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

利用描述种群阶段结构和密度依赖性的转移矩阵模型，研究了多年生植物种群动态和生活史演化。主要研究内容有：（1）密度依赖矩阵模型中多类模型的可侵性条件分析。(2)密度依赖矩阵模型中种群动态分析方法的发展。(3)植物繁殖频率的进化。(4)在（1）中，得到了密度依赖矩阵模型中的入侵条件。（1）的结果于1992年发表在Mathematical Biosciences上，1993年发表在京都大学数学科学研究所Kokyuroku上。在（2）中，我们利用温带阔叶林的调查数据，建立了具有阶段结构和密度依赖的种群动态分析方法。（2）的结果已提交给Journal of Ecology。接下来，我们根据从（1）获得的可侵入条件来分析主题（3）。（3）的结果是有创的。（4）的结果也服从进化论。我将（4）的结果应用于林地草本植物掌叶针吸草，得到了种子和营养繁殖的最优分配策略。从理论上证明，只繁殖蔬菜是掌叶薯蓣的最优配置。应用分析的结果发表在《人口生态学会学报》（日文）上。两年来的系列研究成果包括2篇已发表论文、2篇在刊论文、3篇投稿论文和1篇图书部分论文。

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.