Mathematical Methods to Enable Accurate Parameterization of Density-Dependent Structured Population Models

实现密度相关结构化总体模型精确参数化的数学方法

• 批准号: 1514929
• 负责人: Kevin Flores
• 金额: $ 50万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1514929&HistoricalAwards=false
• 关键词: Mathematical; Methods; Enable; Accurate; Parameterization

The methodology developed in this research project will provide important computational tools, broadly applicable to biological modeling, to study population dynamics across many species. In particular, the modeling results will provide a deeper understanding of fundamental processes underlying population response of Daphnia magna to changes in the environment. The findings will have important implications for environmental sustainability, since D. magna is a toxicologically sensitive species that plays a vital role in freshwater ecosystems as feeders on phytoplankton and as a source of food for other invertebrates and fish. The investigators will hold interdisciplinary workshops to ensure broad application/adaptation of the computational tools developed in this research to other species, stressors, and biological scenarios. These workshops, designed to share the innovative efforts with graduate students, postdoctoral associates, faculty, and researchers in the ecology, toxicology, and mathematics communities, will be held at the National Institute for Mathematical and Biological Synthesis. The investigators will train graduate and undergraduate students, including those from underrepresented minority groups, in multi-disciplinary research involving population biology, toxicology, computer science, statistics, and mathematics.Structured population models (SPMs) are well characterized for describing aggregate ecological data across a wide variety of species and have utility in estimating population-level responses to natural changes in the environment (e.g., climate change) as well as anthropomorphic influences on the environment (e.g., ecotoxicological risk assessments). Yet, the uncertainty involved in parameterizing SPMs using only population-level data (e.g., longitudinal size or age distributions) can be unreasonably high, thereby limiting the practical utility of such models to understand and predict future population change. A fundamental problem associated with this high uncertainty is that inter-individual variability can influence population-level dynamics and may be difficult to estimate from population level alone. The overall objectives in this research include three aims: (Aim 1) To test the ability of a novel parameter estimation framework (involving random differential equations and the Prohorov metric) to estimate inter-individual variability in demographic rates for SPMs from population-level data. (Aim 2) To develop a parameter estimation framework for estimating inter-individual variability in demographic rates for SPMs that utilizes both organismal-level and population-level data. The investigators will quantify the effect of using organismal-level data within this framework on estimating demographic rate distributions and reducing parameter uncertainty. (Aim 3) To extend optimal experimental design theory for application to SPMs within a statistical framework that estimates inter-individual variability. Using this extended theory, the investigators will test the effect of experimental design complexity on the reduction of parameter uncertainty for SPMs using organismal-level and population-level data. To validate these methods, the investigators will collect experimental data using a species of water flea, Daphnia magna, an ecologically important organism in the context of evolution, toxicology, ecology, and genomics. The investigators aim to develop a novel methodology that quantitatively connects and propagates the assessment of D. magna organismal responses (i.e., to environmental change, to the population level), thereby enabling the causal association of organismal responses to ecosystems adversity.

该研究项目中开发的方法将提供重要的计算工具，广泛适用于生物建模，以研究许多物种的人群动态。特别是，建模结果将为水达尼亚·麦格纳（Daphnia Magna）对环境变化的种群反应的基本过程提供更深入的了解。这些发现将对环境的可持续性具有重要意义，因为D. magna是一种具有毒性敏感的物种，在淡水生态系统中起着至关重要的作用，作为对浮游植物的饲养者，并且是其他无脊椎动物和鱼类的食物来源。研究人员将举办跨学科研讨会，以确保对本研究中开发的计算工具的广泛应用/适应其他物种，压力源和生物学情景。这些研讨会旨在与研究生，博士后伙伴，教职员工和生态学，毒理学和数学社区的研究人员分享创新的工作，将在美国国家数学和生物综合研究所举行。调查人员将在涉及人口生物学，毒理学，毒理学，计算机科学，统计和数学的多学科研究中培训研究生和本科生，包括代表性不足的少数群体的学生。拟人化对环境的影响（例如生态毒理风险评估）。但是，仅使用人群级数据（例如纵向大小或年龄分布），参数化SPM的不确定性可能是不合理的，从而限制了此类模型的实际实用性，以理解和预测未来的人群变化。与这种高度不确定性相关的一个基本问题是，个体间的变异性会影响人口水平的动态，并且可能仅从人口水平就很难估算。这项研究的总体目标包括三个目的：（目标1）测试新的参数估计框架（涉及随机微分方程和ProHorov指标）的能力，以估计SPMS中人群中人群中的人口统计学率的个体间变异性。 （AIM 2）开发一个参数估计框架，用于估计使用有机体级别和人口级数据的SPM的人口统计学率的个体变异性。研究人员将量化在此框架内使用生物级数据对估计人口统计学率分布和降低参数不确定性的效果。 （AIM 3）在估计个体间变异性的统计框架内扩展将SPMS应用到SPM的最佳实验设计理论。使用这种扩展的理论，研究人员将使用有机体级别和种群级别数据来测试实验设计复杂性对SPMS参数不确定性降低的影响。为了验证这些方法，研究人员将使用一种水跳蚤，达芙妮·麦克纳（Daphnia Magna）（在进化，毒理学，生态学和基因组学的背景下）收集实验数据。研究人员旨在开发一种新颖的方法，该方法可以定量地连接并传播对麦格纳（D. magna）的生物反应（即环境变化，人口水平）的评估，从而实现了生态系统逆境的生物体反应的因果关系。