, many plants tend to divide the favorable season into an earlier part, where they allocate resources to vegetative growth, and a later part, where they allocate resources to reproduction. The onset of flowering typically indicates the shift from one to the other. We derive and analyze a model for the evolution of flowering onset on the phenotypic level. Our model tracks a continuous phenotype distribution through the various seasons from year to year. We analyze a special case of a monomorphic population with the tools of adaptive dynamics. We analyze the general case by a moment approximation. We find that (the mean of) flowering onset converges to some intermediate time within the favorable season. In the monomorphic case, we prove that this is an ESS. The moment approach reveals that there are different time scales involved on which the plant density, the mean flowering onset, and its variance converge.