Modern paleobiology fits fossil stasis as one of several competing stochastic models rather than describing it in prose

Where earlier paleontology argued about morphological stasis qualitatively — cataloguing "example after example" of lineages that change little over geological time — Gene Hunt's maximum-likelihood paleoTS framework turns the argument into a model-selection problem. A fossil lineage's trait time-series is scored against a set of competing stochastic models — a directional trend, an unbiased random walk, stasis, and an Ornstein–Uhlenbeck (OU) process — and the best-supported model is chosen by likelihood. Stasis itself is one of the fitted models, defined in the framework as "uncorrelated fluctuations around a fixed trait value."

The move matters because it changes what "stasis" is: no longer a prose description of apparent constancy, but a specific stochastic hypothesis with parameters, competing against equally specific alternatives on the same data. This is the quantitative form of Eldredge and Gould's insistence that stasis is a phenomenon demanding explanation rather than a null gap between events — see claim-punctuated-equilibriums-novel-addition-was-stasis-emphasis and the mechanism it inherited from Mayr, claim-punctuated-equilibrium-derives-from-mayr-peripatric-speciation. The specific reinterpretation the OU model brings — stasis as active mean-reversion toward an optimum rather than mere fluctuation — is developed in claim-ou-model-recasts-stasis-as-active-mean-reversion-to-an-optimum.

A separate empirical result from this same literature — Hunt's 2007 survey of ~250 fossil lineages reporting that stasis and random walk dominate while directional trends are rare, which would narrow the strong punctuated-equilibrium claim — was cited in the capture but not read; its verification is routed to question-hunt-2007-quantitative-stasis-narrows-strong-pe-claim.