QEIB - Nonlinearities in Stochastic Population Dynamics

大多数自然过程，从亚原子粒子之间的相互作用到决定天气的大气过程，都是非线性的，这意味着变量之间的关系不能用简单的线条来描述。 非线性会导致混沌和灾变等数学现象，其中系统输入的微小变化会导致输出的巨大变化。 生态系统充满了非线性，此外，它们还经历着由随机的、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。拟议的工作将解决非线性动力学和随机噪声之间的相互作用，在模型生态系统中，试图找到一般属性，将使自然系统更可预测。 尽管非线性动力学和随机噪声之间存在极其复杂的相互作用，但来自真实的生态系统的许多数据集显示出近似噪声但线性系统行为的模式。 该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来证实或反驳这一观察结果。 研究的另一部分将从理论的角度询问非线性随机系统预期表现出什么类型的动态，以及这些预期实际上是否类似于真正的线性随机动态。 许多关键的环境问题需要随机种群模型。这项拟议中的工作将为生态学家解释数据提供新的工具。 将有一个优秀的博士后培训，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