Statistical and Biological Physics

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Range expansion of heterogeneous populations

Matthias Reiter, Steffen Rulands and Erwin Frey

The expansion of populations is a ubiquitous phenomenon in nature which includes the spreading of advantageous genes or infectious diseases, and dispersal of species into new territory. Recently, single cell studies have revealed that even genetically identical bacterial populations exhibit phenotypic heterogeneity, which is generally regarded as a bet-hedging strategy to maximize survival. For example, Bacillus subtilis can exist in a motile state, where flagella are used for locomotion, and a non-motile state, where flagella are absent. This heterogeneity allows the population to exploit nutrients at its current location and at the same time disperse to new, possibly more favorable, niches.

In this Letter, we study range expansion of a bacterial population exhibiting phenotypic heterogeneity, where individual cells may either be able to divide or be flagellated and thereby able to move. We ask what degree of risk spreading is optimal for survival during range expansion. Using a combined analytical and numerical approach we find that while during the initial expansion phase fast growing cells do have a selective advantage, the population is asymptotically dominated by individuals following a 'bet-hedging' strategy with approximately equal rates for motility and reproduction. Starting from a genetically diverse population seed, the range expansion leads to the formation of homogeneous sectors and to a loss of genetic diversity in the front region. Asymptotically, the population is dominated by individuals who migrate and reproduce at approximately equal rates. In particular, these individuals constitute at large times the outer region of the population, while slow individuals are located at the center.