Temporal and Spatial Dynamics in Mathematical Ecology

数学生态学中的时空动力学

基本信息

批准号：
RGPIN-2020-03911
负责人：
Wang, Hao
金额：
$ 1.97万
依托单位：
University of Alberta
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2022
资助国家：
加拿大
起止时间：
2022-01-01 至 2023-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758366
关键词：
Temporal Spatial Dynamics Mathematical Ecology

项目摘要

This program focuses on temporal and spatial dynamics in mathematical ecology. The main objective is mechanistic formulation and rigorous analysis of ecological models. Novel mathematical approaches include nonsmooth differential equations in ecological stoichiometry and ecotoxicology, persistence theory and spreading speeds of hybrid partial differential equation and discrete-time models, and bifurcation theory of delay differential equations with applications to delayed diffusion operators for describing memory-based animal movement. Rich dynamics and new qualitative theory are waiting to be explored. Stoichiometric theory provides a fundamental microscopic approach to understand macroscopic phenomena. It includes multiple biological scales and allows the formulation of robust mechanistic, predictive, and experimentally testable models via chemical and physical laws. Applications include optimal foraging strategies, multi-scale comparison of aquatic and terrestrial ecosystems, impact of global carbon dioxide change, and cyanobacterial blooms. Ecotoxicology is a significant research area for the preservation and restoration of healthy ecosystems from industrial pollution. Via persistence and bifurcation analysis, I will perform risk assessment of toxicants on living organisms and their interactions. Spatial heterogeneity and natural delays are important for mechanistic modelling in biology. Examples include complex animal movement with spatial memory and spatial heterogeneity due to landscapes. Most of the proposed research will be in collaboration with empirical biologists or government researchers for data validation and calibration of new models and for decision making.

该计划侧重于数学生态学中的时间和空间动力学。主要目标是生态模型的机械制定和严格分析。新颖的数学方法包括生态化学计量学和生态毒理学中的非光滑微分方程、混合偏微分方程和离散时间模型的持久性理论和传播速度，以及延迟微分方程的分岔理论以及应用于延迟扩散算子来描述基于记忆的动物运动。丰富的动力学和新的定性理论有待探索。化学计量理论提供了理解宏观现象的基本微观方法。它包括多个生物尺度，并允许通过化学和物理定律制定稳健的机械、预测和可实验测试的模型。应用包括最佳觅食策略、水生和陆地生态系统的多尺度比较、全球二氧化碳变化的影响和蓝藻水华。生态毒理学是保护和恢复免受工业污染的健康生态系统的重要研究领域。通过持久性和分叉分析，我将对生物体及其相互作用的毒物进行风险评估。空间异质性和自然延迟对于生物学的机械建模非常重要。例子包括具有空间记忆的复杂动物运动和由于景观而产生的空间异质性。大多数拟议的研究将与实证生物学家或政府研究人员合作，以进行数据验证和新模型的校准以及决策制定。