The mathematical study on the evolution of life strategy in perennial plants

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Population dynamics and life history evolution in perennial plants are studied in terms of a transition matrix model which describes the stage-structure and the density-dependence. Main subjects are(1) The analysis of the invasible condition of mutant-types in the density-dependent matrix model.(2) The development of the analytical method of population dynamics in the density-dependent matrix model.(3) The evolution of the frequency of reproduction in plants.(4) The optimal allcation to seed reproduction and vegetative reproduction.In (1), invasible condition in the density-dependent matrix model was obtained. The result of (1) was published in Mathematical Biosciences in 1992 and in Kokyuroku, Research Institute for Mathematical Science, Kyoto University in 1993. In (2), we developed the analytical method of the population dynamics with stage-structure and density-dependence, using the census data of a temperate broad-leaved forest. The result of (2) is in submission to Journal of Ecology. Next, we analyzed the subject (3) in terms of the invasible condition obtained from (1). The result of (3) is in invasible condition. The result of (4) is also in submission to Evolution. I applied the result of (4) to a woodland herb, Syneilesis palmata and obtained the optimal allocation strategy to seed and vegetative reproduction. It is shown theoretically that reproducing only vegetatively is the optimal allocation of S.palmata. The result of the applied analysis is in press in Proceedings of Population Ecological Society (Japanese). Totally, the results of a series of studies in these two years are 2 published papers, 2 in-press papers, 3 submitted papers and 1 book-section paper.