I understand that it does not mean
this doesn’t mean 73% of populations are in decline; in fact, around half of the studied populations were in decline, while half were either increasing or stable.
Maybe I should ask why the LPI report uses such a weird number instead?
@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”.
Interesting; the API isn’t good for replies in thread?
Anyway, I did more reading on geometric vs arithmetic applications, and I think I disagree? Arithmetic mean for a bunch of non-sequential %'s gives the expected change in population for a given population (randomly taken), while geometric tells you the average results if you experience each % change in sequence.
Example: if 3 stocks go +5%, +10% and -20%, then the AM is -5/3%, what an investor evenly spread would see happen to their wealth, while the GM is 97%, which corresponds to if you invested everything in stock 1, then took the annual results and a time machine and invested that in stock 2, and then again to stock 3; then rescaling the rate of change for the fact that you used a time machine 3 times…
(I agree the academics seem happy, and this is a basic concern that’s available to all of them, so I know this is fine. But I don’t understand why.)
@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.)
A “population” here is one species in one place: one herd, one reef, one flock. The LPI takes roughly 36,000 of those, measures how the size of each changed since 1970, and averages the relative changes into a single figure: -73%. So it’s the typical trajectory of a monitored population, not a headcount.
What it doesn’t tell you: how many individuals, species, or populations were lost, or even what share are shrinking. Around half of the monitored populations are actually stable or increasing. The average is pulled down because declines tend to be larger in magnitude than gains, and because the index is sensitive to how long each population has been monitored (short, noisy series swing harder).
On “why not just sum the animals”: you can’t add individuals across species (a sardine and a rhino aren’t one unit), and any raw total gets dominated by the most numerous taxa, so you’d mostly be tracking a few exploding populations. Per-population relative change is the attempt to avoid that.
Whether it’s the best indicator is a fair fight, and the OP’s link (Our World in Data, Hannah Ritchie) is the clearest plain-language read on it. The catch is that the headline usually gets reported as a headcount, which is exactly what it isn’t.
I appreciate this reply with the exception that it doesn’t discuss geometric vs linear average, but perhaps I’m just thinking of %'s badly?
Maybe I should ask why the LPI report uses such a weird number instead?
Take your population of 10,000 rhinos. It drops by 90% to 1,000. The next year it increases by 90% to 1,900. If you did a normal average of the changes, you’d get (-90%+90%)/2 = 0% change. That’s a useless number because there has obviously been some major changes between the two years.
If you use a geometric average you’d get sqrt(0.1 × 1.9) ~= 0.436 or roughly a 56% average decrease. This is more meaningful than saying the average change was 0%.
However, you can’t use that number to work out how many rhinos there are. It’s used to measure an overall trend. If the average decrease gets smaller, it would mean more populations are increasing and less populations are decreasing. Overall, that’s good. That’s what the number is meant to be used for.
If the average decline next year is 68% then that’d mean we’re doing something right because last year the average decline was 73%. What are we doing right? Which populations are better? Which are worse? You can’t tell from the average. It’s just a general marker of the overall trend.
But if I take a population that dies out, any population that dies out, in my sample, then the geometric average becomes 100% loss. There are definitely cases where the geometric average also gives a weird answer.
(I’ll also note that their headline number changes quite a bit year-to-year, as they expand the dataset and fiddle with how important they treat each part.)
I strongly agree with the base dataset - I just don’t understand why this is the best indicator. If we care about total population, we could just compute with the sum. If we care about how many populations are stable/growing, those numbers are also easy to get from the same data.
My own attempt, but I’m confused.
There might be many herds of each species, all scattered in different places. The report counts all the animals in each of these herds over time, and looks at how those change. Consider some rhino’s with two herds that are far apart. One of them is a giant herd, with 10000 rhinos, while the other is tiny with just 50. If the giant herd mostly dies out, and drops to 1000, while the tiny herd gets 5 times bigger to 250, then the average percent change is (-90% + 500%)/2 = +205%, even though almost all the rhinos died.
Except this is wrong; they actually take the geometric average, which I think would be sqrt( 0.1 * 5) = 0.25, a 75% decline?
Now, swap which populations do well. the 10000 rhinos become 50000 strong, and the 50 rhinos shrink to just a family or two of 10. The relative percent changes are the same; 500% for one, 10% for the other, so we would still report a 75% decline.
