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Survival probabilities at spherical frontiers

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  • Lavrentovich, Maxim O.
  • Nelson, David R.

Abstract

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: R(t)=R0(1+t/t∗)Θ, where Θ is a growth exponent, R0 is the initial radius, and t∗ is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters t∗ and Θ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary Θ. We compare our results to simulations of linearly inflating expansions (Θ=1 spherical Fisher–Kolmogorov–Petrovsky–Piscunov waves) and treadmilling populations (Θ=0, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of “marginally inflating†(Θ=1/2) expansions.

Suggested Citation

  • Lavrentovich, Maxim O. & Nelson, David R., 2015. "Survival probabilities at spherical frontiers," Theoretical Population Biology, Elsevier, vol. 102(C), pages 26-39.
  • Handle: RePEc:eee:thpobi:v:102:y:2015:i:c:p:26-39
    DOI: 10.1016/j.tpb.2015.03.002
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    References listed on IDEAS

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    1. Andriy Marusyk & Doris P. Tabassum & Philipp M. Altrock & Vanessa Almendro & Franziska Michor & Kornelia Polyak, 2014. "Non-cell-autonomous driving of tumour growth supports sub-clonal heterogeneity," Nature, Nature, vol. 514(7520), pages 54-58, October.
    2. Doering, Charles R. & Mueller, Carl & Smereka, Peter, 2003. "Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 243-259.
    3. Pigolotti, S. & Benzi, R. & Perlekar, P. & Jensen, M.H. & Toschi, F. & Nelson, D.R., 2013. "Growth, competition and cooperation in spatial population genetics," Theoretical Population Biology, Elsevier, vol. 84(C), pages 72-86.
    4. Adnan Ali & Stefan Grosskinsky, 2010. "Pattern Formation Through Genetic Drift At Expanding Population Fronts," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 349-366.
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    Cited by:

    1. Bryant, Adam S. & Lavrentovich, Maxim O., 2022. "Survival in branching cellular populations," Theoretical Population Biology, Elsevier, vol. 144(C), pages 13-23.
    2. Bryan T Weinstein & Maxim O Lavrentovich & Wolfram Möbius & Andrew W Murray & David R Nelson, 2017. "Genetic drift and selection in many-allele range expansions," PLOS Computational Biology, Public Library of Science, vol. 13(12), pages 1-31, December.

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