QEIB - Nonlinearities in Stochastic Population Dynamics

从亚原子粒子之间的相互作用到决定天气的大气过程，大多数自然过程都是非线性的，这意味着变量之间的关系不能用简单的直线来描述。非线性会导致诸如混沌和灾难这样的数学现象，在这些现象中，系统输入的微小变化会导致输出的大变化。生态系统充满了非线性，此外，它们还经历了由随机的、不可预测的环境产生的随机噪声。非线性动力学和随机噪声的结合有可能使生态系统变得无法预测，因为自然系统的噪声加剧了非线性的混沌和灾难。拟议的工作将研究模型生态系统中非线性动力学和随机噪声之间的相互作用，试图找到使自然系统更可预测的一般性质。尽管在非线性动力学和随机噪声之间可能存在极其复杂的相互作用，但来自真实生态系统的许多数据集显示出与噪声但线性系统的行为相似的模式。研究项目的一部分将致力于通过开发统计技术来检测生态数据中的非线性，以证实或驳斥这一观察结果。研究的另一部分将从理论的角度询问非线性随机系统将表现出什么类型的动力学，以及这些期望实际上是否类似于真正的线性随机动力学。许多关键的环境问题都需要随机人口模型。这项拟议的工作将为生态学家提供解释数据的新工具。将为一个博士后提供出色的培训，并为本科生提供许多机会

Most natural processes, from interactions among subatomic particles to atmospheric processes that dictate weather, are nonlinear, meaning that the relationships among variables cannot be described by simple lines. Nonlinearities lead to such mathematical phenomena as chaos and catastrophes, in which small changes to the inputs to a system lead to large changes in the outputs. Ecological systems are full of nonlinearities, and in addition they experience stochastic noise created by a random, unpredictable environment. The combination of nonlinear dynamics and stochastic noise has the potential for making ecological systems impossible to predict, because the chaos and catastrophes of nonlinearities are exacerbated by the noisiness of natural systems.The proposed work will address the interactions between nonlinear dynamics and stochastic noise in model ecological systems in an attempt to find general properties that will make natural systems more predictable. Even though there is the potential for extremely complex interactions between nonlinear dynamics and stochastic noise, many data sets from real ecological systems show patterns approximating the behavior of noisy but linear systems. Part of the research project will be directed towards confirming or refuting this observation by developing statistical techniques to detect nonlinearities in ecological data. The other part of the research will ask from a theoretical perspective what types of dynamics are expected to be exhibited by nonlinear stochastic systems, and whether these expectations are in fact similar to truly linear stochastic dynamics. Many key environmental problems require stochastic population models. The proposed work will offer ecologists new tools for interpreting data. There will be excellent training for one post-doc, and many opportunities for undergraduates