Mathematical models for ecological processes in rivers and fragmented habitats

我的研究计划的主要目标是通过数学模型的开发和分析以及数据模型拟合，机械地理解和解释空间异质环境中物种种群和群落的格局。了解群落的组成、物种的起源和维持多样性在保护生物学和生态系统管理中具有重要意义。在上述问题中，环境在空间和时间上的异质性起着至关重要的作用。通过几种(非线性)反馈机制(竞争、扩散、适应……)，它决定了种群的生存能力、物种范围的扩展和边界以及它们的表型结构。我专注于河流生态系统，在那里单向流动和水池冲刷结构创造了几种形式的异质性。所研究的数学模型在空间上是明确的，在时间上是离散的或连续的。分析揭示了行波持续、存在和速度的条件、定态的稳定性和斑图形成的可能性。

The main objective of my research program is to mechanistically understand and explain patterns of  populations and communities in spatially heterogeneous environments through development and analysis of mathematical models and through data-model fitting. Understanding the composition of communities, the origin of species, and the maintenance of diversity is of major importance in conservation biology and ecosystem management. Environmental heterogeneity in space and time plays a crucial role in all the above questions. Through several (nonlinear) feedback mechanisms (competition, dispersal, adaptation...), it determines viability of populations,  the extend and boundary of species' ranges, and their phenotypic structure. I concentrate on stream ecosystems where unidirectional flow and pool-riffle structure create several forms of heterogeneity. The mathematical models studied are spatially explicit and either discrete or continuous in time. The analysis reveals conditions for persistence, existence and speed of traveling waves, stability of steady states and possibilities of pattern formation.