Persistence and Pattern Formation in Biological Systems

研究者开发和研究了一些群体生态学和生物化学系统模式的反应-扩散模型。在低密度条件下，种群的空间分布会受到生长速度下降的影响，这种效应被称为Allee效应。例如，它可能是由于缺乏配偶，缺乏有效的授粉或收获造成的。主要目标是深入了解Allee和收获效应以及扩散行为如何影响物种的持久性和灭绝以及生物入侵的成败。为研究复杂动力学问题，开发了非线性椭圆型和抛物型偏微分方程和非线性泛函分析的新数学工具。重点是通过线性化无法获得的非线性现象和在简化的一维问题中无法观察到的更高空间域中的非模式。该项目以渔业管理、动物聚集、自催化反应等一系列实际问题为指导。该项目的第二行重点是模式形成机制，概括了艾伦·图灵的先驱工作。为完善图灵模式理论，建立了一种非线性高维机制，并成功地应用于现象学模型、经验底物抑制系统和自催化反应。该项目的一部分是研究人类干预对海洋物种自然进化的影响。在项目的第二部分，研究者考虑了自然界中随处可见的复杂图案的起源，比如贝壳和斑马或豹子身上的斑点图案。这些研究旨在了解和控制许多重要的自然现象，如商业海洋物种的持续和灭绝，以及生物化学过程中的复杂模式。该项目的成果有助于制定商业渔业和森林管理政策，以及开发新的生物技术模拟自然生命形式。

Shi The investigator develops and studies somereaction-diffusion models of population ecology and of patternformations of biochemical systems. The spatial distribution ofpopulations can be affected by depressed growth rate at lowerdensity, which is called the Allee effect. For instance, it canbe caused by shortage of mates, lack of effective pollination,or harvesting. The main goal is to gain insight into the waysthat Allee and harvesting effects and dispersal behaviorinfluence the persistence and extinction of species and thesuccess or failure of biological invasions. New mathematicaltools in nonlinear elliptic and parabolic partial differentialequations and nonlinear functional analysis are developed tostudy the complicated dynamics. Emphasis is on the nonlinearphenomena that can not be obtained through linearization and onpatterns in higher spatial domains that can not be observed insimplified one-dimensional problems. The project is guided by aseries of practical problems, from fishery management, animalaggregation, and autocatalytic reactions. A second line of theproject is focused on a pattern formation mechanism, generalizingthe pioneer work of Alan Turing. A nonlinear and higher spatialdimensional mechanism is established to refine Turing patterntheory, which has been successfully applied to phenomenologicalmodels, empirical substrate-inhibition systems, and autocatalyticreactions. One part of the project studies the impact of humaninterference on the natural evolution of marine species. In thesecond part of the project, the investigator considers the originof the generation of complex patterns found everywhere in thenature, like seashells and spotty patterns on a zebra or aleopard. These studies aim to understand and control manyimportant natural phenomena, such as the persistence andextinction of commercial marine species, and complex patternformations in biochemical processes. Results of the project canbe helpful for formulating policy on managing commercialfisheries and forests, and for developing new biotechnologysimulations of natural life forms.