Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations

We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.本研究从理论层面探讨恒化器（chemostat）中两种相互作用微生物种群的动态演化规律。这两类种群不仅会竞争同一种限制性资源，还会通过交叉喂养（cross-feeding）形成互利共生关系。与既往研究（Assaneo等人，2013；Holland等人，2010；Iwata等人，2011）结论一致，本研究证实该系统具备丰富的动态行为谱，其中包括双稳态（bistability）。标准洛特卡-沃尔泰拉方程（Lotka-Volterra equations）无法准确描述该特定系统，因为这类方程仅能刻画单一类型的相互作用（互利共生或竞争）。本研究表明，扩展版洛特卡-沃尔泰拉模型可较好地拟合该系统的各类稳态解，该模型能够更精准地刻画密度依赖型相互作用：即低密度下表现为互利共生，高密度下则转为竞争关系。相较于恒化器方程，该双变量模型对系统动态行为的描述更为直观清晰。