Biological Dynamics at Intermediate Time Scales

这个项目的目标是发展一个通用的理论在中间时间尺度的生物系统的动力学。 在短时间尺度上，生物系统的当前状态或当前方向提供了对未来状态的良好描述。在很长的时间尺度上，系统会陷入相对容易研究的可预测模式。 中间时间尺度位于这两种状态之间，可能包括系统行为中快速、难以预测但重要的变化。作为理解中间时间尺度的第一步，将在计算机上对基于a）具有少量相互作用物种的生态模型，B）具有少数神经元的神经模型或c）流行病模型的特定案例研究进行数值研究。 这些数值结果，然后将推广使用数学理论的基础上研究的动力学物理系统。由此产生的普遍性将允许确定什么时候像湍流这样的现象（种群规模明显不规则变化）或爆发（种群规模的快速、明显随机的大变化，由没有变化的时期分隔开）将出现在具有分布在空间上的相互作用物种的系统中，并且在各种其他生物系统中也是如此。所发展的理论将是普遍的，并且在生物组织的各个层次上具有广泛的适用性，从细胞水平到神经科学，再到个体种群的动态，再到生态系统。 一组特别重要的应用将是渔业管理、全球气候变化对生态系统服务的影响以及疾病的动态，所有这些都需要在适合人类主导系统的尺度上进行预测。 在这项工作的过程中，博士后学者和研究生将接受跨学科的培训，这将发展人力资本，以应对未来在理解复杂的生物系统方面的挑战。

The goal of this project is to develop a general theory for the dynamics of biological systems at intermediate time scales. At short time scales, the current state or the current direction of a biological system provides a good description of the future state. At very long time scales, systems settle into predictable patterns that are relatively easy to study. Intermediate time scales lie in between these two states and may include rapid, and harder to predict yet important, changes in system behavior. As a first step toward understanding intermediate time scales, specific case studies based on a) ecological models with a small number of interacting species, b) neural models with a few neurons or c) epidemic models will be studied numerically on a computer. These numerical results will then be generalized using mathematical theory based on the study of dynamical physical systems. The resulting generalizations will allow the determination of when phenomena like turbulence (apparently irregular changes in population size) or bursting (rapid, apparently random large changes in population size separated by periods without change) will arise in systems with interacting species distributed over space, and also in a variety of other biological systems.The theory developed will be general and of wide applicability across levels of biological organization ranging from the cellular level to neuroscience to the dynamics of individual populations to ecosystems. A particular set of important applications will be fisheries management, the impact of global climate change on ecosystem services, and the dynamics of diseases, all of which will require prediction on scales appropriate for human dominated systems. In the course of this work postdoctoral scholars and graduate students will receive interdisciplinary training that will develop the human capital to meet future challenges in understanding complex biological systems.