Centre for Mathematical Science, City University, Northampton Square, London EC1V 0HB, UK.
J Theor Biol. 2010 May 21;264(2):266-72. doi: 10.1016/j.jtbi.2010.01.012. Epub 2010 Jan 21.
Kleptoparasitism, the stealing of food items from other animals, is a common behaviour observed across a huge variety of species, and has been subjected to significant modelling effort. Most such modelling has been deterministic, effectively assuming an infinite population, although recently some important stochastic models have been developed. In particular the model of Yates and Broom (Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480-489) introduced a stochastic version following the original model of Ruxton and Moody (The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449-458), and whilst they generated results of interest, they did not solve the model explicitly. In this paper, building on methods used already by van der Meer and Smallegange (A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134-142) we give an exact solution to the distribution of the population over the states for the Yates and Broom model and investigate the effects of some key biological parameters, especially for small populations where stochastic models can be expected to differ most from their deterministic equivalents.
食窃行为，即从其他动物那里窃取食物的行为，是一种在众多物种中观察到的常见行为，并已经受到了大量的模型研究。大多数此类模型都是确定性的，有效地假设了一个无限的种群，尽管最近已经开发了一些重要的随机模型。特别是，Yates 和 Broom 的模型（Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480-489）在 Ruxton 和 Moody 的原始模型（The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449-458）的基础上引入了一个随机版本，尽管他们生成了有趣的结果，但并没有明确地解决该模型。在本文中，我们基于 van der Meer 和 Smallegange 已经使用的方法（A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134-142），为 Yates 和 Broom 模型的种群状态分布提供了一个精确的解决方案，并研究了一些关键生物学参数的影响，特别是在小种群中，随机模型可能与确定性模型有最大的差异。
