Emergent population dynamics of random walkers with cooperative reproduction and spatial selection
TLDR
This paper explores how higher-order asexual reproduction impacts population invasion dynamics, finding qualitative changes beyond binary reproduction.
Key contributions
- Higher-order asexual reproduction qualitatively alters population invasion dynamics.
- Invasion fronts generally cease to exist beyond binary reproduction.
- Binary reproduction's invasion front speed becomes diffusion-independent.
- Ternary reproduction shows critical behavior, from localized "invasion bullets" to diffusive spreading.
Why it matters
This paper offers a theoretical explanation for the prevalence of binary reproduction in nature by demonstrating its unique advantages in population invasion dynamics. It highlights how different reproductive orders fundamentally alter spreading patterns, providing insights into ecological and evolutionary constraints.
Original 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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