Simulation analyses of the evolution of intra-inflorescence flowering patterns assuming selection on anthesis interval among individual flowers

What conditions select flowering patterns within inflorescences, or variation in the anthesis interval within inflorescences among plants? Under what conditions are gradual blooming and simultaneous blooming, both traits related to floral display size, advantageous? We constructed a simulation model in which the opening times and longevities of individual flowers within inflorescences, the sizes of attractive structures of individual flowers, and the numbers of ovules and pollen grains produced by individual flowers evolve. Individual plants in the population compete for pollinators, and plants are selected by pollinators according to their floral display sizes and amounts of resources allocated to attractive structures. We found that, if the proportion of pollen on a pollinator deposited on a stigma was low, gradual blooming did not evolve even if inbreeding depression was greater than 0.5. This is because the amount of outcross-pollen on pollinators decreased at a low rate during flower visits within a single inflorescence, and the selfing rate was suppressed to a low level even if the floral display size was large. On the other hand, if the proportion of pollen deposition was high, gradual blooming evolved even if inbreeding depression was smaller than 0.5. This may be because gradual blooming can enhance pollen delivery to other plants by reducing the loss of self-pollen by geitonogamy. On the other hand, allocation ratios among floral organs (female and male organs and attractive structures) were independent of the degree of simultaneous and gradual blooming within inflorescences. We concluded that the evolution of gradual blooming is more strongly affected by the proportion of pollen on a pollinator deposited on a stigma than by inbreeding depression.