In the paleoTS model set, the Ornstein–Uhlenbeck mode recasts fossil stasis as active mean-reversion toward an adaptive optimum, not a null absence of change

Within the maximum-likelihood model set that modern paleobiology fits to fossil trait time-series (claim-paleots-fits-fossil-stasis-as-a-selected-stochastic-model), the Ornstein–Uhlenbeck (OU) model describes a trait "pulled towards the optimum at a rate given by α." The biological gloss is explicit: the OU process "has been used to describe microevolutionary changes in a population close to a fixed peak in the adaptive landscape." Plain stasis in the same framework is bare "uncorrelated fluctuations around a fixed trait value"; the OU model adds a restoring force whose strength, α, is a fitted parameter.

The conceptual shift is from absence to activity. Naively one expects stasis to be modeled as a null baseline — no change, nothing happening. The OU model instead treats apparent stability as the visible outcome of an active pull toward an optimum: the lineage is held near a fitness peak by selection, and the observed constancy is the signature of that restoring force, not of its absence. Stability becomes something with a measurable magnitude rather than a gap to be explained away — the quantitative descendant of the "stasis is data" stance in claim-punctuated-equilibriums-novel-addition-was-stasis-emphasis.

The "fixed peak in the adaptive landscape" invoked here is Sewall Wright's 1932 adaptive-landscape image; the claim that this same landscape is the conceptual ancestor of the deep-learning "loss landscape" was a further lead in the capture and is routed, unsourced, to question-verify-wright-1932-adaptive-landscape-loss-landscape-lineage. The same OU restoring-force geometry recurs outside biology — in interest-rate models and in stochastic gradient descent near a loss minimum — collected in observation-mean-reversion-to-an-optimum-recurs-across-fossil-stasis-bonds-and-sgd.