Collaborative Research: Consequences of Environmental Stochasticity for the Spatial Dynamics of Savanna-Forest Transitions

全球气温和降雨模式的变化将对植被模式产生重大影响，在某些情况下，生态系统的性质将发生巨大变化，对野生动物和自然系统为人类提供的服务产生影响。 这些“关键过渡”是各种系统环境变化的可能结果，包括本项目将处理的稀树草原和森林过渡，其中火灾频率的变化对改变这些关键生态系统类型的性质特别重要。在项目负责人以前工作的基础上，这项研究将开发和应用最先进的数学模型，与实证研究相结合，预测不断变化的环境条件将如何调节热带草原森林边界的变化。 该项目还将加强多层次的教育和培训，包括培训一名博士后研究员;开发研究生和本科生研究项目;通过与艺术家和教育家Neil Goldberg合作实现数据可视化。 空间效应的引入导致了偏微分或偏微分积分方程的系统，包括随机影响，这当然更复杂的分析，但对于预测边界的变化是至关重要的。 该项目将开发和应用从非平衡统计力学中提取的新方法，并将产生新的数学结果，特别是在平均场极限周围的波动方面，开发这些随机系统的新方法，并应用新的随机通量方法。一个关键因素将涉及一个真正的跨学科博士后研究员的培训，在项目的数学层面和生态数据分析都流利。这个奖项是由数学科学部（DMS）通过数学生物学计划和生物/生物科学的MPS部门共同资助。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响审查标准。

Changing temperature and rainfall patterns globally will have major effects on vegetation patterns, in some cases shifting the nature of ecosystems dramatically with consequences for wildlife, and for the services that natural systems provide to humans. These “critical transitions” are possible outcomes of environmental shifts in a wide variety of systems, including the savanna and forest transitions that this project will address, in which changes in frequency of fires can be especially important in changing the nature of these key ecosystem types. Building on previous work by the project leaders, this research will develop and apply state-of-the-art mathematical models, in concert with empirical studies, to predict how changing environmental conditions will mediate shifts in the savanna-forest boundary. This project will also enhance education and training at multiple levels, including the training of a postdoctoral fellow; development of graduate and undergraduate research projects; and data visualization through collaboration with artist and educator Neil Goldberg.The potential for multiple stable states, respectively forest and savanna, in vegetation systems has been previously demonstrated, combining empirical work with dynamical systems models. The introduction of spatial effects leads to systems of partial-differential or partial differential-integral equations, including stochastic influences, which of course are more complicated to analyze, but are crucial for predicting the shifts of boundaries. This project will develop and apply new methodologies drawn from non-equilibrium statistical mechanics, and will generate novel mathematical results, in particular in terms of fluctuations around the mean-field limit, developing new approaches to these stochastic systems, and applying a novel landscape-flux approach. A key element will involve the training of a truly interdisciplinary postdoctoral fellow to be fluent both in the mathematical dimensions of the project and the ecological data analysis.This award is funded jointly by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and BIO/DEB through the Cluster of Population and Community Ecology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.