School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, China.
Math Biosci Eng. 2012 Apr;9(2):431-44. doi: 10.3934/mbe.2012.9.431.
A mutualism-parasitism system of two species is considered, where mutualism is the dominant interaction when the predators (parasites) are at low density while parasitism is dominant when the predators are at high density. Our aim is to show that mutualism at low density promotes coexistence of the species and leads to high production of the prey (host). The mutualism-parasitism system presented here is a combination of the Lotka-Volterra cooperative model and Lotka-Volterra predator-prey model. By comparing dynamics of this system with those of the Lotka-Volterra predator-prey model, we present the mechanisms by which the mutualism improves the coexistence of the species and production of the prey. Then the parameter space is divided into six regions, which correspond to the four outcomes of mutualism, commensalism, predation/parasitism and neutralism, respectively. When the parameters are varied continuously among the six regions, it is shown that the interaction outcomes of the system transition smoothly among the four outcomes. By comparing the dynamics of the specific system with those of the Lotka-Volterra cooperative model, we show that the parasitism at high density promotes stability of the system. A novel aspect of this paper is the simplicity of the model, which allows rigorous and thorough analysis and transparency of the results.
考虑了两个物种的互利共生-寄生系统，当捕食者（寄生虫）密度较低时，互利共生是主要相互作用，而当捕食者密度较高时，寄生是主要相互作用。我们的目的是表明低密度的互利共生促进了物种的共存，并导致了猎物（宿主）的高产量。这里提出的互利共生-寄生系统是洛特卡-沃尔泰拉合作模型和洛特卡-沃尔泰拉捕食者-猎物模型的组合。通过比较这个系统的动力学与洛特卡-沃尔泰拉捕食者-猎物模型的动力学，我们提出了互利共生改善物种共存和猎物产量的机制。然后，将参数空间划分为六个区域，分别对应互利共生、共栖、捕食/寄生和中性的四个结果。当参数在六个区域之间连续变化时，表明系统的相互作用结果在这四个结果之间平滑过渡。通过比较具体系统的动力学与洛特卡-沃尔泰拉合作模型的动力学，我们表明高密度的寄生促进了系统的稳定性。本文的一个新颖之处在于模型的简单性，它允许进行严格和彻底的分析以及结果的透明度。
