Construction and analysis of mechanistic, predictive, and empirically testable models in ecology and ecotoxicology via rigorous chemical and physical laws

我的主要研究目标是了解营养物质在食草动物的生长和竞争以及细菌的生物降解中的作用，并将这些新的基本认识应用于控制有害种群和有毒有机物，包括物种入侵和生态毒理学。入侵物种的控制一直是全球一个极其重要的话题，因为入侵物种的经济影响是巨大的（据联合国环境规划署估计，全球每年损失1.4万亿美元）。正如美国环境保护署和加拿大环境部长理事会所指出的那样，工业引起的污染已经成为世界范围内一个严重的环境问题。为了指导解决这些世界性问题的实验和管理，数学建模通过连接已知的动态组件起着关键和必要的作用，这些组件通常以复杂的非线性方式组合在一起。****我在数学生物学方面的工作已经从循环种群动力学发展到基础化学计量建模和分析，然后发展到化学计量理论的应用和传染病的传播。在营养缺乏的环境中，考虑营养循环或化学计量学对种群模型至关重要。我计划将化学计量模型推进到更机械的水平，这可能会导致理论生物学的一些基本规律。将其应用于物种入侵可以指导政府改进管理政策。研究营养物、浊度等非生物因素对关键生物反应的影响，是确定外来和外来物种竞争结果的基础。化学计量学概念的另一个应用是生态毒理学。我将构建一个化学计量生物降解模型来估计阿尔伯塔省油砂工业产生的尾矿池和尾坑湖的甲烷产量。一个相关的项目是油砂污染对艾伯塔省生态系统持久性和生物多样性的风险评估，这是一个与艾伯塔省政府的联合项目。另一个单独的项目侧重于传染病的传播，包括其传播方式和比率。****我提出了一个数学、计算和实验研究的综合计划，将提供新一代具有化学和物理约束的机械模型。大多数数学模型都是非光滑动力系统，这可能会产生新的动力学和分岔。分析方法包括局部和全局稳定性分析、分岔分析、单调动力系统理论、持续理论、微扰理论、灵敏度分析、小波分析等。此外，这些机制模型将受到实验数据的挑战和校准

My main research objective is to understand the role of nutrients in the growth and competition of herbivores and biodegradation of bacteria, and to apply these new fundamental understandings to control deleterious populations and toxic organic matter, including species invasions and ecotoxicology. Control of invasive species has been an extremely important topic globally because the economic effects of invasive species are enormous (estimated global damages at $1.4 trillion annually according to the United Nations Environment Programme). Industry-induced pollution has been a severe environmental problem around the world as the US Environmental Protection Agency and the Canadian Council of Ministers of the Environment have indicated. To guide experiments and management for solving these world-wide issues, mathematical modeling plays a pivotal and necessary role by connecting the known dynamical components, which usually fit together in complex nonlinear ways.****My work in mathematical biology has evolved from cyclic population dynamics to fundamental stoichiometric modeling and analysis, and then to applications of stoichiometric theory and the spread of infectious diseases. In nutrient deficient environments, the consideration of nutrient cycling, or stoichiometry, can be essential for population models. I plan to advance the stoichiometric modeling into a more mechanistic level, which may lead to some fundamental laws in theoretical biology. Its application to species invasions can guide the government towards improved management policies. To study the impacts of abiotic factors, such as nutrient and turbidity, on key biological responses is essential for determining the competition result of native and invasive species. The other application of the stoichiometric concept is ecotoxicology. I will construct a stoichiometric biodegradation model to estimate methane production from tailings ponds and end pit lakes, generated by the oil sands industry, in Alberta. An associated project is the risk assessment of oil sands pollution on the persistence and biodiversity of an ecosystem in Alberta, which is a joint project with the Alberta government. Another separate project is focused on the spread of infectious diseases including their transmission modes and rates.****I propose an integrated program of mathematical, computational, and experimental studies that will provide a new generation of mechanistic models with chemical and physical constraints. Most mathematical models are non-smooth dynamical systems which may generate novel dynamics and bifurcations. Analytical techniques include local and global stability analysis, bifurcation analysis, theory of monotone dynamical systems, persistence theory, perturbation theory, sensitivity analysis, wavelet analysis, etc. Furthermore, these mechanistic models will be challenged and calibrated by experimental data.**