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

利用过渡矩阵模型研究了多年生植物种群动态和生活史演化，该模型描述了植物的阶段结构和密度依赖关系。主要研究内容有：(1)密度相关矩阵模型中突变型的不侵条件分析。(2)发展了基于密度依赖矩阵模型的种群动态分析方法。(3)植物繁殖频率的进化。(4)种子繁殖和营养繁殖的优化配置。在(1)中，得到了密度相关矩阵模型的不侵条件。(1)的结果分别发表于1992年的《数理生物科学》和1993年的《京都大学数理科学研究所》。(2)以温带阔叶林为研究对象，建立了具有阶段结构和密度依赖性的种群动态分析方法。(2)的结果已提交给《生态学杂志》。接下来，我们根据从(1)中得到的不侵条件对主体(3)进行分析。(3)的结果处于不可侵入状态。(4)的结果也是服从于进化论。将(4)的结果应用于林地草本植物棕榈木（Syneilesis palmata），得到了种子和营养繁殖的最优配置策略。从理论上证明，只进行营养繁殖是棕藓的最优配置。应用分析的结果发表在《人口生态学会学报》（日文）上。这两年的一系列研究成果共发表论文2篇，出版论文2篇，投稿论文3篇，分书论文1篇。

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.