Decade population trends of birds and moths persisted (noise-corrected r 0.24-0.35) but butterfly trends did not, and the Keith et al. (2015) anchored estimator makes trends seem to reverse

Question: does the population trend of a species in one 10-year period predict its trend in the next period? Keith et al. (2015) reported +0.59 for birds and -0.37 to -0.49 for mammals and fish. Their response-period line starts at the fitted end of the assessment-period line. Method: we show by analysis and simulation that this anchored estimator gives a negative correlation from year-to-year noise alone (limit -0.72 for 10-year windows), and that it also makes real reversal seem stronger. We use free least-squares slopes and a split-half estimator: random site halves have independent sampling noise, so their cross-half covariance gives the correlation of noise-free trends. Data: species indices (Poisson site + year models, windows every 5 years) from North American BBS 1966-2024, UK BBS, Swedish and Czech bird routes, Finnish moth traps, UK butterflies and English river fish; RAM stock biomass; 131,000 local single-site series. Results: split-half persistence was positive in all four bird schemes (0.26-0.35; mean 0.30, 95% CI 0.24-0.36; regression slope 0.26) and in moths (0.24, 0.17-0.32). It was zero in butterflies (-0.01, -0.20 to 0.13) and uncertain in river fish (0.14, -0.27 to 0.49; 33 species). RAM fish stocks reversed (-0.22, -0.38 to -0.06). On the same data the anchored estimator was 0.20-0.72 lower and negative in six of seven schemes (bird mean -0.09). On local series it gave -0.33 to -0.54 in all taxa, birds included, while free correlations were near zero. Single-route BBS trends had split-half persistence of only 0.04. In NA BBS, persistence was 0.09 for 5-year windows and 0.36 for 15-year windows. Conclusion: the reported bird versus mammal-fish contrast is mostly an estimator artefact combined with a difference in series scale. A species decline over 10 years is weak evidence of further decline; a local decline is almost no evidence. Limits: Europe and North America only; no mammal schemes; precision weights chosen after unweighted estimates were unstable in low-reliability schemes; year effects shared by all sites are not removed.

population trends · trend persistence · Red List criterion A · observation error · split-half reliability · Breeding Bird Survey · moths · butterflies · fish stocks · estimator bias · monitoring schemes · regression to the mean