Elliptic partial differential equations with applications to population models with harvesting rates

椭圆偏微分方程及其在具有收获率的群体模型中的应用

• 批准号: 250187-2013
• 负责人: Lan, Kunquan
• 金额: $ 0.8万
• 依托单位: Ryerson University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=524949
• 关键词: Elliptic; partial; differential; equations; applications

Population models for species are used to study the behaviors of the populations or the interaction of two or more species. One important topic is to determine under what circumstances the species either survive or go extinct. According to human needs, the exploitation of biological resources and the harvesting of populations are commonly practiced in fishery, forestry, and wildlife management. To predict whether species will become extinct and to obtain insight into the optimal management of renewable resources, one needs to consider models which incorporate harvesting rates. The aim is to determine a harvestable quantity of the species without having the population die out. According to Clark's book (C. W. Clark, Mathematical Bioeconomics, The Optimal Management of Renewable Resources, second edition, John Wiley & Sons, New York, 1990), the management of renewable resources is thought to be based on the maximum sustainable yield (MSY). If the populations of the species are harvested by some process of over-exploitation (that is, harvesting rate is strictly greater than the MSY), then the species could become extinct.

物种的种群模型用于研究种群的行为或两个或更多物种的相互作用。一个重要的话题是在什么情况下确定该物种生存或灭绝的情况。根据人类的需求，在渔业，林业和野生动植物管理中，通常对生物资源的剥削和人群的收获通常进行。为了预测物种是否会灭绝并洞悉可再生资源的最佳管理，需要考虑包含收获率的模型。目的是确定物种的可收获数量，而不会使种群死亡。根据克拉克的书（C. W. Clark，《数学生物经济学》，《可再生资源的最佳管理》，第二版，John Wiley＆Sons，New York，1990年），可再生资源的管理被认为是基于最大的可持续产量（MSY）。如果该物种的种群是通过某种过度开发的过程收获的（即，收获率严格大于MSY），那么该物种可能会灭绝。