Evolutionary behaviour in ecological systems with trade-offs and non-equilibrium population dynamics

Question: Do non-equilibrium (cycles or chaos) population dynamics change evolutionary behaviour when compared with equilibrium dynamics? Mathematical methods: The theory of adaptive dynamics is applied to a discrete ecological model with an explicit trade-off between reproduction and survival. Simulation techniques are compared with the theoretical findings. Key assumptions: Mutations in life-history parameters are assumed to be small. A separation of the ecological and evolutionary time scales is assumed. There is a feedback loop between the environment and its inhabitants. Conclusions: With equilibrium population dynamics the shape of the trade-off can be used to characterize the evolutionary behaviour. Trade-offs with accelerating costs produce a continuously stable strategy (CSS). Trade-offs with decelerating costs produce a non-evolutionarily stable strategy (non-ESS) repellor. The characterization holds for non-equilibrium dynamics with low amplitude population oscillations. When the magnitude of the population oscillation exceeds a threshold, the characterization fails. Trade-offs with decelerating costs can produce a CSS, multiple CSSs or evolutionary branching points. The evolution of reproduction and survival parameters may be contingent on initial conditions and sensitive to small changes in other life-history parameters. Evolutionary branching allows types with distinct reproduction and survival parameters to evolve and co-exist.