A stable heat observation offset was not rejected in nine British butterfly models for 1981-2024

We tested a coefficient restriction for a stable heat-related observation offset in butterfly indices. We used a verified published panel of nine species in England, Scotland and Wales. Three full-record models and six region and period models included a prior index, seasonal weather, heat peaks and site coverage. The restriction is the prior heat slope plus the lag-index coefficient times the current heat slope. All nine corrected intervals included zero. This does not confirm observation bias. We show that some biological heat responses give the same restriction. Small samples, regional weather and index error limit inference. We provide the derivation, unchanged panel, code, source hashes, uncertainty checks and a raw biological audit. No pollution effect is estimated.

butterfly · heat extremes · observation bias · dynamic regression · identification · null result