Mathematical Sciences: Nonlinear Demographic Dynamics: Mathematical Models, Biological Experiments, and Data Analyses

9625576库欣 种群生物学的一个中心问题是理解和解释观察到的动物数量波动。 非线性动力学的研究开辟了一条道路，人口研究的一个新阶段，实验直接集中在现象，如平衡，周期和非周期循环，混沌。 研究人员进行一系列对非线性种群理论测试至关重要的活动：从生物学翻译成数学的正式语言，到数学模型的分析，到数据分析统计技术的开发和应用，到生物实验的设计和实施。 实验中使用拟谷盗属的面粉甲虫的实验室种群。 通过他们的研究，研究人员提供了严格的实验测试的非线性人口现象和行为。 其中包括：（1）从稳定平衡到不变循环的动态转变（2）瞬态和间歇动力学，旨在定义与随机种群模型一起使用的非周期性的实用概念，并测试随机非线性模型预测的一些不寻常的瞬态行为;（3）以迁移为纽带的甲虫种群的集合种群动态;（4）环境周期性与非线性人口效应相互作用所产生的动态行为。 研究人员研究生物种群（特别是昆虫种群）如何随时间波动，以及不同的环境如何导致这些波动发生截然不同的变化，有时甚至是意想不到的变化。 这项研究是通过一个跨学科的计划，集成了复杂的数学模型和统计分析的设计和实验室实验的实施，使用甲虫的物种，是经济上重要的害虫。 研究人员试图描述和解释人口波动的各种模式，从有规律的和可预测的到无规律的和“混乱的”。“他们试图了解引起这些不同种类的人口行为的环境条件。 如果要预测环境扰动和操纵（人为或自然）对生物种群的影响，这种理解是必不可少的。 这些影响具有深远的后果，从粮食生产和虫害防治到野生动物管理和物种多样性保护。

9625576 Cushing A central question in population biology is that of understanding and explaining observed fluctuations in animal numbers. The study of nonlinear dynamics has opened the way to a new phase of population research in which experiments are focused directly on phenomena such as equilibria, periodic and aperiodic cycles, and chaos. The investigators undertake a spectrum of activities essential to the testing of nonlinear population theory: from the translation of biology into the formal language of mathematics, to the analysis of mathematical models, to the development and application of statistical techniques for the analysis of data, to the design and implementation of biological experiments. Laboratory populations of flour beetles of the genus Tribolium are used in the experiments. By means of their studies the investigators provide rigorous experimental tests of nonlinear population phenomena and behavior. These include: (1) dynamical transitions from stable equilibria, to invariant loops (aperiodicities), to period locking, to strange attractors and chaos; (2) transient and intermittent dynamics with aims towards defining practical concepts of intermittency for use with stochastic population models and the testing of some of the unusual transient behaviors forecast by stochastic nonlinear models; (3) the dynamics of meta-populations using beetle populations linked by migration; and (4) the dynamical behaviors that can be produced by the interaction of environmental periodicities with nonlinear demographic effects. The investigators study how biological populations (in particular, populations of insects) fluctuate in time and how different circumstances can lead to drastically different, and sometimes unexpected, changes in these fluctuations. This study is carried out by means of an interdisciplinary program that integrates the use of sophisticated mathematical models and statistical analysis with the design and implementation of l aboratory experiments using species of beetles that are economically important insect pests. The investigators seek to describe and explain a variety of patterns in population fluctuations, ranging from those that are regular and predictable to those that are irregular and "chaotic." They seek to understand the environmental conditions that give rise to these various kinds of population behavior. This understanding is essential if the impact on biological populations of environmental perturbations and manipulations (by Man or by Nature) is to be predicted. These impacts have far-reaching consequences, ranging from food production and pest control to wildlife management and the conservation of species diversity.