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Related Experiment Video

Updated: Jun 10, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

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

Andy Hoyle¹, Roger G Bowers, Andy White

¹Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK. ash@maths.stir.ac.uk

Bulletin of Mathematical Biology

|July 20, 2010

Summary

Evolutionary outcomes depend on population dynamics. This study shows that trade-off shapes and cyclic population dynamics (2-cycles, 4-cycles, chaos) significantly alter evolutionary trajectories and branching points.

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Area of Science:

Evolutionary Biology
Theoretical Ecology
Population Dynamics

Background:

Life-history evolution studies often assume stable population equilibria.
Evolutionary outcomes can differ substantially under non-equilibrium dynamics.
The shape of trade-offs is a key factor influencing evolutionary behavior.

Purpose of the Study:

To analyze evolutionary dynamics using a discrete-time model with a trade-off.
To investigate how cyclic population dynamics affect evolutionary outcomes.
To explore the role of trade-off shape in evolutionary branching.

Main Methods:

Adaptive dynamics analysis of a discrete-time demographic model.
Derivation of explicit fitness expressions in cyclic regions (2-cycles, 4-cycles).
Numerical simulations to verify analytical results and explore higher-order cycles and chaos.

Main Results:

Trade-off shape determines evolutionary attractors under equilibrium dynamics (CSS vs. non-ES repellor).
Transition to 2-cycles introduces discontinuous changes, including branching regions.
Branching region size decreases with increasing cycle period, with further discontinuous falls towards 4-cycles and chaos.

Conclusions:

Cyclic and chaotic population dynamics can lead to significant shifts in evolutionary trajectories compared to stable equilibria.
Trade-off shape interacts with population dynamics to determine evolutionary stability and branching.
The study highlights the importance of considering non-equilibrium population dynamics in evolutionary biology.