The Optimal Allocation for Seed Reproduction and Vegetative Reproduction in Perennial Plants: An Application to the Density-dependent Transition Matrix Model

The optimal allocation for both seed and vegetative reproduction is analysed for hypothetical perennial plants with three stages of growth (seedling, juvenile and mature). The density-dependent transition matrix model, which describes the density-dependent dynamics with a stage-specific pattern of reproduction and mortality, is employed in the analysis. When the survival rates at younger stages are density-dependent, the following results are obtained. (1) It is necessary for the interior optimal solution that the trade-off curve between the numbers of seeds and vegetative propagules is concave. (2) The optimal allocation between seeds and vegetative propagules is independent of the survival rates at younger stages. Therefore, the causes of decreasing the survival rates at younger stages, such as herbivory of seedlings, do not affect the optimal allocation. (3) In the habitat where the survival rates at older stages are low, due to severe environmental conditions, perennial plants with more seed reproduction are favored. On the contrary, perennial plants with more vegetative reproduction are favored in the habitat where the survival rates at older stages are high due to the favorable environmental condition. Among the above three results, (1) is the same result as was derived in the density-independent model. However, (2) and (3) are derived from the density-dependence of survival rates at younger stages.