Abrams Peter A, Quince Christopher
Department of Zoology, University of Toronto, 25 Harbord St., Toronto, Ont., Canada, M5S 3G5.
Theor Popul Biol. 2005 Dec;68(4):253-66. doi: 10.1016/j.tpb.2005.05.004. Epub 2005 Jul 22.
The relationships between a predator population's mortality rate and its population size and stability are investigated for several simple predator-prey models with stage-structured prey populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's population growth; the nature of stage-transitions; and the stage-selectivity of the predator. Instability occurs at high, rather than low predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable predator population to increase in abundance as its own mortality rate increases in stable systems, provided that the predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in predator population size with increasing predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.
对于几个具有阶段结构猎物种群的简单捕食者 - 猎物模型，研究了捕食者种群的死亡率与其种群大小和稳定性之间的关系。考虑了几种替代模型；这些模型在关于猎物种群增长中密度依赖性的性质、阶段转变的性质以及捕食者的阶段选择性的假设方面有所不同。在大多数具有高度阶段选择性捕食的模型中，不稳定性发生在高捕食者死亡率而非低捕食者死亡率时；这与具有同质猎物种群的模型中死亡率对稳定性的影响相反。阶段选择性捕食还增加了导致稳定平衡的参数范围。结果表明，在稳定系统中，当捕食者具有饱和功能反应时，随着其自身死亡率的增加，稳定的捕食者种群数量增加可能是常见的情况。猎物中足够强的密度依赖性通常会扭转这一结果，并导致捕食者种群数量随着捕食者死亡率的增加而减少。当幼体阶段具有固定持续时间时，稳定性会降低，但在稳定参数空间的大片区域中仍观察到种群数量随着死亡率增加而增加。这提出了两个尚未得到解答的相关问题：（1）在自然界中是否真的会出现随着死亡率升高种群数量增加的情况；（2）如果不会，是什么阻止了它们的发生？具有阶段结构的猎物和与阶段相关的捕食也可以扭转“富集悖论”，当猎物增长增加时导致稳定而非不稳定。
