The Living Planet Index is not a reliable measure of population changes

A widely used index characterizing the average change in population sizes suffers from several mathematical and statistical issues, leading to a bias towards an apparent decrease even for balanced populations. The claim that vertebrate populations declined by 70% since 1970 is thus unsubstantiated.
Published in Ecology & Evolution
The Living Planet Index is not a reliable measure of population changes
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Few people doubt that we live in an era of unprecedented biodiversity loss. However, strong statements require strong support by data – in this case, reliable indicators of biodiversity change. One of the most popular indicators of the current state of nature has been the Living Planet Index (LPI), bi-annually published by the World Wildlife Fund in The Living Planet Report. According to the LPI, population abundances of vertebrates decreased on average by two-thirds since 1970 (1). This number is really terrifying - such population decreases in last 50 years would imply a huge global disaster. Not suprisingly, this statement has been widely cited in media and by world environmental leaders, including Greta Thunberg and David Attenborough.

However, when this number was first published, some researchers suspected it was somehow problematic. We all know that many species rapidly decline, but field ecologists are at the same time aware of many populations that have been rising in recent decades - for instance many large predators in both Europe and North America are now rapidly spreading, as are many non-native species. More importantly, previous analyses based on systematic surveys of all populations of a large taxon across large regions (e.g. the Breeding Bird Survey of all bird populations across most of the North American continent since the 1960s) indicated suprisingly balanced population increases and declines (2). Where then was such a scary number coming from?

The problem might be that standardized surveys typically comprised only some regions of the northern hemisphere, while more comprehensive global sampling may reveal a different picture. In 2019, we started to be interested in the abovementioned discrepancy, so we took the data from the Living Planet Database, the basis of the LPI, to see if vertebrate populations from different parts of the world reveal different proportions of decreasing and increasing trends. To our surprise, this was not the case. Increasing and decreasing populations were more or less balanced regardless of study region or taxon. The same conclusion was reached by several studies published in about the same time (3-5). They have shown that when we take individual populations as data points, the distribution of their trends is typically quite symmetric, indicating, as the title of one of these papers says, „the balance of winners and losers in the Anthropocene“. So how is it possible that the LPI, based on similar types of data, suggests such a pronounced decline?

Instead of further documenting the balance between declining and increasing populations in the Living Planet Database, we have decided to thoroughly explore the LPI itself, i.e. the method of its calculation. After two years of detailed inspection of LPI methodology, we have found several issues that bias the LPI towards indicating an overall population decline even when decreasing and increasing populations are balanced. All these issues stem from the basic principle of the LPI calculation. In contrast to the studies mentioned above that use one population time series as the basic unit for the analysis, the LPI primarily calculates the geometric mean of population change across all available populations between each two consecutive years. The value of the index in a year is then multiplied by this average growth rate to get the value for the following year (the value for 1970, i.e. the first year, is set to 1).

This procedure is perfectly appropriate if we want to express something like mean trajectory of population changes. However, our analysis reveals that it is very sensitive to the initial population change, as any decrease in the beginning of the study period pushes the index down, and the index can hardly rise again. This may be problematic when the data are represented by only a few populations at the beginning of the whole period. And that is the case – we have shown that in the extreme, the decreasing LPI for the whole Palearctic region actually depends on one decreasing population of viper (Vipera berus), as it is the only representative of herptiles for this region for the years 1974-1977, and the index is calculated by averaging across major taxa (i.e. birds, mammals and herptiles in terrestrial ecosystems). If these four records are removed, the LPI for the Palearctic region increases (Fig. 1). Such a sensitivity can be resolved by removing these single-population representatives (and it has been done for the viper in more recent versions of the index), but it is only a partial solution, as some such representatives with overly strong effect will always remain in the data.

Fig. 1: Comparison of the LPI for the terrestrial ecosystems of the Palearctic realm with and without including one population of viper (Vipera berus). This one viper population is the only representative for herptiles in the Palearctic for the four years at the beginning of the whole period (arrows) and is responsible for less-than-one index values for most of the period, erroneously indicating an overall decline in terrestrial Palearctic vertebrate populations.

But we found that other issues with the LPI are even  more substantial, as they are of a mathematical or statistical nature and comprise the way population growth rate is treated. Originally, we thought that the major reason why LPI shows such a high decrease even for balanced increases and decreases lies in the treatment of zeros in population time series. Because population growth rate is calculated in a multiplicative manner (it is the logarithm of the ratios between population sizes in two consecutive years), zero abundances cannot be used in the calculation. The LPI addresses this by replacing zeros with small values. This severely distorts the resulting index towards spurious population decline if zeros occur at the end of time series – and this is typical, as people do not start to count populations if they are absent, but they may record the absence at the end. However, thanks to some comments by the referees, we later realized there is another issue that is even more serious. In short, pure sampling error causes the declining LPI even for stable populations, since it leads to symmetric variation on an arithmetic scale, while population growth rate should be symmetric on the logarithmic scale if the populations are stable on average. This effect concerns very short time series the most – and short time series sensitive to the sampling error actually dominate the data.

We have also found some other (comparatively minor) issues with the LPI calculation, showing that all the revealed issues lead to the bias towards decreasing LPI. After accounting for them, the average decline of vertebrate populations is substantially lower, and for the unweighted version of LPI (in which regions and taxa are not weighted by their species richness), it is undistinguishable from no average decrease at all.

This does not mean that in reality there is no overall decrease in vertebrate populations. Many regions that were severely transformed were almost certainly not sampled, and the most serious population decreases may be thus missing from the Living Planet Database. On the other hand, many vertebrate populations may be recovering from their collapses that happened already before 1970. It would be naïve to assume that the pressure on vertebrate populations started in the 1970s – many vertebrate populations were severely exploited already in the 19th century and the first half of the last century, and they recovered only in the last few decades due to increasing global awareness of environmental issues and socioeconomic changes across the world. The current phase of the Anthropocene is thus characterised by more complex changes than the simple disappereance of vertebrate populations. And this is a good news, after all.

References

1. Almond, R. E. A., Grooten, M., Juffe Bignoli, D. & Petersen, T. (Eds). Living Planet Report 2022 - Building a Nature-Positive Society. (2022)

2. Keitt, T.H. & Stanley, H.E. Dynamics of North American breeding bird populations. Nature 393: 257-260. (1998)

3. Dornelas, M. et al. A balance of winners and losers in the Anthropocene. Ecology Letters 22, 847–854 (2019).

4. Daskalova, G. N., Myers-Smith, I. H. & Godlee, J. L. Rare and common vertebrates span a wide spectrum of population trends. Commun. 11, 4394 (2020).

5. Leung, B. et al. Clustered versus catastrophic global vertebrate declines. Nature 588, 267–271 (2020).

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