Critical Fitness Collapse in Three-Dimensional Spatial Population Genetics

Abstract

If deleterious mutations near a fitness maximum in a spatially distributed population are sufficiently frequent or detrimental, the population can undergo a fitness collapse, similarly to the Muller's ratchet effect in well-mixed populations. Recent studies of one-dimensional habitats (e.g., the frontier of a two-dimensional range expansion) have shown that the onset of the fitness collapse is described by a directed percolation phase transition with its associated critical exponents. We consider population fitness collapse in three-dimensional range expansions with both inflating and fixed-size frontiers (applicable to, e.g., expanding and treadmilling spherical tumors, respectively). We find that the onset of fitness collapse in these two cases obeys different scaling laws, and that competition between species at the frontier leads to a deviation from directed percolation scaling. As in two-dimensional range expansions, inflating frontiers modify the critical behavior by causally disconnecting well-separated portions of the population.

arXiv comment25 pages, 11 figures

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Cited by in corpus (3)

• Active-to-absorbing-state phase transition in an evolving population with mutation
• Shape of population interfaces as an indicator of mutational instability in coexisting cell populations
• Rare beneficial mutations cannot halt Muller's ratchet in spatial populations