Clerc Thomas, Davison Anthony C, Bersier Louis-Félix
Unité d'écologie & évolution, Université de Fribourg, Ch. du Musée 10, CH-1700 Fribourg, Switzerland.
J Theor Biol. 2009 Aug 7;259(3):523-32. doi: 10.1016/j.jtbi.2009.04.017. Epub 2009 May 3.
The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this approach has the drawbacks of assuming continuous population variables and of being deterministic. We propose a general approach to stochastic modelling based on the concept of functional response for a prey depletion process with a constant number of predators. Our model could involve any kind of functional response, and permits a likelihood-based approach to statistical modelling and stable computation using matrix exponentials. To illustrate the method we use the Holling-Juliano functional response and compare the outcomes of our model with a deterministic counterpart considered by Schenk and Bacher [2002. Functional response of a generalist insect predator to one of its prey species in the field. Journal of Animal Ecology 71 (3), 524-531], who observed the depletion of Cassida rubiginosa due to its exclusive predator, Polistes dominulus. The predation was found to be Holling type III, reflecting the ability of the predator to regulate its prey. Our approach corroborates this result, but suggests that the prey depletion census should have been performed more often, and that predation features were significantly different between the two years for which data are available.
猎物 - 捕食者相互作用的建模对于理解种群动态至关重要。传统上，这些相互作用是使用常微分方程进行建模的，但这种方法存在假设种群变量连续以及具有确定性的缺点。我们基于具有恒定数量捕食者的猎物消耗过程的功能反应概念，提出了一种随机建模的通用方法。我们的模型可以涉及任何类型的功能反应，并允许使用基于似然的方法进行统计建模以及使用矩阵指数进行稳定计算。为了说明该方法，我们使用了霍林 - 朱利亚诺功能反应，并将我们模型的结果与申克和巴赫 [2002年。一种多食性昆虫捕食者对其一种猎物在野外的功能反应。《动物生态学杂志》71(3)，524 - 531] 所考虑的确定性对应模型的结果进行比较，他们观察了由于其唯一的捕食者——意大利黄蜂对黄粉虫的消耗情况。发现捕食为霍林Ⅲ型，反映了捕食者调节其猎物的能力。我们的方法证实了这一结果，但表明猎物消耗普查应该更频繁地进行，并且对于可获得数据的两年间，捕食特征存在显著差异。
