On deterministic and stochastic models of kleptoparasitism
Date
2009
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Publisher
Taylor & Francis
Abstract
Kleptoparasitism, the stealing of food items, is a common biological phenomenon that has been studied mostly with the help of deterministic dynamics for infinite populations. The infinite population assumption takes the models far from the biological reality. In this paper we provide a review of the main theoretical works on kleptoparasitism and then focus on the stochastic dynamics of kleptoparasitic individuals in finite populations. We solve the dynamics analytically for populations of 2 and 3 individuals. With the help of numerical solution of the dynamics, we were able to conclude that the behavior of the uptake rate in the population is mostly determined by the uptake rates at populations of 2 and 3 individuals. If the individuals do better in a pair, then the uptake rate is a decreasing function of the population size. If the individuals do better in a triplet than in a pair, then the uptake rate is a zigzag function with lows for even population sizes and ups for uneven population sizes.
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Keywords
Kleptoparasitism, Stochastic models, Animal populations
Citation
Crowe, M. L., Fitzgerald, M., Remington, D. L., & Rychtář, J. (2009). On deterministic and stochastic models of kleptoparasitism. Journal of Interdisciplinary Mathematics, 12(2), 161-180. https://doi.org/10.1080/09720502.2009.10700620