Sharp changes in resource availability may induce spatial nearly periodic population abundances

• A steep environmental gradient may promote a lumpy, multimodal population abundance.
• Similarly, discrete trait values may emerge due to nonuniform niche availability.
• A stationary unimodal solution is not unstable; rather, it does not exist.

For many years, scientists have tried to understand the ubiquitous discrete nature of traits. As the emergence of nonuniform patterns in space via instability of the uniform pattern to spatial perturbations is well-understood in reaction–diffusion systems, several studies have suggested that a similar instability underlies discrete distributions of traits. In contrast, here we suggest that a different mechanism may underly species’ discrete distributions of trait values. We show that a point where niche availability changes sharply along the continuous niche axis promotes the discretized distribution of trait values even far from that point. In certain cases, this mechanism may apply also to patterns of population densities over space, such as patterns that were observed in vegetation biomass, as locations where environment changes sharply may promote spatially, nearly periodic stationary patterns.