Maximizing final yield when growth is limited by time or by limiting resources

A mathematical model is developed of growth and seed production in plants when the growing period is limited. The time course of the partition coefficient of photosynthetic products between vegetative and reproductive growth which maximizes final seed yield, i.e. the optimal strategy, has been worked out. For a given growing period t_s, the optimal strategy is to switch over from 100% vegetative growth to 100% reproductive growth at a time t_rM = t_s + r R - 1 RL, where R is the net photosynthetic production per unit leaf weight, L is the weight ratio of the leaves in the whole vegetative body of the plant, and r is the fraction of the leaf weight which is re-utilized for making seeds at the end of the growing period. When t_s is a random variable, the optimal transition from vegetative to reproductive growth is gradual, its spread increasing with the variance of t_s. The implications of the model are discussed with respect to the expected difference between wild and crop plants, and when the growing period is terminated by lack of water in the soil.