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

TL;DR

This paper presents a mathematical model showing that oyster reef populations can have multiple stable states, influenced by initial reef height, which has implications for restoration strategies.

Contribution

It introduces a differential equation model demonstrating the existence of alternative stable states in oyster reef height and sediment accumulation.

Findings

Multiple nonnegative equilibria exist for oyster and sediment volumes.

Initial reef height determines the stable state reached.

Model provides a framework to improve oyster restoration success.

Abstract

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.