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Pathogen evolution in switching environments: a hybrid dynamical system approach.

József Z Farkas1, Peter Hinow, Jan Engelstädter

  • 1Division of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, United Kingdom. jzf@maths.stir.ac.uk

Mathematical Biosciences
|July 4, 2012
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Summary
This summary is machine-generated.

We model pathogen evolution with changing environments using a hybrid dynamical system. A genotype with highest mean fitness is stable in fluctuating environments, but polymorphism can persist if host switching depends on population genetics.

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Area of Science:

  • Mathematical Biology
  • Evolutionary Dynamics
  • Population Genetics

Background:

  • Pathogen evolution is influenced by environmental changes and selective pressures.
  • Stochastic processes play a crucial role in shaping evolutionary trajectories.
  • Understanding the stability of pathogen populations in fluctuating environments is vital.

Purpose of the Study:

  • To develop a hybrid dynamical system model for pathogen evolution under varying selective pressures.
  • To analyze the impact of stochastic environmental switching on population dynamics.
  • To investigate the conditions for stable monomorphic and polymorphic equilibria.

Main Methods:

  • Utilizing a hybrid dynamical system combining Fisher-Haldane-Wright equations with Markov jump processes.
  • Analyzing the stability in probability of monomorphic equilibria in a single-host model.
  • Exploring how genotype-dependent host switching affects population stability.

Main Results:

  • In constantly fluctuating environments, the genotype with the highest mean fitness achieves asymptotic stability in probability.
  • Other genotypes become unstable in probability under constant fluctuations.
  • Polymorphism can be stably maintained when host switching probability is dependent on genotype composition.

Conclusions:

  • Hybrid dynamical systems offer a robust framework for modeling pathogen evolution in stochastic environments.
  • Environmental fluctuations can lead to the dominance of the fittest genotype.
  • Genotype-dependent host switching presents a mechanism for maintaining pathogen diversity.