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arXiv · 2605.01770

Emergent population dynamics of random walkers with cooperative reproduction and spatial selection

Ohad Vilk·Baruch Meerson
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Abstract

We extend the $N$ branching Brownian motions model of population invasion to higher-order asexual reproduction. Increasing reproduction order leads to qualitative changes: invasion fronts generically cease to exist beyond binary reproduction; and in the binary case itself, their speed becomes diffusion-independent. Ternary reproduction shows critical behavior, with collapse into a strongly localized `invasion bullet' in the supercritical regime, diffusive spreading in the subcritical regime, and a continuous family of fronts at criticality. These results suggest that the dominance of division and binary reproduction in nature reflects fundamental constraints on invasion dynamics.

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Ohad Vilk, Baruch Meerson. 2026-05-03. Emergent population dynamics of random walkers with cooperative reproduction and spatial selection. https://doi.org/10.1103/x1ns-ln24

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