The stochastic modelling of kleptoparasitism using a Markov process

JOURNAL OF THEORETICAL BIOLOGY

卷:264

Article

Broom, Mark²  Crowe, Mary L.³  Fitzgerald, Meghan R.⁴  Rychtar, Jan¹ 

[1] Univ N Carolina Greensboro, Dept Math & Stat, Greensboro, NC 27402 USA

[2] City Univ London, Ctr Math Sci, London EC1V 0HB, England

[3] Univ N Carolina, Off Undergrad Res, Greensboro, NC 27402 USA

[4] Univ N Carolina, Dept Biol, Greensboro, NC 27402 USA

关键词: Stealing;    Finite population;    Uptake rate;    Interference;    Detailed balance;   

DOI  :  10.1016/j.jtbi.2010.01.012

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Ltd. All rights reserved.

【 授权许可】

Free