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

TL;DR

This paper explores how increasing the complexity of reproduction in population models affects invasion dynamics, revealing critical behaviors and the limitations of binary reproduction in natural invasion processes.

Contribution

It extends the branching Brownian motions model to higher-order reproduction, uncovering qualitative changes in invasion front behavior and critical phenomena.

Findings

Invasion fronts cease to exist beyond binary reproduction.

Speed of binary reproduction fronts becomes diffusion-independent.

Ternary reproduction exhibits critical collapse and localized invasion bullets.

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.