Adaptive behaviour and multiple equilibrium states in a predator-prey model

Theoretical Population Biology
Alexander PimenovDmitrii Rachinskii

Abstract

There is evidence that multiple stable equilibrium states are possible in real-life ecological systems. Phenomenological mathematical models which exhibit such properties can be constructed rather straightforwardly. For instance, for a predator-prey system this result can be achieved through the use of non-monotonic functional response for the predator. However, while formal formulation of such a model is not a problem, the biological justification for such functional responses and models is usually inconclusive. In this note, we explore a conjecture that a multitude of equilibrium states can be caused by an adaptation of animal behaviour to changes of environmental conditions. In order to verify this hypothesis, we consider a simple predator-prey model, which is a straightforward extension of the classic Lotka-Volterra predator-prey model. In this model, we made an intuitively transparent assumption that the prey can change a mode of behaviour in response to the pressure of predation, choosing either "safe" of "risky" (or "business as usual") behaviour. In order to avoid a situation where one of the modes gives an absolute advantage, we introduce the concept of the "cost of a policy" into the model. A simple conceptual two-dim...Continue Reading

References

Apr 9, 1999·Mathematical Biosciences·G ChiorinoS Charles
Aug 12, 1999·Journal of Theoretical Biology·I Scheuring
Sep 11, 1999·Trends in Ecology & Evolution·P A Stephens, W J Sutherland
Apr 22, 2009·Mathematical Medicine and Biology : a Journal of the IMA·Andrei Korobeinikov

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Citations

Oct 6, 2016·Journal of Mathematical Biology·Alexander PimenovDmitrii Rachinskii
Jun 14, 2017·Mathematical Biosciences and Engineering : MBE·Cruz Vargas-De-Leon, Alberto d'Onofrio
May 31, 2021·Theoretical Population Biology·Prabir Das AdhikaryBapan Ghosh

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