Spectral analysis of population time series using nonlinear stochastic models: quantitative tools and experiments

提案Id: DMS - 0443803机构：洛克菲勒大学；项目：数学生物学；主要研究者和共同负责人：Cohen， Joel E., Constantino, Robert F., and deccharnais, Robert, a .标题：摘要了解动态模型（包括物理模型和生物模型）的非线性与动态模型参数的随机变化之间的相互作用是包括生态学和种群生物学在内的许多自然科学分支的基本挑战。到目前为止，人们对种群动态中的非线性效应与环境变化的相互作用知之甚少。该项目旨在了解内部和外部产生的人口波动来源之间的相互作用及其相对重要性。它还试图了解低频对许多外地人口时间序列的支配作用与低频对许多环境波动的支配作用之间的关系。项目目标：1)开发新的计算数学方法，在频域上拟合生态时间序列数据的非线性随机模型；2)开发推断影响经验种群时间序列的环境扰动的频谱特性的方法；3)将新的频域拟合技术应用于面粉甲虫种群动态实验中没有施加环境变异性的现有数据，以及这些数据在时域上已经经过良好测试的模型；4)设计、实施和分析实验，以测试红移、白移和蓝移环境可变性对具有已知种群动态的系统的影响（类比于光，以低频波动为主的可变性称为红移，以高频波动为主的可变性称为蓝移，所有频率均代表的可变性称为白移）；5)将获得的见解应用于该领域的重要生态系统（与实验室中的相比）。决定某些动物种群动态的固有生物过程可能导致它们混乱地波动。外部环境的变化（例如，天气或人为干扰）也可能导致动物种群不可预测的波动。环境波动和固有生物过程之间的相互作用可以产生目前无法简单解释的巨大、复杂和多样的影响。影响系统的环境噪声性质的微小变化有时会被内部系统动力学放大和改变，从而在种群波动方面产生实质性和多样化的质的变化。该项目旨在开发数学和统计工具，以了解和模拟动物种群内部驱动的波动和外部驱动的波动之间的相互作用。研究的重点是改变主要环境波动频率的影响。例如，初步的模型预测，被广泛用作动物种群动态实验模型的Tribolium粉甲虫的实验室种群的平均种群规模可以随着主导环境变化频率在固定范围内的变化而增加或减少，这取决于系统的内部动态。了解环境噪声和内部动态之间复杂的相互作用对于预测哪种影响会发生至关重要，因此，当需要更大的种群（濒危物种）或不需要（害虫，包括疾病的昆虫媒介）时，可能会产生影响。面粉甲虫系统的新实验将研究环境变异和内部动力学之间的相互作用。从这些实验中获得的知识和本项目开发的新分析技术可能对害虫控制、保护和控制人类疾病具有实际意义。

PROPOSAL Id : DMS - 0443803INSTITUTION: Rockefeller UniversityNSF PROGRAM: MATHEMATICAL BIOLOGYPRINCIPAL INVESTIGATOR and co-PI's: Cohen, Joel E., Constantino, Robert F., and Decharnais, Robert, A.TITLE: Spectral Analysis of Population Time Series using Nonlinear Stochastic Models Quantitative Tools and Exeriments ABSTRACTUnderstanding the interactions between nonlinearities in dynamical models (both physical and biological) and stochastic variation in the parameters of dynamical models is a fundamental challenge in many branches of the natural sciences, including ecology and population biology. Nonlinear effects in population dynamics interact with environmental variability in ways that are, thus far, poorly understood. This project seeks to understand the interactions between, and the relative importance of, internally and externally generated sources of population fluctuation. It also seeks to understand the relationship between the domination of many field population time series by low frequencies and the domination of many environmental fluctuations by low frequencies. The project aims to: 1) Develop new computational mathematical methods for fitting nonlinear stochastic models to ecological time series data in the frequency-domain; 2) Develop methods of inferring the spectral properties of environmental perturbations that affect empirical population time series; 3) Apply the new frequency-domain fitting techniques to existing data from population dynamics experiments on the flour beetle Tribolium that did not impose environmental variability, and to models of these data that are already well tested in the time-domain; 4) Design, conduct and analyze experiments to test the impact of red-shifted, white, and blue-shifted environmental variability on systems exhibiting known population dynamics (by analogy to light, variability dominated by low-frequency fluctuations is called red-shifted, variability dominated by high-frequency fluctuations is called blue-shifted, and variability with all frequencies equally represented is called white); and 5) Apply gained insights to important ecological systems in the field (by contrast to those in the laboratory). The inherent biological processes that determine the dynamics of some animal populations can lead them to fluctuate chaotically. Variations in the external environment (for example, weather or anthropogenic perturbations) can also lead to unpredictable fluctuations of animal populations. The interactions between the environmental fluctuations and the inherent biological processes can produce large, complex and varied effects that presently defy simple explanations. Small changes in the nature of the environmental noise affecting a system can sometimes be magnified and transfigured by the internal system dynamics to produce substantial and diverse qualitative changes in how a population fluctuates. This project seeks to develop mathematical and statistical tools to understand and model the interactions between internally driven fluctuations and externally driven fluctuations of animal populations. The research focuses on the effects of changing the frequencies of the dominant environmental fluctuations. Preliminary modeling predicts, for instance, that the average population size in a laboratory population of Tribolium flour beetles, widely used as an experimental model for animal population dynamics, can be increased or decreased as the dominant environmental-variation frequency changes across a fixed range, depending on the internal dynamics of the system. Understanding the complex interaction between environmental noise and internal dynamics is essential for predicting which effect will occur, and therefore could have implications when larger populations are desirable (endangered species), or undesirable (pests, including insect vectors of disease). New experiments on the flour beetle system will investigate the interactions between environmental variability and internal dynamics. The knowledge gained from these experiments and the novel analytical techniques developed in this project may have practical importance in pest control, conservation, and the control of human disease.