Collaborative Research: Multiscale Modeling of Oyster Reef Dynamics

本地牡蛎在历史上是主要的生态系统工程师，通过渔业提供重要的生态系统服务，如生物过滤和经济价值。在上个世纪，由于过度捕捞和栖息地退化，它们的数量大幅减少，通常不到历史数量的1%。世界范围内，包括切萨皮克湾在内，正在进行大量的努力来恢复本地牡蛎物种的数量，但这些努力在很大程度上是无效的，部分原因是缺乏对复杂非线性系统中牡蛎-珊瑚礁-沉积物动力学的理解。一个能够解释不同空间尺度上的动力学的现实数学模型将使我们能够研究这些系统的潜在过程。通过了解牡蛎与自然环境之间反馈的多种稳定状态以及不同空间尺度对种群活力的影响等非线性动力学，可以制定有效的恢复策略。在这个项目中，牡蛎-珊瑚礁-沉积物动力学将在三个尺度上建模：局部、整个珊瑚礁和超种群。局部模型将解决珊瑚礁几何形状及其如何影响反馈相互作用。在珊瑚礁尺度上，牡蛎和沉积物的反应-扩散-平流模型将被用来解释珊瑚礁的空间格局，并确定最佳的珊瑚礁几何形状。超种群模型，包括在各种动态条件下基于现实水动力学建模的珊瑚礁之间的连通性模型，将用于定位潜在的恢复地点和估计由于环境扰动而灭绝的风险。该项目将推动多个数学分支的发展，包括时空格局形成、元种群模型分析与仿真以及随机耦合系统。该项目的结果将指导联邦、州和非营利机构在切萨皮克湾、大西洋和墨西哥湾沿岸的其他地区以及全球其他本地牡蛎物种的东部牡蛎恢复工作。这样，该项目将为实现2009年签署的13508号行政命令做出重大贡献，该命令的目标是到2025年恢复切萨皮克湾20条支流的牡蛎种群。该项目将与一个积极的实地研究项目相辅相成，并将与之相结合，以参数化模型，并最终为相关机构提供最佳恢复策略。该项目还将培养数学生物学方面的本科生和研究生。这种类型的培训是及时的，因为缺乏能够模拟海洋保护生物学和渔业资源评估的科学家。

Native oyster species were historically dominant ecosystem engineers that provided critical ecosystem services such as biofiltration and economic value through fisheries. Their populations were decimated over the last century through overfishing and habitat degradation, often to less than 1% of historical abundance. Extensive efforts are underway worldwide to restore populations of native oyster species, including in the Chesapeake Bay, but these have largely been ineffectual, partly due to the lack of understanding of oyster-reef-sediment dynamics in complex nonlinear systems. A realistic mathematical model that can account for the dynamics at various spatial scales will enable us to study the underlying processes of these systems. With an understanding of nonlinear dynamics, such as multiple stable states due to feedbacks between oysters and the physical environment, and the effects of different spatial scales on population viability, effective restoration strategies can be devised. In this project, oyster-reef-sediment dynamics will be modeled at three scales: local, whole reef, and metapopulation. Local models will address reef geometry and how it affects feedback interactions. At the reef scale, a reaction-diffusion-advection model for oysters and sediment will be used to explain the spatial pattern of the reef and determine optimal reef geometries for restoration. Metapopulation models, including ones with connectivity between reefs based on realistic hydrodynamic modeling under various dynamic conditions, will be used to locate potential restoration sites and to estimate the risk of extinction due to environmental perturbations. This project will lead to advances in several branches of mathematics, including spatiotemporal pattern formation, metapopulation model analysis and simulation, and stochastic coupled systems. Results of the project will guide ongoing eastern oyster restoration efforts by federal, state and nonprofit agencies in the Chesapeake Bay and other locations along the Atlantic and Gulf of Mexico coasts, as well as for other native oyster species globally. In doing so, the project will contribute significantly to achievement of Executive Order 13508, signed in 2009, which has the goal of restoring oyster populations in 20 tributaries of Chesapeake Bay by 2025. The project is complementary to and will be integrated with an active field research program to parameterize the models and ultimately inform the relevant agencies on optimal restoration strategies. The project will also lead to training of undergraduate and graduate students in mathematical biology. This type of training is timely due to the scarcity of scientists capable of modeling in marine conservation biology and fisheries stock assessment.