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Noise Driven Evolutionary Waves

By Oskar Hallatschek

Abstract

Adaptation in spatially extended populations entails the propagation of evolutionary novelties across habitat ranges. Driven by natural selection, beneficial mutations sweep through the population in a “wave of advance”. The standard model for these traveling waves, due to R. Fisher and A. Kolmogorov, plays an important role in many scientific areas besides evolution, such as ecology, epidemiology, chemical kinetics, and recently even in particle physics. Here, we extend the Fisher–Kolmogorov model to account for mutations that confer an increase in the density of the population, for instance as a result of an improved metabolic efficiency. We show that these mutations invade by the action of random genetic drift, even if the mutations are slightly deleterious. The ensuing class of noise-driven waves are characterized by a wave speed that decreases with increasing population sizes, contrary to conventional Fisher–Kolmogorov waves. When a trade-off exists between density and growth rate, an evolutionary optimal population density can be predicted. Our simulations and analytical results show that genetic drift in conjunction with spatial structure promotes the economical use of limited resources. The simplicity of our model, which lacks any complex interactions between individuals, suggests that noise-induced pattern formation may arise in many complex biological systems including evolution

Topics: Research Article
Publisher: Public Library of Science
OAI identifier: oai:pubmedcentral.nih.gov:3053316
Provided by: PubMed Central

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Citations

  1. (2009). A mathematical analysis for a model arising from public goods games.
  2. (2006). A mathematical analysis on public goods games in the continuous space.
  3. (2004). Biofilms promote altruism.
  4. (1990). Clark A
  5. (2006). Consequences of strong fluctuations on high-energy QCD evolution.
  6. (2001). Cooperation and competition in the evolution of atp-producing pathways.
  7. (1931). Evolution in mendelian populations.
  8. (2007). Evolution of cooperation in spatial public goods games with common resource dynamics.
  9. (1998). Evolutionary Games and Population Dynamics.
  10. (2007). Fermentative lifestyle in yeasts belonging to the Saccharomyces complex.
  11. (2009). Fisher waves in the strong noise limit.
  12. (1999). Formation of colony patterns by a bacterial cell population.
  13. (2000). Front propagation in heterogeneous media.
  14. (2003). Front propagation into unstable states.
  15. (2010). Genetic demixing and evolution in linear stepping stone models.
  16. (2003). Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality.
  17. (2004). Mathematical Biology I.
  18. (2002). Neutral evolution in spatially continuous populations.
  19. (2008). Neutralism and selectionism: a network-based reconciliation.
  20. (1951). On a quasi-linear parabolic equation occuring in aerodynamics.
  21. (1997). Principles of population genetics. Sinauer Associates
  22. (2007). Propagating waves of self-assembly in organosilane monolayers.
  23. (2006). Resource competition and social conflict in experimental populations of yeast.
  24. (1996). Rna virus evolution via a fitness-space model.
  25. (2005). Selectionism and neutralism in molecular evolution.
  26. (1997). Shift in the velocity of a front due to a cutoff.
  27. (1977). Spatial contact models for ecological and epidemic spread.
  28. (2009). Spatial dynamics of ecological public goods.
  29. (1964). Stepping stone model of population structure and decrease of genetic correlation with distance.
  30. (2001). Stochastic processes in physics and chemistry.
  31. (1937). Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem.
  32. (2007). The frailty of adaptive hypotheses for the origins of organismal complexity.
  33. (1964). The genetic evolution of social behavior.
  34. (2005). The geographic spread of the ccr5 delta32 hiv-resistance allele.
  35. (2011). The noisy edge of traveling waves.
  36. (1950). The partial differential equation ut+uux=muxx.
  37. (2006). The scaling laws of human travel.
  38. (2008). The tragedy of the commons in microbial populations: insights from theoretical, comparative and experimental studies.
  39. (1968). The tragedy of the commons.
  40. (1937). The wave of advance of advantageous genes.
  41. (2001). Travelling waves and spatial hierarchies in measles epidemics.