Variable timing of reproduction in unpredictable environments: adaption of flood plain plants

We study the evolutionarily stable reproductive timing of annual plants that face unpredictable environmental disturbances. Plants living in a riverbed often experience a disturbance before they reproduce, suffering major fitness loss. Plants reproducing prior to the flood season are free from the risk of lost reproduction, but a small flowering plant can produce only a few numbers of seeds. If the date of disturbance is unpredictable, a mixed strategy of reproductive timing may evolve in which individuals of the same genotype have different reproductive dates. We calculate the evolutionarily stable phenotype distribution analytically. Depending on parameters, the ESS distribution is either (1) a timid strategy-the plant reproduces when small, prior to the major disturbance season; (2) a bold strategy-the plant reproduces only when it is fully grown; (3) a mixture of early and late reproduction; or (4) dates of reproduction spread over a wide interval. We also examine the effects of developmental and environmental noises that make realized flowering dates deviate from that programmed by the genotype, which follows the ESS distribution. In the presence of noise, the ESS distribution of programmed timing of reproduction is discrete.