Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics

Bulletin of Mathematical Biology
Andy HoyleAndy White

Abstract

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with...Continue Reading

References

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Citations

Dec 28, 2012·Journal of the Royal Society, Interface·Alex BestMike Boots
Jan 5, 2013·Theoretical Population Biology·Andrea Mathias, Peter Chesson
Jan 5, 2011·Journal of Theoretical Biology·Emily Hackett-JonesChristina A Cobbold
Jan 12, 2013·Journal of Theoretical Biology·Tuomas Nurmi, Kalle Parvinen
Jun 21, 2017·Ecology Letters·Frédéric BarraquandRebecca C Tyson

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