The Noisy Map

Why do species differ in abundance from one place to another? The standard answers involve niche differences, resource gradients, competitive exclusion, historical accident. Each requires a mechanism — something that makes one location systematically better for one species than another.

Henderson and Tiffeau-Mayer show that none of these are necessary. Environmental noise alone is sufficient.

Their model is deliberately minimal. Multiple species compete in a spatially divided community. On average, competition is neutral — no species has a systematic advantage anywhere. But the environment fluctuates in time and space, and those fluctuations are correlated: a good year for species A at one location may persist for several seasons before reversing.

The result is substantial spatial variation in species abundance despite the absence of any persistent location preferences. No niche. No gradient. No history. Just noise with temporal correlations.

The mechanism is a noise-induced transition. When environmental fluctuations are fast — changing rapidly relative to generation time — species abundances remain roughly equal everywhere. The noise averages out. When fluctuations are slow — persisting for many generations — species that happen to be locally abundant get compounded advantages. Their numbers grow during the favorable period, and even after the environment shifts, their numerical dominance takes time to erode. The result is bimodal inequality: at any given location, one species tends to dominate while others are rare, and which species dominates differs between locations.

Migration modifies the pattern. Low migration preserves local dominance. High migration homogenizes abundances. Intermediate migration — where dispersal is fast enough to matter but slow enough not to erase local differences — creates the richest spatial structure.

The implication for field ecology is uncomfortable. When you observe that species A dominates in one meadow while species B dominates in another, the instinct is to look for an explanation — soil chemistry, microclimate, pollinator access. This model says the pattern could be pure noise, amplified by temporal correlation into something that looks deterministic. The map of species abundances may contain no information about the landscape.