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Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):021923. Epub 2012 Feb 27.

Reproduction-time statistics and segregation patterns in growing populations.

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  • 1Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom.


Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns. Generalizing the standard Eden growth model, we introduce a simple one-parameter family of reproduction time distributions indexed by the variation coefficient δ∈[0,1], which includes deterministic (δ=0) and memory-less exponential distribution (δ=1) as extreme cases. We present convincing numerical evidence and heuristic arguments that the generalized model is still in the Kardar-Parisi-Zhang (KPZ) universality class, and the changes in patterns are due to changing prefactors in the scaling relations, which we are able to predict quantitatively. With the example of Saccharomyces cerevisiae, we show that our approach using the variation coefficient also works for more realistic reproduction time distributions.

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