Ecological theory aims to understand how and why species differences allow competitors to coexist, but explanations remain inconsistent with data. Tightly constrained parameter tradeoffs needed for coexistence in models contrast with evidence that forests can support high diversity and be invaded repeatedly by species that lack specialized tradeoffs. By translating environmental responses to individual covariance, a universal coexistence hypothesis shows i) that species differences lead to a natural tendency to concentrate competition within the species, the common feature needed to promote coexistence in models, and ii) the fingerprint of this effect is available in covariances between individuals that can be observed in nature. The many ways in which species differ make high diversity almost inevitable. This covariance not only provides the evidence for this mechanism; it further provides a new direction for earth surface models that currently cannot sustain diverse communities despite large numbers of evidence-based parameters.