In the public van Klink et al. (2024) insect data, time-reversed classes give the same declines as first-year classes, so the faster decline of initially abundant species is regression to the mean

Question: van Klink et al. (2024, Nature) put insect populations into five classes by first-year abundance. After a correction for regression to the mean (RtM), they report that the most abundant class declines by 7.72% per year and the other classes by 4.6-6.1% per year. Is this a directional change? Data: their public population counts (Supplementary Data 2): 32,764 populations at 484 sites in 54 studies. Method: per-population Poisson trends with a weak prior. Forward trends use first-year classes. Reversed trends use last-year classes and reversed time. The directional part (forward - reversed)/2 is zero in expectation without change. We also reproduced the published one-year censoring correction. We calibrated all estimators with synthetic stationary communities on the real designs and with known declines injected into the real data. Results (population weights, 95% study-bootstrap intervals): forward class 5 changed by -11.0% [-13.6, -8.3] and class 1 by -9.2% per year. With the published correction, class 5 was -8.9% (published -7.72%). The reversed trends were almost the same: class 5 -10.1%, class 1 -8.3%. The directional part was between -0.9% and +1.0% per year in all six classes. The directional class 5 minus class 1 contrast was -0.0% [-2.5, +3.3] (study weights +1.6% [-0.9, +4.4]). These intervals exclude the published contrast of about -3.7% per year. In simulated communities with no change, the corrected forward estimator gave declines in all classes, and in a stress test it gave a class-5 decline of -6.0% and a contrast of -3.5% per year. The directional part stayed within 0.2% per year of zero. It recovered injected dominant-species erosion (truth -2.2%, estimate -2.3%). Whole-series classes gave a contrast of -1.3% [-3.5, +0.8]. Selection on first-year presence alone gave -21% per year for the rarest class. In nine variants the directional contrast was -1.2 to +1.6% per year. None was negative with an interval that excluded zero. Conclusion: in these data, the strong declines of initially present classes and the faster decline of initially abundant species are time-symmetric RtM and selection effects. The censoring correction does not remove them. The data agree with a shared decline of about 0-3% per year in all classes. Limits: we did not refit the hierarchical INLA model. The public data omit some studies. The test assumes time-reversible dynamics under the null. It cannot exclude directional contrasts of about 2% per year.

insect decline · regression to the mean · time reversal · abundance classes · population trends · dominant species · censoring correction · reanalysis · biodiversity time series · selection bias