Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/9037

Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics
Authors: Hoyle, Andrew
Bowers, Roger
White, Andrew
Contact Email: ash@cs.stir.ac.uk
Keywords: Adaptive dynamics
Trade-offs
Logistic equation
Evolutionary branching
Chaos
Issue Date: May-2011
Publisher: Springer Verlag for the Society for Mathematical Biology
Citation: Hoyle A, Bowers R & White A (2011) Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics, Bulletin of Mathematical Biology, 73 (5), pp. 1154-1169.
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 simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.
Type: Journal Article
URI: http://hdl.handle.net/1893/9037
DOI Link: http://dx.doi.org/10.1007/s11538-010-9567-7
Rights: The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.
Affiliation: Computing Science - CSM Dept
Mathematics - CSM Dept
Heriot-Watt University

Files in This Item:
File Description SizeFormat 
Hoyle_2011_Evolutionary_Behaviour.pdf638.2 kBAdobe PDFUnder Embargo until 31/12/2999     Request a copy

Note: If any of the files in this item are currently embargoed, you can request a copy directly from the author by clicking the padlock icon above. However, this facility is dependant on the depositor still being contactable at their original email address.

This item is protected by original copyright



Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

If you believe that any material held in STORRE infringes copyright, please contact library@stir.ac.uk providing details and we will remove the Work from public display in STORRE and investigate your claim.