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Beneficial mutations during range expansions can sweep to fixation, but this is rare in most scenarios. Our model provides simple formulas for sweep probabilities, explaining why sweeps are uncommon in solid tumors.

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Area of Science:

  • Evolutionary biology
  • Mathematical modeling
  • Population genetics

Background:

  • Range expansions are crucial in shaping biological systems, from microbes to invasive species.
  • Understanding selective sweeps during expansions is key, but previous models often ignored spatial structure or constant population sizes.

Purpose of the Study:

  • To investigate the probability and timing of selective sweeps during range expansions.
  • To develop mathematical models applicable to scenarios including mutants displacing wildtypes.
  • To provide insights into evolutionary dynamics in spatially expanding populations.

Main Methods:

  • Mathematical modeling and analysis of selective sweep probabilities.
  • Development of approximate and exact expressions for sweep probabilities in 1, 2, and 3 dimensions.
  • Agent-based simulations to validate predictions using the spatial Moran process.

Main Results:

  • Derived simple, dimension-independent expressions for sweep probabilities, independent of mutation rate.
  • Confirmed model accuracy with agent-based simulations, even with random multiplicative fitness effects.
  • Model predicts selective sweeps are rare in solid tumors, except during early growth.

Conclusions:

  • Selective sweeps during range expansions are rare, particularly in established solid tumors.
  • The developed models offer a general explanation for observed evolutionary patterns in cancer.
  • Findings have implications for understanding evolution in various spatially expanding biological systems.