Mathematical Models of Selection and Interaction Among Populations

人类是生态群落中的一个物种。生态群落的功能可以强烈地影响人类的福祉。了解生态群落的一种方法是利用食物网。食物网描述了生态群落中谁吃谁。食物网对人类健康和福祉很重要，因为在食物网的每一个捕食者-猎物环节中，化学和生物毒素往往集中在一起，代谢的能量也会损失。本研究的目的是表明，食物网的多样性结构可以用少数的一般原则来解释，并利用这些一般原则来理解生态群落的结构和动态。对食物网的理解已经有了实际应用。将与菲律宾的国际水稻研究所合作，构建和分析稻田的食物网。这项研究可能为改进农业害虫的生物防治提供新的建议，并为检验关于食物网结构的基本科学概括提供了机会。大量的工作将致力于回答由生态学和种群研究提出的数学、统计学和计算方面的新问题。在开发用于研究生物学问题的数学工具时，存在智力杠杆作用，因为经验表明，在一种生物学环境中开发的概念、模型和分析技术通常对其他环境有帮助。

Humans are one species in an ecological community. The functioning of the ecological community can strongly affect human well-being. One approach to understanding an ecological community uses food webs. Food webs describe who eats whom in an ecological community. Food webs are important to human health and well-being because chemical and biological toxins are often concentrated, and metabolized energy is lost, in each predator-prey link of the food webs. The aim of the study is to show that the diverse structures of reported food webs may be explained by a small number of general principles, and to use these general principles to understand the structure and dynamics of ecological communities. An understanding of food webs has practiced applications. In collaboration with the International Rice Research Institute in the Philippines, the food web of rice fields will be constructed and analyzed. This study may yield novel suggestions for improved biological control of agricultural pests and provides an opportunity to test basic scientific generalizations about food web structure. A substantial effort will be devoted to answering new questions of mathematics, statistics, and computation raised by the study of ecology and populations. There is intellectual leverage in developing mathematical tools for studying biological problems, because experience shows that concepts, models, and analytical techniques developed in one biological setting are frequently helpful in others.