标题： 微分方程模型中牡蛎礁高度和沉积物积累的双稳态 显示英文标题

标题： Bistability in a differential equation model of oyster reef height and sediment accumulation

摘要： 本地牡蛎种群在切萨皮克湾已经成为了三十年恢复努力的重点，但这些努力通常未能重建种群和牡蛎礁结构。 最近的恢复成功和野外实验表明，高起伏的礁石可以抵消大量的沉积物，并促进牡蛎的存活、抗病能力和生长，这与低起伏的礁石在几年内退化的现象形成对比。 这些发现表明牡蛎礁种群中存在替代稳定状态。 我们开发了一个由三个微分方程组成的数学模型，代表活牡蛎的体积、死亡牡蛎壳（=堆积的礁石）和沉积物的体积。 分支分析和数值模拟表明，在生态上合理的参数值范围内，活牡蛎、堆积礁石和沉积物体积可以存在多个非负平衡；牡蛎礁的初始高度决定了达到哪种平衡。 因此，这项研究为本地牡蛎种群的替代稳定状态提供了一个概念框架，并可作为提高恢复工作成功可能性的工具。 显示英文摘要

摘要： Native oyster populations in Chesapeake Bay have been the focus of three decades of restoration attempts, which have generally failed to rebuild the populations and oyster reef structure. Recent restoration successes and field experiments suggest that high-relief reefs offset heavy sedimentation and promote oyster survival, disease resistance and growth, in contrast to low-relief reefs which degrade in just a few years. These findings suggest the existence of alternative stable states in oyster reef populations. We developed a mathematical model consisting of three differential equations that represent volumes of live oysters, dead oyster shells (= accreting reef), and sediment. Bifurcation analysis and numerical simulations demonstrated that multiple nonnegative equilibria can exist for live oyster, accreting reef and sediment volume at an ecologically reasonable range of parameter values; the initial height of oyster reefs determined which equilibrium was reached. This investigation thus provides a conceptual framework for alternative stable states in native oyster populations, and can be used as a tool to improve the likelihood of success in restoration efforts.