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Following the Dynamics of Structural Variants in Experimentally Evolved Populations
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An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment.

Russell Lande1, Steinar Engen, Bernt-Erik Saether

  • 1Division of Biology, Imperial College London, Silwood Park Campus, Ascot, Berkshire, UK. r.lande@imperial.ac.uk

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|May 6, 2009
PubMed
Summary

Population evolution in changing environments favors increased growth rates (r) and carrying capacity (K), while environmental variance (sigma(e)(2)) decreases. Genetic trade-offs exist among these factors.

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Area of Science:

  • Population Ecology
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Population dynamics are influenced by density-dependence and environmental stochasticity.
  • Genetic variation in key parameters like intrinsic rate of increase (r) and carrying capacity (K) affects population persistence.
  • Environmental variance in population growth rate (sigma(e)(2)) introduces unpredictability.

Purpose of the Study:

  • To analyze the evolutionary dynamics of populations in stochastic environments.
  • To investigate the role of genetic variation in density-dependent population regulation.
  • To determine how selection acts on parameters governing population growth and environmental variance.

Main Methods:

  • A continuous-time population model with genetic variation in r, K, and sigma(e)(2).
  • Assumptions of large population size and a stationary, non-autocorrelated environment.
  • Calculation of expected selection gradients and genotype fitness based on Malthusian fitness and covariance.

Main Results:

  • Selection consistently favors increased population growth rate (r) and carrying capacity (K).
  • Environmental variance in population growth rate (sigma(e)(2)) is always selected to decrease.
  • In the theta-logistic model, long-term evolution maximizes E[N(theta)] = [1-sigma(e)(2)/(2r)]K(theta).

Conclusions:

  • Evolutionary pressures in stochastic environments lead to genetic changes in population parameters.
  • A genetic trade-off exists between increasing r and K, and decreasing sigma(e)(2).
  • The parameter theta, governing density dependence, exhibits an intermediate optimum value.