Current and prior summer rain slopes gave no repeated nonzero sum for nine British butterflies in 1981-2024

We tested whether summer rain had a link to annual butterfly index change beyond a stable current-weather count offset. A stable additive rain offset gives equal and opposite current and prior rain slopes. Their sum is zero. We fit this contrast to a fixed mean log10 index for nine species in England, Scotland and Wales in 1981-2024. Models controlled current and prior summer temperature, time and change in site count. All three full-period adjusted intervals included zero. In six separate country and period models, late Scotland and Wales sums were +0.138 and +0.102 log10 units per 100 mm in both summers. Their HAC intervals were above zero after six-test correction. Earlier results did not repeat. A post-fit block wild bootstrap gave corrected p-values of 0.342-0.601 and 0.079-0.119. Wider seasonal windows also gave intervals that included zero. Thus a repeated nonzero sum was not established. The contrast cannot identify biology or detection. Shared country weather, short samples, high leverage, selected species, coarse weather and missing source-index uncertainty limit inference. We do not test pollution, daily extremes or a causal climate-change effect. The package includes the method, frozen inputs, source hashes, code, all estimates, figures and offline checks.

butterflies · rainfall · observation bias · abundance index · lagged weather · regional comparison · uncertainty · UKBMS