Cortez Michael H
Dept. of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA.
J Theor Biol. 2016 Dec 21;411:59-67. doi: 10.1016/j.jtbi.2016.09.021. Epub 2016 Sep 28.
A species exhibits a hydra effect when, counter-intuitively, increased mortality of the species causes an increase in its abundance. Hydra effects have been studied in many continuous time (differential equation) multispecies models, but only rarely have hydra effects been observed in or studied with discrete time (difference equation) multispecies models. In addition most discrete time theory focuses on single-species models. Thus, it is unclear what unifying characteristics determine when hydra effects arise in discrete time models. Here, using discrete time multispecies models (where total abundance is the single variable describing each population), I show that a species exhibits a hydra effect in a stable system only when fixing that species' density at its equilibrium density destabilizes the system. This general characteristic is referred to as subsystem instability. I apply this result to two-species models and identify specific mechanisms that cause hydra effects in stable communities, e.g., in host--parasitoid models, host Allee effects and saturating parasitoid functional responses can cause parasitoid hydra effects. I discuss how the general characteristic can be used to identify mechanisms causing hydra effects in communities with three or more species. I also show that the condition for hydra effects at stable equilibria implies the system is reactive (i.e., density perturbations can grow before ultimately declining). This study extends previous work on conditions for hydra effects in single-species models by identifying necessary conditions for stable systems and sufficient conditions for cyclic systems. In total, these results show that hydra effects can arise in many more communities than previously appreciated and that hydra effects were present, but unrecognized, in previously studied discrete time models.
当一个物种出现九头蛇效应时，与直觉相反的是，该物种死亡率的增加会导致其数量的增加。九头蛇效应已在许多连续时间（微分方程）多物种模型中得到研究，但在离散时间（差分方程）多物种模型中很少被观察到或研究。此外，大多数离散时间理论都集中在单物种模型上。因此，尚不清楚哪些统一特征决定了离散时间模型中何时会出现九头蛇效应。在这里，使用离散时间多物种模型（其中总数量是描述每个种群的单一变量），我表明一个物种只有在将其密度固定在平衡密度时使系统不稳定的情况下，才会在稳定系统中表现出九头蛇效应。这种一般特征被称为子系统不稳定性。我将这一结果应用于两物种模型，并确定了在稳定群落中导致九头蛇效应的具体机制，例如，在宿主 - 寄生蜂模型中，宿主阿利效应和饱和寄生蜂功能反应会导致寄生蜂的九头蛇效应。我讨论了如何利用这一一般特征来识别在具有三个或更多物种的群落中导致九头蛇效应的机制。我还表明，稳定平衡时九头蛇效应的条件意味着系统是有反应性的（即密度扰动在最终下降之前可以增长）。这项研究通过确定稳定系统的必要条件和循环系统的充分条件，扩展了先前关于单物种模型中九头蛇效应条件的工作。总的来说，这些结果表明，九头蛇效应可能出现在比以前认识到的更多的群落中，并且在先前研究的离散时间模型中已经存在但未被识别。
