Department of Mathematics, College of William & Mary, Williamsburg, VA 23187-8795, USA.
J Theor Biol. 2011 Nov 21;289:1-11. doi: 10.1016/j.jtbi.2011.08.013. Epub 2011 Aug 22.
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 indicate that high-relief reefs persist, likely due to elevated reef height which offsets heavy sedimentation and promotes 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.
三十年来，切萨皮克湾的本地牡蛎种群一直是恢复尝试的焦点，但这些尝试普遍未能重建种群和牡蛎礁结构。最近的恢复成功和实地实验表明，高浮雕礁持续存在，这可能是由于礁体高度升高，抵消了大量沉积物的影响，并促进了牡蛎的生存、抗病能力和生长，而低浮雕礁在短短几年内就会退化。这些发现表明牡蛎礁种群中存在着不同的稳定状态。我们开发了一个由三个微分方程组成的数学模型，分别代表活牡蛎、死牡蛎壳（=附着礁）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、附着礁和沉积物体积可以存在多个非负平衡点；牡蛎礁的初始高度决定了达到的平衡点。因此，这项研究为本地牡蛎种群的不同稳定状态提供了一个概念框架，并可用作提高恢复努力成功率的工具。
