Mathematical study on global dynamics in ecological systems

本研究旨在结合环境问题的各个方面，从理论上认识全球生态系统的时空变化。具体课题包括生态系统多样性保护、外来物种入侵、珍稀物种灭绝、生态系统功能等。代表性结果总结如下1。研究了两种竞争物种入侵开放空间的数学模型。研究了引起环境在时间和空间上变化的干扰的影响，并探讨了入侵物种和本地物种共存的原则。本文从C-N平衡的可能机制探讨了白蚁在社会性和共生进化驱动下的全球多样化。采用格构森林模型分析了森林生态系统林隙的形成过程。应用对逼近技术预测了间隙形成、扩展、再生和闭合的动力学过程。4 .利用1970-1992年期间日本外太平洋各渔场对幼鲭鱼种群的特定年龄的年繁殖能力和年龄捕获量的数据，评价了两种渔场即围网渔场和低网渔场影响的长期波动。采用分层扩散模型对入侵过程进行了分析，该模型同时考虑了近程扩散和长距离扩散。将模型应用于家雀的入侵，分别评估了远距离和短距离扩散对范围扩展的影响。

This study has aimed at theoretical understanding of global spatial and temporal changes in ecological systems with reference to various aspects of environmental issues. Specific subjects include conservation of diversity of ecosystems, invasion of alien species, extinction of rare species, function of ecosystems and so on. Representative results are summarized below.1. A mathematical model for invasions of two competing species into open spaces is investigated. The effect of disturbances that cause the environment to change in both time and space is examined, and principles of coexistence between the invading and native species are explored.2. Global diversification of termites driven by the evolution of sociality and symbiosis is discussed by means of the possible mechanism of C-N balance.3. Gap formation process in forested ecosystems is analyzed by using a lattice-structured forest model. A pair approximation technique is applied to predict the dynamics of gap formation, gap expansion, regeneration, and gap closure.4. By using data on the age-specific annual fecundity and catches-at-age by each fishery in a cub mackerel population in the Pacific Ocean off Japan during 1970-1992, the long-term fluctuation in impacts of two types of fisheries, the purse-seine fishery and the dip-net fishery, is evaluated.5. Invasion process is analyzed by using a stratified diffusion model, in which both the short and long range dispersals are taken into account. Applying models to the invasion of the House Finch, the effects of long- and short- distance dispersals on the range expansion are evaluated separately.