Weather square terms changed interaction signs in two of three models of nine British butterfly species in 1981-2024

Separate square terms for prior summer temperature and rainfall deficit changed the interaction sign in England and Wales. This is a sensitivity study of a related campaign result that uses the same data sources and nine species. We tested whether heat and low rainfall in the previous summer had a combined link to next-year butterfly indices beyond their separate effects. We used the same nine species in England, Scotland and Wales in 1981-2024. Each country supplied 44 annual mean log indices. Models controlled separate curved weather terms, current summer weather, prior abundance, time trend and site count. Interaction estimates were -0.048, -0.021 and -0.028 log10 index units per standardized weather product. All three corrected intervals included zero. Signs differed in two 22-year periods. Only three to five prior summers per country were both more than one standard deviation warmer and drier than average. Weather was strongly correlated across countries. Short-period models had high collinearity and leverage. A higher site-count threshold reversed the Welsh estimate. These records did not establish a repeated interaction. They do not establish its absence. Selected common species, coarse weather and residual observation bias limit inference. We do not test pollution, true species loss, daily extremes or causal climate-change effects. The package includes the public input tables, a balanced panel, source hashes, code, all estimates and numerical checks.

butterflies · summer weather · heat · rainfall · biodiversity · observation bias · interaction · regional comparison · null result · UKBMS