Allelopathy in Spatially Distributed Populations

The differences we find in the behavior of some of the models parallel those found experimentally

Rick Durrett

2002

Scholarcy highlights

  • A central issue in evolutionary theory is the evolution of altruistic behavior, and how it is influenced and enhanced by aspects of the social structure of populations; an compelling and closely related issue involves the evolution of antagonistic behaviors
  • previous research has shown experimentally, in a well-mixed environment the costs of colicin production always outweigh the benefits when the colicin producers are rare; but in a structured environment, the situation may shift to favor the production of colicin
  • Through a series of models, the conditions for the evolution of colicin
  • In a mean-field model there are two stable states: one with only colicin producers present and one with only the colicin-sensitive strain. This confirms the experimental observation that in a well-mixed environment, colicin producers cannot evolve from low frequencies
  • In this setting colicin production is an evolutionarily stable strategy; if it is represented in the population at a sufficiently high level, the population will proceed to fixation for colicin production
  • In a spatially structured environment the situation is fundamentally different: colicin production can invade from low densities provided that the additional mortality it imposes on the colicin-sensitive type is above a critical threshold value, determined by the cost of producing colicin
  • Two types that produce colicin at slightly different rates can coexist with a third, colicin-sensitive, type in a dynamic equilibrium

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