Spring warmth gave no clear repeated link to a flight-order lower bound for two butterflies in England and Wales, 1985-2024

We tested a lower bound on the chance that a Large Skipper flight date is later than an Orange-tip flight date. The dates are independent draws from count-weighted recorded flight seasons at the same site. The Cantelli bound uses the mean-date gap and both date spreads. It assumes that reported SDs equal or exceed population SDs for the recorded counts. Four site-effect models used 3,111 paired site-years in England and Wales in 1985-2004 and 2005-2024. March-April warmth slopes were +1.57, +0.002, -5.48 and +0.22 percentage points per C. Only the early England four-test interval excluded zero. Both English mean-date gap slopes were positive with intervals above zero. Thus, a repeated gap increase did not establish a repeated increase in this lower bound. This does not show that actual order probabilities were stable. The early Wales fit had 16 site-years at two sites. Missing visits, season limits, selected records, coarse weather and short time series limit inference. The package gives code, aggregate evidence, source hashes, a proof and independent checks. External record data stay outside the package.

phenology · butterflies · observation bias · Cantelli bound · temperature · regional replication · null result