Math. Model. Nat. Phenom.
Volume 9, Number 3, 2014Biological evolution
|148 - 164
|28 May 2014
The Evolutionary Dynamics of Aposematism: a Numerical Analysis of Co-Evolution in Finite Populations
1 Department of Mathematical Science, City University London
Northampton Square, London EC1V 0HB
2 Department of Computer Science, City University London Northampton Square, London EC1V 0HB
Corresponding author. E-mail: Jan.Teichmann.firstname.lastname@example.org
The majority of species are under predatory risk in their natural habitat and targeted by predators as part of the food web. During the evolution of ecosystems, manifold mechanisms have emerged to avoid predation. So called secondary defences, which are used after a predator has initiated prey-catching behaviour, commonly involve the expression of toxins or deterrent substances which are not observable by the predator. Hence, the possession of such secondary defence in many prey species comes with a specific signal of that defence (aposematism). This paper builds on the ideas of existing models of such signalling behaviour, using a model of co-evolution and generalisation of aversive information and introduces a new methodology of numerical analysis for finite populations. This new methodology significantly improves the accessibility of previous models.
In finite populations, investigating the co-evolution of defence and signalling requires an understanding of natural selection as well as an assessment of the effects of drift as an additional force acting on stability. The new methodology is able to reproduce the predicted solutions of preceding models and finds additional solutions involving negative correlation between signal strength and the extent of secondary defence. In addition, genetic drift extends the range of stable aposematic solutions through the introduction of a new pseudo-stability and gives new insights into the diversification of aposematic displays.
Mathematics Subject Classification: 91A22 / 92D40
Key words: predator-prey, co-evolution / drift / finite population / adaptive dynamics
© EDP Sciences, 2014
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