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Colloquium : Inclusions, boundaries, and disorder in scalar active matter

https://doi.org/10.1103/RevModPhys.96.031003

Granek, Omer ; Kafri, Yariv ; Kardar, Mehran ; Ro, Sunghan ; Tailleur, Julien ; Solon, Alexandre ( September 2024 , Reviews of Modern Physics)
Specialization at an expanding front

https://doi.org/10.1103/PhysRevE.108.L032402

Li, Lauren H. ; Kardar, Mehran ( September 2023 , Physical Review E)

As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical simulations that, by gaining fitness through accumulating mutations, progeny of the initial seed population can differentiate into distinct specialists. With competition and selection limited to the growth front, the emerging specialists first segregate into sectors, which then expand to dominate the entire population. We quantify the scaling of the fixation time with the size of the population and observe different behaviors corresponding to distinct universality classes: unbounded and bounded gains in fitness lead to superdiffusive (z = 3/2) and diffusive (z = 2) stochastic wanderings of the sector boundaries, respectively.
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Interplay between morphology and competition in two-dimensional colony expansion

https://doi.org/10.1103/PhysRevE.108.L032301

Swartz, Daniel W. ; Lee, Hyunseok ; Kardar, Mehran ; Korolev, Kirill S. ( September 2023 , Physical Review E)

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (Kardar-Parisi-Zhang equation). We solve these equations and find three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition.
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