@Artisian@lemmy.world You’re not thinking of it badly. Ratios have to be combined multiplicatively, so you can’t add per-population percentage changes linearly - and the LPI doesn’t. It aggregates trends with a weighted geometric mean (the ZSL method, see their rlpi package), i.e. through a log scale, then averages the terrestrial/freshwater/marine indices. So “geometric vs linear” is already resolved in the geometric direction.
The live arguments are elsewhere:
- Outlier sensitivity: Leung et al. 2020, Nature 588:267-271. The global decline trend was driven by a small fraction of populations (under 3%); remove those and it flattens drastically.
- Random-fluctuation bias: Buschke et al. 2021, Nat Ecol Evol 5:1145-1152. The framework doesn’t account for random population fluctuation, which can bias even stable populations toward apparent decline.
- Calculation bias: Toszogyova et al. 2024, Nat Commun 15:5295. Fix several mathematical issues and most populations show balanced decline and growth - amphibians are the clear exception, still falling steadily.
- The counter to all three: Loreau & Cardinale 2022, Nature 601:E27, “Do not downplay biodiversity loss”.
Underneath it, the thing most people (and headlines) get wrong, and what the LPI’s own FAQ flags: this is not absolute abundance. It’s the average rate of change across monitored populations - about 5,790 species and 35,803 populations - not a headcount of all animals. The headline is the index ending near 27% of its 1970 level, reported as an “average 73% decline”.
@Artisian@lemmy.world You’re right about your example, and that’s the useful split. Split one period evenly across three stocks and hold, and your wealth moves by the arithmetic mean of that period’s returns. AM is the correct answer there.
But that is a cross-sectional average for a single period. The LPI is a rate-of-change index over time, and it wants one number that stands in for “the average change.” A rate you can compose has to multiply, not add. The geometric mean is the constant factor r such that r^n = the product of the individual factors. The arithmetic mean is not, and the gap is not small:
factors 1.05, 1.10, 0.80 -> product = 0.924 AM = 0.9833. Apply it three times: 0.9833^3 = 0.951. Wrong total. GM = 0.9740. Apply it three times: 0.9740^3 = 0.924. Right total.
So the time machine isn’t a cheat, it’s the definition of an average rate: the single rate that, repeated n times, lands you where you actually landed. AM answers “what did the average stock do in one period.” GM answers “what constant rate reproduces the trajectory.” The LPI is a rate-of-change index, so it wants the second. (ZSL/WWF describe the method exactly as a weighted geometric mean, weighted to offset uneven data coverage across regions and taxa.)
A second argument points the same way, and it matters because these are ratios. A ratio index should be reversible: a 50% decline and a doubling should cancel. Geometric: GM(0.5, 2) = 1.0 exactly. Arithmetic: AM(0.5, 2) = 1.25, i.e. it calls a balanced pair a 25% increase. Arithmetic averaging of ratios is biased upward (bounded below at -100%, unbounded above) and isn’t reciprocal-consistent: GM(1/x) = 1/GM(x), but AM(1/x) != 1/AM(x). A quantity that multiplies should be averaged in its own space, which is the log space.
Honest caveat, because “geometric is right” settles the aggregation, not the headline number: because it works in logs, the GM is sensitive to extreme declines (one population down 99% contributes log(0.01) = -4.6 by itself). That is why Leung et al. 2020 (Nature 588:267-271) argued the global trend is driven by a small cluster of severe declines. That is a critique of the data and the weighting, not of the choice of mean. Separate question.
(Threading looked fine on my side, fwiw. Your reply had to be pulled across to my instance just now, which is probably why it looked odd in the tree.)