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Start Over Author "Hoyle, Andrew" Topic adaptive dynamics
3 results on '"Hoyle, Andrew"'

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

Author

Hoyle, Andrew, Bowers, Roger, and White, Andrew

Subjects
Trade-offs, Logistic equation, Chaos, Evolutionary branching, Adaptive dynamics
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.

Published
2011

2. Can possible evolutionary outcomes be determined directly from the population dynamics?

Author

Hoyle, Andrew and Bowers, Roger G.

Subjects
*POPULATION dynamics, *BIOLOGICAL evolution, *BRANCHING processes, *ADAPTIVE sampling (Statistics), *BEHAVIOR genetics, *ECOLOGICAL systems theory, *MATHEMATICAL models
Abstract

Abstract: Traditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria — one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply. [Copyright &y& Elsevier]

Published
2008
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3. When is evolutionary branching in predator–prey systems possible with an explicit carrying capacity?

Author

Hoyle, Andrew and Bowers, Roger G.

Subjects
*STATICS, *COATING processes, *SURFACE coatings, *POPULATION density
Abstract

Abstract: In this study we use the theory of adaptive dynamics firstly to explore the differences in evolutionary behaviour of a generalist predator (or more specifically an omnivorous or intraguild predator) in a predator–prey model, with a Holling Type II functional response, when two distinct forms for the carrying capacity are used. The first of these involves the carrying capacity as an emergent property, whilst in the second it appears explicitly in the dynamics. The resultant effect this has on the intraspecific competition in each case is compared. Taking an identical trade-off in each case, we find that only with an emergent carrying capacity is evolutionary branching possible. Our study then concentrates solely on the case where the carrying capacity appears explicitly. Using the same model as above, but choosing alternate trade-offs, we find branching can occur with an explicit carrying capacity. Our investigation finishes by taking a more general functional response in an attempt to derive a condition for when branching can or cannot occur. For a predator–prey model, branching cannot occur if the functional response can be separated into two components, one a function of the population densities, X and Z, and the other a function of the evolving parameter z (traded off against the intrinsic growth rate), i.e. if F(z, X, Z)= F 1(z)F 2(X, Z). This search for evolutionary branching is motivated by its possible role in speciation. [Copyright &y& Elsevier]

Published
2007
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