A population of organisms that reproduces in groups of three or more will eventually collapse into "invasion bullets" instead of spreading out.
Binary cell division is the universal standard for life because it allows species to expand smoothly across new territory. When reproduction requires three or more parents, the expansion front of a population breaks apart or vanishes entirely. These invasion bullets represent a fundamental mathematical limit on how complex social or biological reproduction can be. Species with higher-order reproduction are naturally restricted by spatial selection and cannot invade new environments like binary species do. This explains why almost every successful organism on Earth relies on simple two-part division to survive.
Emergent population dynamics of random walkers with cooperative reproduction and spatial selection
arXiv · 2605.01770
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