具有人口统计随机性的May-Leonard模型的异宿循环和绝灭
Heteroclinic cycling and extinction in May-Leonard models with demographic stochasticity
摘要：
May和Leonard（SIAM J. Appl. Math 1975）提出了一个具有异宿循环的三种群Lotka-Volterra型种群模型。而不是产生一个周期性的极限环，轨迹需要越来越长的时间来完成每个“周期”，越来越接近不稳定的固定点，其中一个人口占主导地位，其他人接近零。非周期异宿动态随后在生态系统中进行了研究（侧斑蜥蜴;大肠杆菌E。大肠杆菌）、免疫系统、神经信息处理模型（"无赢家竞争"）和神经中枢模式发生器的模型中。然而，正如梅和伦纳德所观察到的那样："从生物学上讲，（由模型产生的）行为是毫无意义的。一旦承认变量代表动物，因此不能低于1，很明显，系统将在几个周期后收敛于某个单一种群，消灭其他两个种群。"在这里，我们探索不同的方式引入离散随机动力学的基础上，五月和伦纳德的ODE模型，应用生态种群动力学，和神经运动中枢模式发生器系统。我们研究了几个数量上不同的渐近行为的例子，包括所有物种的灭绝，灭绝到一个单一的物种，和持久的周期优势有限的平均周期长度。
英文摘要：
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic E. coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.
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