van Baalen M, Krivan V, van Rijn P C, Sabelis M W
Institute of Biodiversity and Ecosystem Dynamics, Population Biology Section, University of Amsterdam, Kruislaan 320, 1098 SM Amsterdam, The Netherlands.
Am Nat. 2001 May;157(5):512-24. doi: 10.1086/319933.
Sigmoid functional responses may arise from a variety of mechanisms, one of which is switching to alternative food sources. It has long been known that sigmoid (Holling's Type III) functional responses may stabilize an otherwise unstable equilibrium of prey and predators in Lotka-Volterra models. This poses the question of under what conditions such switching-mediated stability is likely to occur. A more complete understanding of the effect of predator switching would therefore require the analysis of one-predator/two-prey models, but these are difficult to analyze. We studied a model based on the simplifying assumption that the alternative food source has a fixed density. A well-known result from optimal foraging theory is that when prey density drops below a threshold density, optimally foraging predators will switch to alternative food, either by including the alternative food in their diet (in a fine-grained environment) or by moving to the alternative food source (in a coarse-grained environment). Analyzing the population dynamical consequences of such stepwise switches, we found that equilibria will not be stable at all. For suboptimal predators, a more gradual change will occur, resulting in stable equilibria for a limited range of alternative food types. This range is notably narrow in a fine-grained environment. Yet, even if switching to alternative food does not stabilize the equilibrium, it may prevent unbounded oscillations and thus promote persistence. These dynamics can well be understood from the occurrence of an abrupt (or at least steep) change in the prey isocline. Whereas local stability is favored only by specific types of alternative food, persistence of prey and predators is promoted by a much wider range of food types.
S型功能反应可能源于多种机制，其中之一是转向替代食物来源。长期以来，人们一直知道S型（霍林第三型）功能反应可能会在洛特卡-沃尔泰拉模型中稳定原本不稳定的猎物和捕食者平衡。这就引出了一个问题，即在什么条件下这种由转换介导的稳定性可能会发生。因此，要更全面地理解捕食者转换的影响，就需要分析单捕食者/双猎物模型，但这些模型很难分析。我们研究了一个基于简化假设的模型，即替代食物来源具有固定密度。最优觅食理论的一个著名结果是，当猎物密度降至阈值密度以下时，最优觅食的捕食者将转向替代食物，要么将替代食物纳入其饮食（在细粒度环境中），要么转移到替代食物来源（在粗粒度环境中）。分析这种逐步转换的种群动态后果，我们发现平衡点根本不会稳定。对于次优捕食者，会发生更渐进的变化，导致在有限范围的替代食物类型中出现稳定的平衡点。在细粒度环境中，这个范围明显很窄。然而，即使转向替代食物并不能稳定平衡点，它也可能防止无界振荡，从而促进持久性。从猎物等斜线的突然（或至少陡峭）变化的发生可以很好地理解这些动态。虽然局部稳定性仅受特定类型的替代食物青睐，但更广泛的食物类型范围促进了猎物和捕食者的持久性。
