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

本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，模拟结果将提供一个更深入的了解的基本过程的大型蚤的人口响应的环境变化。这些发现将对环境的可持续性产生重要的影响，因为D。麦格纳是一种毒性敏感的物种，在淡水生态系统中发挥着至关重要的作用，是浮游植物的摄食者，也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，旨在与研究生，博士后，教师和生态学，毒理学和数学界的研究人员分享创新的努力，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，包括那些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、结构化种群模型（SPM）被很好地表征为用于描述跨越各种物种的聚集生态数据，并且在估计种群水平对环境中的自然变化的响应（例如，气候变化）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，纵向尺寸或年龄分布）可能高得不合理，从而限制了这些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，并且可能难以单独从种群水平进行估计。本研究的总体目标包括三个目的：（目的1）测试一种新的参数估计框架（包括随机微分方程和Prohorov度量）的能力，以估计人口水平数据中SPM的人口统计率的个体间变异性。(Aim 2）开发一个参数估计框架，用于估计SPM人口统计学比率的个体间变异性，该框架利用生物体水平和人口水平数据。研究人员将量化在此框架内使用生物体水平数据对估计人口统计率分布和降低参数不确定性的影响。(Aim 3）在估计个体间变异性的统计框架内，将最优实验设计理论扩展到SPM的应用。使用这个扩展的理论，研究人员将测试实验设计复杂性对减少SPM参数不确定性的影响，使用生物体水平和人口水平的数据。为了验证这些方法，研究人员将使用一种水蚤（Daphnia magna）收集实验数据，这是一种在进化、毒理学、生态学和基因组学方面具有重要生态意义的生物。研究人员的目标是开发一种新的方法，定量地连接和传播的评估D。大有机体反应（即，环境变化，人口水平），从而使生物体对生态系统逆境的反应的因果关系。

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.