Sensitivity Analysis of Populations: New Models, New Applications

人口模型提供了诸如人口增长率、短期和长期人口动态、人口结构和灭绝风险等重要数量的估计。在所有这些情况下，重要的是评估模型结果对参数变化的敏感性，例如出生率、生长率、死亡率和迁移率。这些变化可能是由环境变化、进化变化、管理行动或根据新数据修订的估计造成的。该项目将为非线性人口模型的敏感性分析提供新的数学工具。结果将使用矩阵演算进行开发，并将应用于空间模型、流行病模型、收获模型以及育种和配对形成模型。敏感性分析在种群生物学的许多领域都具有重要意义。在进化生物学中，敏感性分析显示了生活史变化的适应度结果。在种群管理（包括濒危物种的保护、害虫的控制和资源的收获）中，它被用来评价管理策略的效果。这里开发的数学方法在生态学的许多其他领域也将有价值。该项目将通过教育推广、向有关人口管理的政府机构提供咨询以及培训一名博士后研究员，产生更广泛的影响。

Population models provide estimates of such important quantities as population growth rate, short- and long-term population dynamics, population structure, and extinction risk. In all these cases, it is important to evaluate the sensitivity of model results to changes in parameters, such as rates of birth, growth, death, and movement. Such changes can result from environmental change, evolutionary change, management actions, or revised estimates from new data. This project will produce new mathematical tools for the sensitivity analysis of nonlinear population models. The results will be developed using matrix calculus, and will be applied to spatial models, epidemic models, harvest models, and models for breeding and pair formation. Sensitivity analysis is significant to several areas of population biology. In evolutionary biology, sensitivity analysis shows the fitness consequences of changes in life histories. In population management (including the conservation of threatened species, the control of pests, and the harvest of resources) it is used to evaluate the effects of management strategies. The mathematical methods developed here will also be of value in many other areas of ecology. The project will have broader impacts through educational outreach, advice to government agencies concerned with population management, and training of a post-doctoral researcher.