Collaborative Research: Nonlinear Population Dynamics: Mathematical Models, Biological Experiments, Data Analyses

Costantino9981374了解动物数量的波动是种群生物学中的一个核心问题，具有深远的影响，并对从食品生产到物种保护等一系列问题都有影响。非线性动力学为种群研究开辟了一个新的阶段，理论和实验主要集中在周期和准周期、混沌和奇异吸引子、多重吸引子和复杂吸引盆、鞍集及其稳定流形等现象。这个由罗伯特·科斯坦蒂诺、吉姆·库欣、布莱恩·丹尼斯、罗伯特·德沙奈斯和尚德尔·汉森合作的跨学科项目涵盖了对测试非线性人口理论至关重要的一系列活动：将生物学翻译成数学语言并返回，确定性和随机模型的分析，用于数据分析的统计技术的开发和应用，以及生物实验的设计和实现。对粉甲虫的一系列实验为非线性现象提供了严格的实验测试。主题包括随机、混沌和种群控制背景下的非线性，周期性环境对动物数量的影响，人口动态和自然选择，非平衡物种相互作用，以及与模型的参数和验证有关的统计问题。通过对动物种群潜在动态的良好理解，生态学家可以预测环境退化的后果，并学习更好的方法来管理自然种群和控制害虫种群。例如，其中一项实验表明，通过利用无菌系统的特点--对初始条件的敏感性，管理者可以在关键时间进行微小扰动，在不使用化学杀虫剂的情况下大幅减少害虫种群数量。跨学科研究团队将生态学理论与实验相结合，为数学在生态问题中的应用带来了新的技术。该项目得到了MPS中的应用数学、计算数学和统计程序以及BIONAL中的种群生物学和生态学程序的支持。

Costantino9981374 Understanding the fluctuations in animal numbers is acentral issue in population biology that has far-reaching impacton and implications for problems ranging from food production tothe conservation of species. Nonlinear dynamics opens the way toa new phase of population research in which theory andexperimentation focus on phenomena such as cycles andquasi-periodicity, chaos and strange attractors, multipleattractors and complicated basins of attraction, saddle sets andtheir stable manifolds, and so on. This interdisciplinaryproject, in which Robert Costantino, Jim Cushing, Brian Dennis,Robert Desharnais, and Shandelle Henson collaborate, covers aspectrum of activities essential to testing nonlinear populationtheory: the translation of the biology into the language ofmathematics and back again, the analysis of deterministic andstochastic models, the development and application of statisticaltechniques for the analysis of data, and the design andimplementation of biological experiments. A series of experimentswith flour beetles of the genus Tribolium provide rigorousexperimental tests of nonlinear phenomena. Topics includenonlinearity in the context of stochasticity, chaos andpopulation control, the impact of periodic environments on animalabundance, demographic dynamics and natural selection,nonequilibrium species interactions, and statistical questionsconcerning parameterization and validation of models. With a sound understanding of the underlying dynamics ofanimal populations, ecologists can anticipate the consequences ofenvironmental degradation and learn better ways to manage naturalpopulations and control populations of pests. For example, one ofthe experiments suggests that, by taking advantage of the"sensitivity to initial conditions" that is the hallmark of achaotic system, managers can dramatically decrease pestpopulation numbers without the use of chemical pesticides bymaking small perturbations at critical times. The marriage ofecological theory and experiments by the interdisciplinaryresearch team leads to new techniques for the application ofmathematics to ecological problems. The project is supported bythe Applied Mathematics, Computational Mathematics, andStatistics programs in MPS and the Population Biology and Ecologyprograms in BIO.