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

提案ID：DMS-0443803研究：洛克菲勒大学NSF计划：数学生物学调查员和合作者：Cohen，Joel E.，Constantino，Robert F.和Decharneis，Robert，A.TITLE：使用非线性随机模型定量工具和实验进行种群时间序列的频谱分析了解动力学模型(物理和生物)中的非线性和动力学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。人口动态中的非线性效应以迄今为止鲜为人知的方式与环境变异性相互作用。这个项目试图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。它还试图理解许多田间种群时间序列受低频支配和许多环境波动受低频支配之间的关系。该项目的目标是：1)发展新的计算数学方法，将非线性随机模型与生态时间序列数据在频域中拟合；2)发展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现有的没有施加环境变异性的粉甲种群动力学实验数据，以及这些数据的模型，这些数据在时间域中已经得到了很好的测试；4)设计、进行和分析实验，以测试红移、白移和蓝移环境变异性对展现已知种群动态的系统的影响(类比于光，由低频波动主导的变异性称为红移，由高频波动主导的变异性称为蓝移，所有频率相等的变异性称为白移)；以及5)将所获得的见解应用于野外重要的生态系统(与实验室中的研究形成对比)。决定某些动物种群动态的内在生物过程可能会导致它们的无序波动。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的不可预测的波动。环境波动和内在生物过程之间的相互作用可能产生巨大、复杂和多样的影响，目前难以简单解释。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态放大和改变，从而在人口波动方面产生实质性和多样化的质变。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。研究重点是改变主导环境波动的频率所产生的影响。例如，初步建模预测，被广泛用作动物种群动态实验模型的粉甲虫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的复杂相互作用对于预测将发生哪种影响至关重要，因此当更大的种群是可取的(濒危物种)或不可取的(害虫，包括传播疾病的昆虫)时，可能会产生影响。关于面粉甲虫系统的新实验将研究环境变异性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在该项目中开发的新的分析技术可能在害虫控制、保护和控制人类疾病方面具有实际意义。

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.