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，以研究许多物种的种群动态。特别是，建模结果将有助于更深入地了解大型溞种群对环境变化反应的基本过程。这些发现将对环境的可持续性产生重要影响，因为D. magna是一种毒理学敏感物种，作为浮游植物的饲养者以及其他无脊椎动物和鱼类的食物来源，在淡水生态系统中发挥着至关重要的作用。研究人员将举办跨学科研讨会，以确保本研究中开发的计算工具广泛应用/适应其他物种、压力源和生物场景。这些研讨会旨在与生态学、毒理学和数学界的研究生、博士后、教师和研究人员分享创新成果，将在国家数学和生物合成研究所举行。研究人员将培训研究生和本科生，包括来自代表性不足的少数群体的学生，进行涉及人口生物学、毒理学、计算机科学、统计学和数学的多学科研究。结构化人口模型（SPM）具有很好的特征，可以描述跨领域的总体生态数据。种类繁多，可用于估计人口水平对环境自然变化（例如气候变化）的反应以及对环境的拟人化影响（例如生态毒理学风险）评估）。然而，仅使用人口水平数据（例如，纵向规模或年龄分布）对 SPM 进行参数化所涉及的不确定性可能非常高，从而限制了此类模型在理解和预测未来人口变化方面的实际效用。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种群水平的动态，并且可能很难仅从种群水平进行估计。本研究的总体目标包括三个目标：（目标 1）测试新颖的参数估计框架（涉及随机微分方程和 Prohorov 度量）从人口水平数据估计 SPM 的人口比率个体间变异的能力。 （目标 2）开发一个参数估计框架，利用组织层面和群体层面的数据来估计 SPM 人口统计比率的个体间变异性。研究人员将量化在此框架内使用有机体水平数据对估计人口比率分布和减少参数不确定性的影响。 （目标 3）将最优实验设计理论扩展到估计个体间变异性的统计框架内的 SPM。利用这一扩展理论，研究人员将使用有机体水平和群体水平数据来测试实验设计复杂性对减少 SPM 参数不确定性的影响。为了验证这些方法，研究人员将使用一种水蚤（大型溞）收集实验数据，这是一种在进化、毒理学、生态学和基因组学背景下具有重要生态意义的生物体。研究人员的目标是开发一种新的方法，定量连接和传播对 D. magna 生物体反应（即对环境变化、种群水平）的评估，从而实现生物体对生态系统逆境反应的因果关系。