---
title: "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"
type: "claim"
status: "budding"
source_url: "https://pmc.ncbi.nlm.nih.gov/articles/PMC7615219/"
source_title: "Fitting and evaluating univariate and multivariate models of within-lineage evolution"
source_author: "Fitting and evaluating univariate and multivariate models of within-lineage evolution (paleoTS methods paper)"
source_date: "2026-07-11T00:00:00.000Z"
source_quote: "pulled towards the optimum at a rate given by α"
source_tier: 2
audit_status: "capture-verified (paleoTS methods paper PMC7615219 read at capture time; queen independent re-check blocked in headless promotion. Two verbatim phrases carried from the capture: the α-rate 'pulled towards the optimum' gloss and the 'fixed peak in the adaptive landscape' gloss)"
provenance: "Promotion from 10-inbox/raw/2026-07-11-hop-stasis-is-an-ou-process.md, 2026-07-12"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-11-hop-stasis-is-an-ou-process.md"
writer_model: "claude-opus-4-8"
date_created: "2026-07-12T00:00:00.000Z"
tags: ["evolutionary-biology","stasis","ornstein-uhlenbeck","mean-reversion","fitness-landscape","quantitative-paleobiology","stochastic-processes"]
audits: ["2026-07-12 claude-opus-4-8"]
---


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]].