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Survival probabilities at spherical frontiers.

Maxim O Lavrentovich1, David R Nelson1

  • 1Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA.

Theoretical Population Biology
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Mutant cells with a selective advantage are more likely to survive at the frontiers of expanding populations. This survival probability is significantly enhanced in linearly inflating populations compared to static ones.

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Area of Science:

  • Evolutionary dynamics
  • Spatial population genetics
  • Mathematical biology

Background:

  • Tumor growth and spatial population genetics involve complex evolutionary and spatial dynamics.
  • Range expansions, particularly on spherical surfaces, present unique challenges for studying these dynamics.
  • Previous studies on two-dimensional inflating ranges provide a basis for understanding three-dimensional expansions.

Purpose of the Study:

  • To investigate the interplay between evolutionary and spatial dynamics in three-dimensional, spherical range expansions.
  • To determine the survival probability of advantageous mutants at the expanding population frontier.
  • To analyze how different growth regimes, characterized by the growth exponent (Θ), affect mutant survival.

Main Methods:

  • Mathematical modeling of spherical range expansions with time-dependent radii (R(t) = R0(1 + t/t∗)Θ).
  • Identification of key dimensionless parameters governing mutant survival probability.
  • Analytical calculation of survival probability for arbitrary growth exponents (Θ).
  • Comparison with simulations of linearly inflating (Θ = 1) and treadmilling (Θ = 0) populations.

Main Results:

  • Survival probability of advantageous mutants is strongly dependent on the growth dynamics of the population.
  • Mutations at linearly inflating fronts (Θ = 1) exhibit survival probabilities over 100 times higher than those at treadmilling fronts (Θ = 0).
  • Special properties of marginally inflating (Θ = 1/2) expansions were identified.

Conclusions:

  • The geometry and growth rate of expanding populations significantly influence evolutionary outcomes.
  • Inflating population fronts provide a strong selective advantage for new mutations compared to static fronts.
  • These findings have implications for understanding tumor evolution and the spread of genetic traits in spatially structured populations.