Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline

Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline Anna Toszogyova, Jan Smycka, David Storch This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2887653/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The Living Planet Index (LPI) measures the overall population trend of vertebrate species over recent decades and has been repeatedly used to assess the changing state of global biodiversity. The LPI indicates that vertebrate populations have decreased by almost 70% over the last 50 years. This is in striking contrast with current studies based on the same population data that show that increasing and decreasing populations are balanced on average. We examined the methodological pipeline of calculating the LPI to search for the source of this discrepancy. We found that the calculation of the LPI is biased by several mathematical issues which impose an imbalance between detected increasing and decreasing trends and overestimate population declines. Rather than indicating that vertebrate populations do not substantially change, our findings imply that population time series used in the Living Planet Database are not suitable for a proper evaluation of current biodiversity changes. Biological sciences/Ecology/Biodiversity Earth and environmental sciences/Ecology/Population dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The indicators of ecological changes are of paramount importance for monitoring and understanding the biodiversity crisis. An influential methodology for measuring biodiversity change was provided by World Wildlife Fund (WWF) in collaboration with the World Conservation Monitoring Centre in 1997, and is commonly known as the Living Planet Index (LPI) 1 . The LPI uses available population time series to calculate average trend in populations of vertebrate species from terrestrial, freshwater and marine ecosystems 1–3 . It was firstly published in the WWF's Living Planet Report 1998 4 , and in a collaborative partnership with the Zoological Society of London has been reported every two years. In 2006 it has been adopted by the Convention on Biological Diversity (CBD) as one of the headline indicators of progress towards its Strategic Plan for Biodiversity 2011-2020 5 with its Aichi targets, and the Post-2020 Global Biodiversity Framework 6 , and later on by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES). The LPI message is often reported in media and has become a key tool for convincing the public that the changing state of nature is serious and requires solutions. The most recently published Living Planet Report 2022 7 shows an average 69% decrease in almost 32,000 monitored populations of mammals, birds, amphibians, reptiles and fish between 1970 and 2018, although there is a variation among biogeographical regions and ecosystem types 7 . The worrying overall decline of vertebrate populations indicated by the LPI is in contrast with several current studies based on the same data that show that population increases and decreases are surprisingly well balanced 8,9 . Moreover, the removal of less than 3% of the most declining vertebrate populations completely reverses the overall population trend as expressed by the LPI towards overall increase, revealing a strong sensitivity of the LPI to extreme population trends 10 . These findings have raised the question whether there is not a bias in the calculation of the LPI. One such bias may stem from the weighted averaging procedure, when the taxa and regions are weighted by estimated species richness of respective groups. The weighted form of the global LPI shows a decline which is by 38% greater than the unweighted form 3 (see also Table 1, Extended Data Table 1 and Methods 'Calculating the Living Planet Index'). The weighting is not necessarily a problem per se, but weighting by the species richness of given taxon and region means that the poorly represented species-rich regions (typically tropical ones) may be driving the global LPI trajectory. Another potential issue is that the data used for the LPI calculation include many extremely short time series, which are prone to high measurement errors due to interannual variability and sampling issues 11,12 . Recently, Buschke et al. 13 pointed out several other potential sources of bias in the LPI calculation. One problem can be due to using the GAM method for smoothing the time series and the fact that LPI values are affected by the values of the previous period. A general feature of GAM models is that they misestimate the marginal values of the population series, even more so the more the population fluctuates. This effect causes the LPI to spuriously decline by about 9.6% 13 . These authors have also used a simple simulation model to show that there is a fundamental asymmetry in the calculation of the LPI, as populations that fluctuate randomly and symmetrically from the same initial point reveal a decreasing LPI. Potentially, there may be multiple issues in the way the LPI is calculated, as well as in the data which are used for this calculation, that may lead to various biases and misunderstandings. It is thus worth exploring the LPI calculation in more depth. Here we provide a detailed inspection of the methodological pipeline and computer codes used for calculating the LPI. We identify potential methodological flaws in the calculation, some of them previously reported in the literature 10,13 , but most of them unnoticed before. A thorough analysis of these potential shortcomings suggests that some of them have the potential to weaken or even revert the trends of the LPI, dramatically altering the conclusions given by the Living Planet Reports 7,14 . We also point out that the major issues related to the LPI are not only caused by the calculation itself, but are deeply related to the quality and representativeness of the underlying data. Results Errors in the code We have explored the code used for the calculation of the LPI. Although Loh et al. 1 , Collen et al. 2 and McRae et al. 3 provide the basic principle of calculating the LPI, the exact methodological procedure is clear only from the code of the package rlpi (v.0.1.0) in R 15 . This package was created and made available by the Zoological Society of London in 2017 and presented in McRae et al. 3 , who also introduced the diversity-weighted form of the LPI. In fact, without the precise procedure it is not possible to replicate the calculation to obtain the LPI identical to the one presented in the Living Planet Reports 7,14 . The procedure consists in several steps; addition of a constant to the whole time series if it contains zeros, estimation of new population values by the GAM or chain method, calculating mean population growth of each population for each year, hierarchical averaging of population growth from populations to species, taxa, biogeographical realms and ecosystems (Fig. 1; see Methods 'Calculating the Living Planet Index' for a detailed description and Methods 'The Living Planet Database' for a description of the database used). In a detailed R-code inspection we found errors in the original calculation of the LPI; see Supplementary Notes for their complete list and R-scripts with marked errors (Supplementary Data). All calculation errors in the code have a negligible effect on the final shape of the global LPI trajectory, but are evident in some cases where the LPI is calculated for a smaller subset of data - a certain taxon or biogeographical realm (Extended Data Fig. 1). We provide the R-code with all errors corrected (Supplementary Data). The effect of the number of records in the time series While the length of time series (in years) and/or the number of time series used in the calculation do not systematically affect the LPI, the number of records in time series does have an effect (Methods 'The effect of the duration and the number of records in the time series', Table 1, Extended Data Table 1, Extended Data Fig. 2, 3). The time series with fewer records tend to be declining on average, which could be one of the reasons why some studies 8,9 that did not include these time series (less than 5 or 10 recorded time points) did not show the prevalence of decreasing populations. Extreme sensitivity of the LPI to the initial decline of a few populations We found two major issues that lead to the biased LPI that consequently severely exacerbates population declines in vertebrates. First, the LPI is extremely sensitive to the availability of population time series at the beginning of the study period. It follows from the step-by-step calculation of the LPI, where the population change (N year+1 /N year ) is calculated between every two consecutive years and the index values are based on the multiplication of the previous value of the index by the geometric mean of population change (Fig. 1, Methods 'Calculating the Living Planet Index'). It means that the population increases/declines at the beginning of the time series transcribe through all the subsequent years. This is especially problematic because the population data from 1970's are sparse and of contestable quality (Extended Data Fig. 4 and 5). This property suggests that the low values of the LPI may easily result from few declining populations at the beginning of the study period. It is important to point out that the LPI is presented in the arithmetic scale and in this respect is asymmetric – since its value is calculated as the product of the previous year's value and the geometric mean of population change, the index does not fluctuate much if the previous value is way below 1 even if the population growth rate is relatively high, while it may fluctuate considerably if the previous value is high. An initial decrease of the LPI thus typically does not permit its later increase. This effect is strengthened by the hierarchical averaging procedure – if some taxa are represented by only a few populations, these populations have the potential to disproportionately affect the global index. An extreme case is the situation when herptiles in the Palearctic region are for the period 1974-1977 represented by only one (declining) population of viper Vipera berus . Hierarchical averaging across taxa and biogeographical regions leads to the situation when these four records of the viper population cause an 89.5% greater decrease (the index changes from the original value of 0.826 to 1.721 after removing these four records) in the final state of the LPI for the Palearctic realm (Fig. 2) and a 3.3% greater decrease in the LPI for the whole terrestrial system in comparison to the LPI without these four records. For the cases of single-population representatives of freshwater and marine ecosystems and their effects on the LPI, see Supplementary Notes. All the single-population representatives of population trends occur at the beginning of the measurement of population growth of a particular taxon and biogeographical realm. Although there are few populations also at the end of the study period, restricting the population data to a particular end year does not change the final shape of the index. Note that the effect of the hierarchical averaging and underrepresentation of some taxa/realms depends on the grouping. If one (relatively smaller) group shows a significantly negative/positive population trend, this will strongly affect the resulting average of all groups. Conversely, if this group is merged with another group, its negative/positive values are dissolved among all the values of both groups, and only then this merged group is averaged with other groups. For example, if we consider 5 realms and 3 taxa (in the unweighted form, as we compare it with the unweighted form of the next grouping) it decreases the decline in the LPI by 6.3% (leading to less decreasing LPI) compared to the situation when 6 realms and 4 taxa are distinguished (again in the unweighted form, as the weights are not available for this grouping) (Methods 'The number of biogeographical realms and vertebrate taxa'). The problem of zeros in population time series The second, conceptually more important issue comprises the way how zeros are treated when calculating the index. The LPI is based on averaging the interannual growth rate log 10 (N year+1 /N year ), which cannot be calculated if the population size is zero in one of the compared years. There are several possible solutions, the one used in the LPI calculation is that zeros are replaced by a small value. In particular, a constant of 1% of the population mean is added to all values in the time series if any year contains zero (Fig. 1, Methods 'Calculating the Living Planet Index'). This is in fact equivalent to a drop (in the case zero is at the end of time series) or an increase (if it is at the beginning) of the population size by two orders of magnitude, i.e. typically by much larger extent than usual population fluctuations. Such population change is entirely arbitrary, and using a different proportion than 1% of the population mean would lead to very different interannual growth rate of given population, and consequently a different LPI. If zeros were randomly distributed across population time series, this effect would cause just an increasing error, but not necessarily a bias towards the declining LPI. However, it is reasonable to assume that zeros occur with a higher frequency at the end of the time series, since populations are rarely studied when there are no individuals at the beginning. Such an asymmetry could cause the bias towards apparently declining populations. Indeed, the time series with zeros at the end outnumber those that begin with zero values in the Living Planet Database (Extended Data Table 2). Although the middle zeros or the middle sequences of zeros predominate overall, they cannot cause any bias. To explore the extent of this effect, we recalculated the LPI with the removed zeros from all population time series (if zeros were in the middle of the time series, the series splitted into multiple independent series; note that a sifgnificant number of population time series included sequences of several zeros; Extended Data Table 2). The change was substantial (Fig. 3, Table 1, Extended Data Table 1) – the decline of the global LPI was reduced by 19.2%, from the original drop to 32.7% (assuming the value of 1 in 1970) to 51.9% – but diferred among ecosystems. The reduction of the LPI decline was 33.8% in the case of the terrestrial ecosystem (from the original decrease to 36.8% to the decrease to only 70.6%), 19.3% for the freshwater ecosystem (from 18% to 37.3%), and less than 1% for the marine ecosystem (from 52.6% to 53.2%) (Extended Data Fig. 6, Table 1, Extended Data Table 1). The differences between ecosystems appear to be due to the different prevalence of zero-valued ends of the time series (Extended Data Table 2). Importantly, removing zeros sometimes led to considerable broadening of confidence intervals, so that these overlapped 1, implying that often it is impossible to say with certainty whether there is any significant population decrease (Fig. 3, Extended Data Fig. 6). Although the removal of zeros from population time series may look contentious, we argue that it is more appropriate than leaving the zeros in there. Population fluctuations represent a process which is well characterized by the ratio of population sizes in consecutive time steps, corresponding to per-capita population vital rates that link population sizes in consecutive years. In contrast, colonization and extinction represent different processes which break this inter-annual link and thus cannot be mixed with population fluctuations even if the fluctuations sometimes do result in extinction. If a population is non-existent in one of the two years, population growth does not have any meaning. Replacing zeros with any value then arbitrarily modifies the link (or its absence) between population state in consecutive years and seriously distorts statistical properties of population fluctuations. This holds even if the zeros in population time series do not represent real population absence but just a sampling effect. The LPI reflects the stationarity of the system rather than changes in abundance A recently published criticism of the LPI by Buschke et al. 13 has been based on the finding that the index declined even if the population trends were stable on average. Buschke et al. 13 derived the index value for simulated randomly fluctuating populations, where population changes adhered to a Poisson distribution with equal probability of being either positive or negative on arithmetic scale. Such populations diffusely diverged from one initial point (see Fig. 1 in ref. 13 ) and the whole set of all populations revealed the declining LPI. The problem is that such a process does lead to unrealistic non-stationary population size distributions. Even though the mean community abundance remains stable in the initial part of the simulation (50 years in Buschke et al. 13 ), the population sizes steadily diverge, and community equitability thus decreases with time, the community being characterized by increasing difference between abundant and rare species. Moreover, such a simulation process has an absorption boundary at zero, so that all populations would eventually go extinct after a finite number of steps. This non-stationary situation is thus appropriately reflected by the declining LPI even if the mean of population values remains unchanged. Discussion After the examination of the methodology of construction of the Living Planet Index, we found that all of the identified issues lead to an overestimation of population declines (note the positive effects, depicted by green colour, of the adjustments of the LPI in Table 1, Extended Data Table 1 and Fig. 4). The LPI seems biased due to calculation settings (hierarchy of averaging, grouping and weighting) and the problems with the character of the data (zeros in the time series, single-population representatives and the number of records in the time series). The LPI thus does not seem as a reliable measure of the changing state of nature – an indicator of the global state of nature should not be sensitive to the fact that 50 years ago one population of viper did not thrive well, and should not be affected by the particular way how population sizes were measured and how was treated population absence in the end or the beginning of the time series. Similarly, a universal index of population change should not be sensitive to particular grouping to taxa and biogeographical realms if its aim is to provide a rigorous, repeateble indicator with a straightforward interpretation. These shortcomings deserve particular attention if the LPI is calculated for individual regions or countries. There is a remedy to some of these issues. The LPI calculation should not comprise taxa and realms that are represented by only a few, or (in extreme) a single population. Due to the fact that the geometric mean is strongly influenced by outliers, especially if the number of values entering the calculation is low, the Index could use all variants of the removal of the single-population-representatives (i.e. sort of sensitivity analysis) or the variants of the shifted reference year to limit the small number of populations at the beginning of the study period or reshuffling population time series within the study period (see also ref. 11,12,16 ). It is also worth considering whether it is appropriate to use time series shorter than 2-5 years or with less than 3-5 recorded time points (see ref. 11 ). Additionally, since the procedure of the LPI calculation based on averaging the interannual population growth rates is not compatible with the zeros in the time series data, the only solution is not to include zeros. We are aware that the presence of zeros can be understood as an indication of population colonization or extinction, but these are essentially different processes from population fluctuations and should be thus treated separately (see ref. 8 for an example how to do it). The LPI corrected for the above explained biases does not indicate as strong global population declines as the original LPI, published in the Living Planet Reports 7,14 . However, this does not necessarily mean that the situation is in reality better. Population time series in the Living Planet Database do not represent results of a systematic survey, but simply comprise all populations sampled for very different reasons. It is possible that the data does not include many populations that actually rapidly declined without even being documented, and ultimately disappeared – many habitats which were entirely converted to intensive agriculture, plantations or human settlements were not explored before the transformation, and are typically not studied after the transformation to document population disapearance. Many populations have been studied in pristine and/or protected areas, so that the overall sample may be biased towards stable or increasing populations. On the other hand, there may be some bias also in the opposite direction, stemming from the fact that ecologists typically begin to study populations which are already established and not those recently emerging 16 . Relative weight of these biases is hard to compare, so that the suitability of the database for balanced evaluation of current changes is compromised. A solution of this problem would be to use only population time series from systematic surveys where all populations have been sampled regardless of their size, trends and environmental changes, but such studies are rare and strongly geographically biased 17-19 . Therefore, although there is a potential for evaluating the state of nature in some regions, global evaluation remains problematic. We have shown that there are serious issues with the calculation of the Living Planet Index that lead to an overestimation of vertebrate population declines. Some biases may be in principle corrected (and we provide tools how to do it), but the LPI will be still necessarily sensitive to the way how population time series are hierarchically grouped, and will be subject to several problems stemming from the fact that the data are extremely heterogeneous. There are multiple ways how to evaluate current trends in biodiversity and abundance of organisms, but it is improbable that all the complex changes can be reliably encompassed by a single number. Methods Calculating the Living Planet Index The methodological procedure for calculating the LPI consists from these steps: 1. Addition of a constant of 1% of the population mean (the mean from all non-zero values) to all values of the time series if the time series contains zero in any year. If the population series contains only zeros, the added constant is 10 -17 (we removed these cases). 2. Estimation of the new population values by two methods (also the way how to estimate missing values, i.e. values for years without population records): - GAM method is used if the length of the time series is equal to or longer than 6 records and only if the GAM fits well. The GAM smoothing parameter is set to 1/2 of the length of the time series. The GAM method is implemented on logarithmic (base e) values and the values estimated by the model are subsequently delogarithmized. - chain method is used if the length of the time series is less than 6 records or if the GAM does not fit well (or if all population values are the same). It is a log-linear interpolation for missing values in the population series (see Equation 2 in Collen et al. 2 ). 3. Logarithmic transformation (base 10) of the population values. 4. Calculating the difference between the (logarithmized) population values between every two consecutive years = the logarithm of the ratio of population values = population growth = lambda ( λ = log 10 ( N year+1 / N year )). 5. Calculating the arithmetic mean of lambdas (the logarithm of the geometric mean) of all populations of one species within one biogeographical realm (for an individual year). There are 5 (for the terrestrial and freshwater ecosystem) or 6 (for the marine ecosystem) biogeographical realms distinguished (see below). 6. Calculating the arithmetic mean of species-specific lambdas across all species of one taxon within one realm (for an individual year). There are 3 (for the terrestrial ecosystem) or 4 (for the freshwater and marine ecosystem) taxa distinguished (see below). 7. Calculating the weighted arithmetic mean of taxon-specific lambdas across all taxa within one realm (for an individual year). The taxon-specific lambdas are weighted by the ratio of the species richness of a given taxon and the species richness of all the taxa together (the weighted method was implemented by McRae at el. 3 ). 8. Calculating the weighted arithmetic mean of realm-specific lambdas across all realms (for an individual year). The realm-specific lambdas are weighted by the ratio of the species richness of a given realm and the species richness of all the realms together (the weighted method was implemented by McRae at el. 3 ). The result is one lambda for a certain year. 9. Calculating the arithmetic mean of ecosystem-specific lambdas across all ecosystems (for an individual year) is obtained by dividing the realm-specific weights by the number of ecosystems (only in the case when the global LPI is calculated), i.e all the realm-specific weights are multiplied by 1/3 (this procedure is not implemented in the code). 10. The calculation of the LPI as I = I p x 10 λ , where I p is the index of the previous year and the index of the starting year 1970 was set to 1. 11. The bootstrap calculation of the confidence intervals of the index. The method involves 100 resamplings of species from each taxon with replacement. The last 7 steps run in a loop for each year. More formally, the global LPI is calculated as a hierarchical sequence of five geometric means: The R-function from the package rlpi (https://github.com/Zoological-Society-of-London/rlpi) allows various calculation settings of the LPI. It is possible to change the minimum length of the time series (the number of records, but not the number of years) included in the calculation, the constant replacing zeros, the length of the time series for which the GAM or chain method is used, the GAM smoothing parameter, the limit value for outlying lambda and whether to replace the outlying lambdas, and the use of weighting. The weights of particular taxa and realms were obtained from McRae et al. 3 . The shape of the LPI curve is mostly influenced by two parameters; the number of records in the time series (fullness) and the use of weights (see ref. 3 ). The difference between the weighted and unweighted form of the global LPI is 44.5% (much greater decline in the weighted than unweighted form). The effect of weighting for the terrestrial, freshwater and marine LPI causes a 14.8%, 47.3% and 83.5% greater decline, respectively, in the weighted than unweighted form (Extended Data Table 1). The effect of the duration and the number of records in the time series The original method of calculating the index takes into consideration all time series longer than one record (2 or more). If the global LPI is calculated only with the time series with at least 3, 5, 10 records, the decline in the index is reduced by 14.3%, 14.7% and 26.4%, respectively (Extended Data Table 1, Extended Data Fig. 2). In the case of the terrestrial LPI, the inclusion of only time series with at least 5 records causes a 5.5% reduction in the decline. If the freshwater LPI is calculated with time series equal to or longer than 5 records, the decline in the index is reduced by 14.2%. Similarly for the marine LPI, the decline in the index is reduced by 25.6% (Extended Data Table 1 for all 3/5/10-records options, Extended Data Fig. 3). However, the length of the time series of estimated values can be longer than the length of the time series of population records. If the individual records are not consecutive in each year, the missing values are calculated (by the GAM or chain method). Therefore, it can happen that a time series having five records can enter the index calculation as a time series of more than five estimated population values - longer than four years. In any case, the number of the records in the time series (adjustable parameter in the R-code) limits the minimum length of the time series, i.e. its duration in years (which is not an adjustable parameter in the original code). On the other hand, the length of the time series (the duration) does not affect the minimum number of records, as it can be always as few as two records. Relatively smaller decline in the index after removing the time series with fewer records suggests that time series with lower fullness (as defined here) are on average those comprising decreasing populations. In contrast, the length of the time series (the interval between the first and last observation) has very little effect on the overall trend (Extended Data Table 1, Extended Data Fig. 2 and 3; see also ref. 20 ). The index calculation includes a smaller number of populations when limited by the duration of the time series (19,205/16,555/12,660 populations considered for at least 3/5/10-year-long time series). Even fewer populations are included when the limitation is based on the number of records in the time series (17,753/13,868/9,528 populations considered for at least 3/5/10-record-long time series). However, the resulting index is affected only by the limit on the number of records in the time series. This suggests that the LPI does not demonstrate a systematic trend based on the number of population series utilized and duration of time series, but it does reveal a trend influenced by the number of records within the time series. The Living Planet Database The data for the LPI calculation was obtained from the Living Planet Database (LPD) (https://livingplanetindex.org), which currently includes freely available time series data since 1970 to present (the data on many realms and taxa are there only until 2014) for 22,175 populations of 4,777 mammal, bird, reptile, amphibian and fish species from terrestrial, freshwater and marine ecosystems (data downloaded at 5/2021 and 1/2022) (Supplementary Table 1). The LPD is repeatedly updated with new population time series throughout the considered time frame, so that each new round of the LPI calculation works with a different data collection. The basic data units (records) are population sizes or various proxies of abundances (e.g. the number of individuals, breeding pairs, eggs, the number of burrows) or population densities or biomass (based on pitfall or camera traps, weight of net catch, various records per area or time) for different years. The population time series begin and end in different years and the records were sampled with different frequencies and often irregularly. The original LPI calculation considers 5 biogeographical realms and 3 taxa for the terrestrial ecosystem, 5 realms and 4 taxa for the freshwater ecosystem, and 6 realms and 4 taxa for the marine ecosystem (see SI in McRae et al. 3 ). The number of biogeographical realms and vertebrate taxa In the LPD, there are 6 biogeographical realms distinguished for the terrestrial/freshwater ecosystem; Afrotropical, Palearctic, Nearctic, Neotropical, Australasia and Indo-Malayan. The alternative is that Australasia and Indo-Malayan realms are merged into the Indo-Pacific. For vertebrate taxa, 5 groups are distinguished; birds, mammals, fish, reptiles and amphibians. Reptiles and amphibians can be merged into one group of herptiles. For the marine ecosystem there are 6 realms; Arctic, Atlantic North Temperate, Atlantic Tropical and Subtropical, Pacific North Temperate, Tropical and Subtropical Indo-Pacific, South Temperate and Antarctic. As there were weights for only 5 terrestrial/freshwater realms (Australasia and Indo-Malayan as one Indo-Pacific realm) and 3 and 4 taxa, respectively (reptiles and amphibians as herptiles), it was necessary to use the merged alternatives. Such a distinction of realm/taxon groups is established in the current LPD, but the latest two Living Planet Report 2020 14 and 2022 7 already state a different distinction for biogeographical realms, based on the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) regions; Africa, Europe and central Asia, North America, Latin Amerika and Caribbean, Asia Pacific. The LPD and Living Planet Report 2020 14 and 2022 7 regions thus do not fully overlap. Declarations Data availability Data of population time series stored within the Living Planet Database are managed and maintained by the Indicators & Assessments Unit at the Zoological Society of London (ZSL) and WWF International (WWF) and available on their website (https://livingplanetindex.org/data_portal). The values for weighting individual groups are available in Supplementary Tables S10-S13 from McRae et al. 2017. 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Grassland bird population declines at three Breeding Bird Survey spatial scales in contrast to a large native prairie. Ecosphere 13, e4309 (2022). Storch, D. et al. Decomposing trends in bird populations: Climate, life histories and habitat affect different aspects of population change. Divers. Distrib. 29, 572–585 (2023). Schipper, A.M. et al. Contrasting changes in the abundance and diversity of North American bird assemblages from 1971 to 2010. Glob. Change Biol. 22, 3948–3959 (2016). Westveer, J. et al. A Deep Dive into the Living Planet Index: A Technical Report. (WWF, 2022); https://www.livingplanetindex.org/documents/LPR_2022_TechnicalSupplement_DeepDiveLPI.pdf Table Table 1: The calculation of the global LPI and the LPI for each ecosystem adjusted (i) by increasing the number of records in individual populations included (time series with at least 5 records), (ii) by increasing the length of the population series included (time series at least 5 years long), (iii) by removing zeros from the population time series, (iv) by removing zeros from the population time series and including those with at least 5 records, (v) by removing zeros from the population time series and including those at least 5 years long, (vi) by not using the weights (compensating different species richness) for taxa and realms, (vii) and the unweighted LPI of the time series with at least 5 records, or (viii) at least 5 years long. (ix) The unweighted LPI without zeros in the population time series, (x) and unweighted without zeros in the population time series included with at least 5 records, or (xi) at least 5 years long. The values represent the final LPI values (the value of 1 was set for 1970). The green gradient shows the rate of decrease in the index decline (a positive difference between the adjusted and original value - the adjusted index declines less than the original). The red gradient shows the rate of increase in the index decline (a negative difference between the adjusted and original value - the adjusted index declines more than the original). Black colour refers to the rate of decrease in the index decline higher than 100%. For an extended version of the Table, see Extended Data Table 1. Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryData.zip Supplementary Data SupplementaryInformation.docx ExtendedData.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2887653","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":197142199,"identity":"f88db949-ab69-409c-8d5a-a2d411d38cb5","order_by":0,"name":"Anna Toszogyova","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYLCCDz9sSNTBOLMnjUQtzDxsh0lQzj+79+DHGTzn7fn5zx78dIPBzp6gFok755IlPljcTpzZcC5ZOochmZmwNTdyDCRn8NxOMDjYYwDUcoCNoA75GznGv3nYztnbH+Yx/g3UwkNQi8GNHDNpHrYDjBvYeMxAtkgQ1GII1GI5syc5ccYZHjPrHINkA4Ja5IAOu/Hhh509f/8Z49s5FUSEGLo7SdUwCkbBKBgFowArAACr5DcgaCMRcwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-6084-625X","institution":"Charles University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Anna","middleName":"","lastName":"Toszogyova","suffix":""},{"id":197142200,"identity":"b7248bff-cf2a-4fb9-a546-620c075372c6","order_by":1,"name":"Jan Smycka","email":"","orcid":"https://orcid.org/0000-0001-6142-5510","institution":"Charles University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"Smycka","suffix":""},{"id":197142201,"identity":"8a8ce352-999d-4ef9-bb17-8593ab0c991b","order_by":2,"name":"David Storch","email":"","orcid":"https://orcid.org/0000-0001-5967-1544","institution":"Charles University in Prague","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"Storch","suffix":""}],"badges":[],"createdAt":"2023-05-03 02:15:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2887653/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2887653/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":36821650,"identity":"8ac4c481-cb5e-4f5a-8244-18015c210c76","added_by":"auto","created_at":"2023-05-11 15:56:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":79559,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic description of the methodological procedure of the LPI calculation. (1) Addition of a constant of 1% of the population mean to all values of the time series, if the time series contains zero in any year. (2) Estimation of the new population values by two methods; GAM method (time series \u0026gt;5 records) or chain method (time series \u0026lt;=5 records or if the GAM does not fit well). (3) Logarithmic transformation (using base 10) of the population values. (4) Calculation of the population growth rate (λ) as the difference between (logarithmized) population values between every two consecutive years = the logarithm of the ratio of population values λ = log\u003csub\u003e10\u003c/sub\u003e(N\u003csub\u003eyear+1\u003c/sub\u003e/N\u003csub\u003eyear\u003c/sub\u003e). (5 - 9) Sequence of hierarchical averaging of population growth across populations, species, taxa, realms and ecosystems for a single year. (10) Calculation of the LPI as I = I\u003csub\u003eyear-1\u003c/sub\u003e x 10\u003csup\u003eλ \u003c/sup\u003e. The index of the initial year 1970 is set to 1. (11) The bootstrap calculation of the confidence intervals of the index. For a detailed description of individual steps of the calculation, see Methods 'Calculating the Living Planet Index'.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/b4e8ade130e36950ff67fae0.png"},{"id":36821653,"identity":"79b0b7ab-e5b8-477e-9a0a-a0a49d897c8b","added_by":"auto","created_at":"2023-05-11 15:56:05","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":71328,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of a single-population representative of a whole taxon in a certain realm. The original LPI for the whole Palearctic realm is green and the LPI calculated without the 4 records (1974-1977) of one population of viper \u003cem\u003eVipera berus\u003c/em\u003e is coral. The Palearctic LPI consists from the averaged population growth rate of three taxa, one of which in 1974-1977 was represented by only one declining population, causing the entire index to decline, subsequently affecting the remaining trajectory. Note that removing the effect of the four values of the viper, marked with arrows, changes not only the overall level of the LPI, but also its relative fluctuation, as low index values fluctuate less in the arithmetic scale by the very definition of the LPI. The coloured area shows the confidence intervals and the lines show the LPI values.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/63e2073753ea845661321822.png"},{"id":36821439,"identity":"05d6452d-7e4e-4891-ac2c-ee080ecaaed2","added_by":"auto","created_at":"2023-05-11 15:48:05","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":57968,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of removing zeros from population time series. The original global LPI is green and the LPI calculated without zeros in the population time series is coral. The coloured area shows the confidence intervals and the lines show the LPI values. For the effect of removing zeros for individual ecosystems, see Extended Data Fig. 6.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/2201fa911e4abceab1d6b156.png"},{"id":36821651,"identity":"b7e1b4b6-ace7-4c5d-9d4c-7af631315e7a","added_by":"auto","created_at":"2023-05-11 15:56:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":103894,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of adjustments of the LPI. The original LPI is green and the adjusted LPI is coral, calculated without zeros in the time series of populations included with at least 5 records globally (a) and separately for the terrestrial (b), freshwater (c) and marine (d) ecosystem. The coloured area shows the confidence intervals and the lines show the LPI values.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/7d0652729939fc8a1d07d1ea.png"},{"id":38860573,"identity":"ff62a5e5-95c2-4013-8c40-ae5e7e26ac43","added_by":"auto","created_at":"2023-06-21 08:00:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":633737,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/835caf4d-99e4-4576-9d81-587109d0eb8a.pdf"},{"id":36822128,"identity":"4a9751ac-9a6f-4863-a7a8-7bb54cfc1fa6","added_by":"auto","created_at":"2023-05-11 16:04:05","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":6762817,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Data\u003c/p\u003e","description":"","filename":"SupplementaryData.zip","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/711d1b49e5461873c936f2ab.zip"},{"id":36821438,"identity":"9ac72e29-129b-42e2-a9b2-db3048954ec6","added_by":"auto","created_at":"2023-05-11 15:48:04","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":13928,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/87e0f77150ccd2f45a75da90.docx"},{"id":36821443,"identity":"3de0f006-8355-4c8f-9c0f-649b962818aa","added_by":"auto","created_at":"2023-05-11 15:48:05","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":747863,"visible":true,"origin":"","legend":"","description":"","filename":"ExtendedData.docx","url":"https://assets-eu.researchsquare.com/files/rs-2887653/v1/e02da69f526b6e2b1a1600f7.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe indicators of ecological changes are of paramount importance for monitoring and understanding the biodiversity crisis.\u0026nbsp;An influential methodology for\u0026nbsp;measuring\u0026nbsp;biodiversity change was provided by World Wildlife Fund (WWF) in collaboration with the World Conservation Monitoring Centre in 1997, and is commonly known as the Living Planet Index (LPI)\u003csup\u003e1\u003c/sup\u003e. The LPI uses available population time series to calculate average trend in populations of vertebrate species from terrestrial, freshwater and marine ecosystems\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. It was firstly published in the WWF\u0026apos;s Living Planet Report 1998\u003csup\u003e4\u003c/sup\u003e, and in a collaborative partnership with the Zoological Society of London has been reported every two years. In 2006 it has been adopted by the Convention on Biological Diversity (CBD) as one of the headline indicators of progress towards its Strategic Plan for Biodiversity 2011-2020\u003csup\u003e5\u003c/sup\u003e with its Aichi targets, and the Post-2020 Global Biodiversity Framework\u003csup\u003e6\u003c/sup\u003e, and later on by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES). The LPI message is often reported in media and has become a key tool for convincing the public that the changing state of nature is serious and requires solutions. The most recently published Living Planet Report 2022\u003csup\u003e7\u003c/sup\u003e shows an average 69% decrease in almost 32,000 monitored populations of mammals, birds, amphibians, reptiles and fish between 1970 and 2018, although there is a variation among biogeographical regions and ecosystem types\u003csup\u003e7\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; The worrying overall decline of vertebrate populations indicated by the LPI is in contrast with several current studies based on the same data that show that population increases and decreases are surprisingly well balanced\u003csup\u003e8,9\u003c/sup\u003e. Moreover, the removal of less than 3% of the most declining vertebrate populations completely reverses the overall population trend as expressed by the LPI towards overall increase, revealing a strong sensitivity of the LPI to extreme population trends\u003csup\u003e10\u003c/sup\u003e. These findings have raised the question whether there is not a bias in the calculation of the LPI. One such bias may stem from the weighted averaging procedure, when the taxa and regions are weighted by estimated species richness of respective groups. The weighted form of the global LPI shows a decline which is by 38% greater than the unweighted form\u003csup\u003e3\u003c/sup\u003e (see also Table 1, Extended Data Table 1 and Methods \u0026apos;Calculating the Living Planet Index\u0026apos;). The weighting is not necessarily a problem per se, but weighting by the species richness of given taxon and region means that the poorly represented species-rich regions (typically tropical ones) may be driving the global LPI trajectory. Another potential issue is that the data used for the LPI calculation include many extremely short time series, which are prone to high measurement errors due to interannual variability and sampling issues\u003csup\u003e11,12\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Recently, Buschke et al.\u003csup\u003e13\u0026nbsp;\u003c/sup\u003epointed out several other potential sources of bias in the LPI calculation. One problem can be due to using the GAM method for smoothing the time series and the fact that LPI values are affected by the values of the previous period. A general feature of GAM models is that they misestimate the marginal values of the population series, even more so the more the population fluctuates. This effect causes the LPI to spuriously decline by about 9.6%\u003csup\u003e13\u003c/sup\u003e. These authors have also used a simple simulation model to show that there is a fundamental asymmetry in the calculation of the LPI, as populations that fluctuate randomly and symmetrically from the same initial point reveal a decreasing LPI. Potentially, there may be multiple issues in the way the LPI is calculated, as well as in the data which are used for this calculation, that may lead to various biases and misunderstandings. It is thus worth exploring the LPI calculation in more depth.\u003c/p\u003e\n\u003cp\u003eHere we provide a detailed inspection of the methodological pipeline and computer codes used for calculating the LPI. We identify potential methodological flaws in the calculation, some of them previously reported in the literature\u003csup\u003e10,13\u003c/sup\u003e, but most of them unnoticed before. A thorough analysis of these potential shortcomings suggests that some of them have the potential to weaken or even revert the trends of the LPI, dramatically altering the conclusions given by the Living Planet Reports\u003csup\u003e7,14\u003c/sup\u003e. We also point out that the major issues related to the LPI are not only caused by the calculation itself, but are deeply related to the quality and representativeness of the underlying data.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eErrors in the code\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe have explored the code used for the calculation of the LPI. Although Loh et al.\u003csup\u003e1\u003c/sup\u003e, Collen et al.\u003csup\u003e2\u003c/sup\u003e and McRae et al.\u003csup\u003e3\u003c/sup\u003e provide the basic principle of calculating the LPI, the exact methodological procedure is clear only from the code of the package rlpi (v.0.1.0) in R\u003csup\u003e15\u003c/sup\u003e. This package was created and made available by the Zoological Society of London in 2017 and presented in McRae et al.\u003csup\u003e3\u003c/sup\u003e, who also introduced the diversity-weighted form of the LPI. In fact, without the precise procedure it is not possible to replicate the calculation to obtain the LPI identical to the one presented in the Living Planet Reports\u003csup\u003e7,14\u003c/sup\u003e. The procedure consists in several steps; addition of a constant to the whole time series if it contains zeros, estimation of new population values by the GAM or chain method, calculating mean population growth of each population for each year, hierarchical averaging of population growth from populations to species, taxa, biogeographical realms and ecosystems (Fig. 1; see Methods 'Calculating the Living Planet Index' for a detailed description and Methods 'The Living Planet Database' for a description of the database used). In a detailed R-code inspection we found errors in the original calculation of the LPI; see Supplementary Notes for their complete list and R-scripts with marked errors (Supplementary Data). All calculation errors in the code have a negligible effect on the final shape of the global LPI trajectory, but are evident in some cases where the LPI is calculated for a smaller subset of data - a certain taxon or biogeographical realm (Extended Data Fig. 1). We provide the R-code with all errors corrected (Supplementary Data).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe effect of the number of records in the time series\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWhile the length of time series (in years) and/or the number of time series used in the calculation do not systematically affect the LPI, the number of records in time series does have an effect (Methods 'The effect of the duration and the number of records in the time series', Table 1, Extended Data Table 1, Extended Data Fig. 2, 3). The time series with fewer records tend to be declining on average, which could be one of the reasons why some studies\u003csup\u003e8,9\u003c/sup\u003e that did not include these time series (less than 5 or 10 recorded time points) did not show the prevalence of decreasing populations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eExtreme sensitivity of the LPI to the initial decline of a few populations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe found two major issues that lead to the biased LPI that consequently severely exacerbates population declines in vertebrates. First, the LPI is extremely sensitive to the availability of population time series at the beginning of the study period. It follows from the step-by-step calculation of the LPI, where the population change (N\u003csub\u003eyear+1\u003c/sub\u003e/N\u003csub\u003eyear\u003c/sub\u003e) is calculated between every two consecutive years and the index values are based on the multiplication of the previous value of the index by the geometric mean of population change (Fig. 1, Methods 'Calculating the Living Planet Index'). It means that the population increases/declines at the beginning of the time series transcribe through all the subsequent years. This is especially problematic because the population data from 1970's are sparse and of contestable quality (Extended Data Fig. 4 and 5). This property suggests that the low values of the LPI may easily result from few declining populations at the beginning of the study period. It is important to point out that the LPI is presented in the arithmetic scale and in this respect is asymmetric – since its value is calculated as the product of the previous year's value and the geometric mean of population change, the index does not fluctuate much if the previous value is way below 1 even if the population growth rate is relatively high, while it may fluctuate considerably if the previous value is high. An initial decrease of the LPI thus typically does not permit its later increase.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; This effect is strengthened by the hierarchical averaging procedure – if some taxa are represented by only a few populations, these populations have the potential to disproportionately affect the global index. An extreme case is the situation when herptiles in the Palearctic region are for the period 1974-1977 represented by only one (declining) population of viper \u003cem\u003eVipera berus\u003c/em\u003e. Hierarchical averaging across taxa and biogeographical regions leads to the situation when these four records of the viper population cause an 89.5% greater decrease (the index changes from the original value of 0.826 to 1.721 after removing these four records) in the final state of the LPI for the Palearctic realm (Fig. 2) and a 3.3% greater decrease in the LPI for the whole terrestrial system in comparison to the LPI without these four records.\u0026nbsp;For the cases of single-population representatives of freshwater and marine ecosystems and their effects on the LPI, see Supplementary Notes. All the single-population representatives of population trends occur at the beginning of the measurement of population growth of a particular taxon and biogeographical realm. Although there are few populations also at the end of the study period, restricting the population data to a particular end year does not change the final shape of the index.\u003c/p\u003e\n\u003cp\u003eNote that the effect of the hierarchical averaging and underrepresentation of some taxa/realms depends on the grouping. If one (relatively smaller) group shows a significantly negative/positive population trend, this will strongly affect the resulting average of all groups. Conversely, if this group is merged with another group, its negative/positive values are dissolved among all the values of both groups, and only then this merged group is averaged with other groups. For example, if we consider 5 realms and 3 taxa (in the unweighted form, as we compare it with the unweighted form of the next grouping) it decreases the decline in the LPI by 6.3% (leading to less decreasing LPI) compared to the situation when 6 realms and 4 taxa are distinguished (again in the unweighted form, as the weights are not available for this grouping) (Methods 'The number of biogeographical realms and vertebrate taxa').\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe problem of zeros in population time series\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe second, conceptually more important issue comprises the way how zeros are treated when calculating the index. The LPI is based on averaging the interannual growth rate log\u003csub\u003e10\u003c/sub\u003e(N\u003csub\u003eyear+1\u003c/sub\u003e/N\u003csub\u003eyear\u003c/sub\u003e), which cannot be calculated if the population size is zero in one of the compared years. There are several possible solutions, the one used in the LPI calculation is that zeros are replaced by a small value. In particular, a constant of 1% of the population mean is added to all values in the time series if any year contains zero (Fig. 1, Methods 'Calculating the Living Planet Index'). This is in fact equivalent to a drop (in the case zero is at the end of time series) or an increase (if it is at the beginning) of the population size by two orders of magnitude, i.e. typically by much larger extent than usual population fluctuations. Such population change is entirely arbitrary, and using a different proportion than 1% of the population mean would lead to very different interannual growth rate of given population, and consequently a different LPI. If zeros were randomly distributed across population time series, this effect would cause just an increasing error, but not necessarily a bias towards the declining LPI. However, it is reasonable to assume that zeros occur with a higher frequency at the end of the time series, since populations are rarely studied when there are no individuals at the beginning. Such an asymmetry could cause the bias towards apparently declining populations. Indeed, the time series with zeros at the end outnumber those that begin with zero values in the Living Planet Database (Extended Data Table 2). Although the middle zeros or the middle sequences of zeros predominate overall, they cannot cause any bias.\u003c/p\u003e\n\u003cp\u003eTo explore the extent of this effect, we recalculated the LPI with the removed zeros from all population time series (if zeros were in the middle of the time series, the series splitted into multiple independent series; note that a sifgnificant number of population time series included sequences of several zeros; Extended Data Table 2). The change was substantial (Fig. 3, Table 1, Extended Data Table 1) – the decline of the global LPI was reduced by 19.2%, from the original drop to 32.7% (assuming the value of 1 in 1970) to 51.9% – but diferred among ecosystems. The reduction of the LPI decline was 33.8% in the case of the terrestrial ecosystem (from the original decrease to 36.8% to the decrease to only 70.6%), 19.3% for the freshwater ecosystem (from 18% to 37.3%), and less than 1% for the marine ecosystem (from 52.6% to 53.2%) (Extended Data Fig. 6, Table 1, Extended Data Table 1). The differences between ecosystems appear to be due to the different prevalence of zero-valued ends of the time series (Extended Data Table 2). Importantly, removing zeros sometimes led to considerable broadening of confidence intervals, so that these overlapped 1, implying that often it is impossible to say with certainty whether there is any significant population decrease (Fig. 3, Extended Data Fig. 6).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Although the removal of zeros from population time series may look contentious, we argue that it is more appropriate than leaving the zeros in there. Population fluctuations represent a process which is well characterized by the ratio of population sizes in consecutive time steps, corresponding to per-capita population vital rates that link population sizes in consecutive years. In contrast, colonization and extinction represent different processes which break this inter-annual link and thus cannot be mixed with population fluctuations even if the fluctuations sometimes do result in extinction. If a population is non-existent in one of the two years, population growth does not have any meaning. Replacing zeros with any value then arbitrarily modifies the link (or its absence) between population state in consecutive years and seriously distorts statistical properties of population fluctuations. This holds even if the zeros in population time series do not represent real population absence but just a sampling effect.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe LPI reflects the stationarity of the system rather than changes in abundance\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA recently published criticism of the LPI by Buschke et al.\u003csup\u003e13\u003c/sup\u003e has been based on the finding that the index declined even if the population trends were stable on average. Buschke et al.\u003csup\u003e13\u003c/sup\u003e derived the index value for simulated randomly fluctuating populations, where population changes adhered to a Poisson distribution with equal probability of being either positive or negative on arithmetic scale. Such populations diffusely diverged from one initial point (see Fig. 1 in ref.\u003csup\u003e13\u003c/sup\u003e) and the whole set of all populations revealed the declining LPI. The problem is that such a process does lead to unrealistic non-stationary population size distributions. Even though the mean community abundance remains stable in the initial part of the simulation (50 years in Buschke et al.\u003csup\u003e13\u003c/sup\u003e), the population sizes steadily diverge, and community equitability thus decreases with time, the community being characterized by increasing difference between abundant and rare species. Moreover, such a simulation process has an absorption boundary at zero, so that all populations would eventually go extinct after a finite number of steps. This non-stationary situation is thus appropriately reflected by the declining LPI even if the mean of population values remains unchanged.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eAfter the examination of the methodology of construction of the Living Planet Index, we found that all of the identified issues lead to an overestimation of population declines (note the positive effects, depicted by green colour, of the adjustments of the LPI in Table 1, Extended Data Table 1 and Fig. 4). The LPI seems biased due to calculation settings (hierarchy of averaging, grouping and weighting) and the problems with the character of the data (zeros in the time series, single-population representatives and the number of records in the time series). The LPI thus does not seem as a reliable measure of the changing state of nature – an indicator of the global state of nature should not be sensitive to the fact that 50 years ago one population of viper did not thrive well, and should not be affected by the particular way how population sizes were measured and how was treated population absence in the end or the beginning of the time series. Similarly, a universal index of population change should not be sensitive to particular grouping to taxa and biogeographical realms if its aim is to provide a rigorous, repeateble indicator with a straightforward interpretation. These shortcomings deserve particular attention if the LPI is calculated for individual regions or countries.\u003c/p\u003e\n\u003cp\u003eThere is a remedy to some of these issues. The LPI calculation should not comprise taxa and realms that are represented by only a few, or (in extreme) a single population. Due to the fact that the geometric mean is strongly influenced by outliers, especially if the number of values entering the calculation is low, the Index could use all variants of the removal of the single-population-representatives (i.e. sort of sensitivity analysis) or the variants of the shifted reference year to limit the small number of populations at the beginning of the study period or reshuffling population time series within the study period (see also ref.\u003csup\u003e11,12,16\u003c/sup\u003e). It is also worth considering whether it is appropriate to use time series shorter than 2-5 years or with less than 3-5 recorded time points (see ref.\u003csup\u003e11\u003c/sup\u003e). Additionally, since the procedure of the LPI calculation based on averaging the interannual population growth rates is not compatible with the zeros in the time series data, the only solution is not to include zeros. We are aware that the presence of zeros can be understood as an indication of population colonization or extinction, but these are essentially different processes from population fluctuations and should be thus treated separately (see ref.\u003csup\u003e8\u003c/sup\u003e for an example how to do it).\u003c/p\u003e\n\u003cp\u003eThe LPI corrected for the above explained biases does not indicate as strong global population declines as the original LPI, published in the Living Planet Reports\u003csup\u003e7,14\u003c/sup\u003e. However, this does not necessarily mean that the situation is in reality better. Population time series in the Living Planet Database do not represent results of a systematic survey, but simply comprise all populations sampled for very different reasons. It is possible that the data does not include many populations that actually rapidly declined without even being documented, and ultimately disappeared – many habitats which were entirely converted to intensive agriculture, plantations or human settlements were not explored before the transformation, and are typically not studied after the transformation to document population disapearance. Many populations have been studied in pristine and/or protected areas, so that the overall sample may be biased towards stable or increasing populations. On the other hand, there may be some bias also in the opposite direction, stemming from the fact that ecologists typically begin to study populations which are already established and not those recently emerging\u003csup\u003e16\u003c/sup\u003e. Relative weight of these biases is hard to compare, so that the suitability of the database for balanced evaluation of current changes is compromised. A solution of this problem would be to use only population time series from systematic surveys where all populations have been sampled regardless of their size, trends and environmental changes, but such studies are rare and strongly geographically biased\u003csup\u003e17-19\u003c/sup\u003e. Therefore, although there is a potential for evaluating the state of nature in some regions, global evaluation remains problematic.\u003c/p\u003e\n\u003cp\u003eWe have shown that there are serious issues with the calculation of the Living Planet Index that lead to an overestimation of vertebrate population declines. Some biases may be in principle corrected (and we provide tools how to do it), but the LPI will be still necessarily sensitive to the way how population time series are hierarchically grouped, and will be subject to several problems stemming from the fact that the data are extremely heterogeneous. There are multiple ways how to evaluate current trends in biodiversity and abundance of organisms, but it is improbable that all the complex changes can be reliably encompassed by a single number.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eCalculating the Living Planet Index\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe methodological procedure for calculating the LPI consists from these steps:\u003c/p\u003e\n\u003cp\u003e1. Addition of a constant of 1% of the population mean (the mean from all non-zero values) to all values of the time series if the time series contains zero in any year. If the population series contains only zeros, the added constant is 10\u003csup\u003e-17\u003c/sup\u003e (we removed these cases).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e2. Estimation of the new population values by two methods (also the way how to estimate missing values, i.e. values for years without population records):\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;- GAM method is used if the length of the time series is equal to or longer than 6 records and only if the GAM fits well. The GAM smoothing parameter is set to 1/2 of the length of the time series. The GAM method is implemented on logarithmic (base e) values and the values estimated by the model are subsequently delogarithmized.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;- chain method is used if the length of the time series is less than 6 records or if the GAM does not fit well (or if all population values are the same). It is a log-linear interpolation for missing values in the population series (see Equation 2 in Collen et al.\u003csup\u003e2\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003e3. Logarithmic transformation (base 10) of the population values.\u003c/p\u003e\n\u003cp\u003e4. Calculating the difference between the (logarithmized) population values between every two consecutive years = the logarithm of the ratio of population values = population growth = lambda (\u003cem\u003e\u0026lambda;\u003c/em\u003e = log\u003csub\u003e10\u003c/sub\u003e(\u003cem\u003eN\u003csub\u003eyear+1\u003c/sub\u003e\u003c/em\u003e/\u003cem\u003eN\u003csub\u003eyear\u003c/sub\u003e\u003c/em\u003e)).\u003c/p\u003e\n\u003cp\u003e5. Calculating the arithmetic mean of lambdas (the logarithm of the geometric mean) of all populations of one species within one biogeographical realm (for an individual year). There are 5 (for the terrestrial and freshwater ecosystem) or 6 (for the marine ecosystem) biogeographical realms distinguished (see below).\u003c/p\u003e\n\u003cp\u003e6. Calculating the arithmetic mean of species-specific lambdas across all species of one taxon within one realm (for an individual year). There are 3 (for the terrestrial ecosystem) or 4 (for the freshwater and marine ecosystem) taxa distinguished (see below).\u003c/p\u003e\n\u003cp\u003e7. Calculating the weighted arithmetic mean of taxon-specific lambdas across all taxa within one realm (for an individual year). The taxon-specific lambdas are weighted by the ratio of the species richness of a given taxon and the species richness of all the taxa together (the weighted method was implemented by McRae at el.\u003csup\u003e3\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003e8. Calculating the weighted arithmetic mean of realm-specific lambdas across all realms (for an individual year). The realm-specific lambdas are weighted by the ratio of the species richness of a given realm and the species richness of all the realms together (the weighted method was implemented by McRae at el.\u003csup\u003e3\u003c/sup\u003e). The result is one lambda for a certain year.\u003c/p\u003e\n\u003cp\u003e9. Calculating the arithmetic mean of ecosystem-specific lambdas across all ecosystems (for an individual year) is obtained by dividing the realm-specific weights by the number of ecosystems (only in the case when the global LPI is calculated), i.e all the realm-specific weights are multiplied by 1/3 (this procedure is not implemented in the code).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e10. The calculation of the LPI as I = I\u003csub\u003ep\u003c/sub\u003e x 10\u003csup\u003e\u0026lambda;\u003c/sup\u003e, where I\u003csub\u003ep\u003c/sub\u003e is the index of the previous year and the index of the starting year 1970 was set to 1.\u003c/p\u003e\n\u003cp\u003e11. The bootstrap calculation of the confidence intervals of the index. The method involves 100 resamplings of species from each taxon with replacement.\u003c/p\u003e\n\u003cp\u003eThe last 7 steps run in a loop for each year.\u003c/p\u003e\n\u003cp\u003eMore formally, the global LPI is calculated as a hierarchical sequence of five geometric means:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eThe R-function from the package rlpi (https://github.com/Zoological-Society-of-London/rlpi) allows various calculation settings of the LPI. It is possible to change the minimum length of the time series (the number of records, but not the number of years) included in the calculation, the constant replacing zeros, the length of the time series for which the GAM or chain method is used, the GAM smoothing parameter, the limit value for outlying lambda and whether to replace the outlying lambdas, and the use of weighting. The weights of particular taxa and realms were obtained from McRae et al.\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe shape of the LPI curve is mostly influenced by two parameters; the number of records in the time series (fullness) and the use of weights (see ref.\u003csup\u003e3\u003c/sup\u003e). The difference between the weighted and unweighted form of the global LPI is 44.5% (much greater decline in the weighted than unweighted form). The effect of weighting for the terrestrial, freshwater and marine LPI causes a 14.8%, 47.3% and 83.5% greater decline, respectively, in the weighted than unweighted form (Extended Data Table 1).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe effect of the duration and the number of records in the time series\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe original method of calculating the index takes into consideration all time series longer than one record (2 or more). If the global LPI is calculated only with the time series with at least 3, 5, 10 records, the decline in the index is reduced by 14.3%, 14.7% and 26.4%, respectively (Extended Data Table 1, Extended Data Fig. 2). In the case of the terrestrial LPI, the inclusion of only time series with at least 5 records causes a 5.5% reduction in the decline. If the freshwater LPI is calculated with time series equal to or longer than 5 records, the decline in the index is reduced by 14.2%. Similarly for the marine LPI, the decline in the index is reduced by 25.6% (Extended Data Table 1 for all 3/5/10-records options, Extended Data Fig. 3). However, the length of the time series of estimated values can be longer than the length of the time series of population records. If the individual records are not consecutive in each year, the missing values are calculated (by the GAM or chain method). Therefore, it can happen that a time series having five records can enter the index calculation as a time series of more than five estimated population values - longer than four years. In any case, the number of the records in the time series (adjustable parameter in the R-code) limits the minimum length of the time series, i.e. its duration in years (which is not an adjustable parameter in the original code). On the other hand, the length of the time series (the duration) does not affect the minimum number of records, as it can be always as few as two records. Relatively smaller decline in the index after removing the time series with fewer records suggests that time series with lower fullness (as defined here) are on average those comprising decreasing populations. In contrast, the length of the time series (the interval between the first and last observation) has very little effect on the overall trend (Extended Data Table 1, Extended Data Fig. 2 and 3; see also ref.\u003csup\u003e20\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003eThe index calculation includes a smaller number of populations when limited by the duration of the time series (19,205/16,555/12,660 populations considered for at least 3/5/10-year-long time series). Even fewer populations are included when the limitation is based on the number of records in the time series (17,753/13,868/9,528 populations considered for at least 3/5/10-record-long time series). However, the resulting index is affected only by the limit on the number of records in the time series. This suggests that the LPI does not demonstrate a systematic trend based on the number of population series utilized and duration of time series, but it does reveal a trend influenced by the number of records within the time series.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe Living Planet Database\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data for the LPI calculation was obtained from the Living Planet Database (LPD) (https://livingplanetindex.org), which currently includes freely available time series data since 1970 to present (the data on many realms and taxa are there only until 2014) for 22,175 populations of 4,777 mammal, bird, reptile, amphibian and fish species from terrestrial, freshwater and marine ecosystems (data downloaded at 5/2021 and 1/2022) (Supplementary Table 1). The LPD is repeatedly updated with new population time series throughout the considered time frame, so that each new round of the LPI calculation works with a different data collection. The basic data units (records) are population sizes or various proxies of abundances (e.g. the number of individuals, breeding pairs, eggs, the number of burrows) or population densities or biomass (based on pitfall or camera traps, weight of net catch, various records per area or time) for different years. The population time series begin and end in different years and the records were sampled with different frequencies and often irregularly. The original LPI calculation considers 5 biogeographical realms and 3 taxa for the terrestrial ecosystem, 5 realms and 4 taxa for the freshwater ecosystem, and 6 realms and 4 taxa for the marine ecosystem (see SI in McRae et al.\u003csup\u003e3\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe number of biogeographical realms and vertebrate taxa\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the LPD, there are 6 biogeographical realms distinguished for the terrestrial/freshwater ecosystem; Afrotropical, Palearctic, Nearctic, Neotropical, Australasia and Indo-Malayan. The alternative is that Australasia and Indo-Malayan realms are merged into the Indo-Pacific. For vertebrate taxa, 5 groups are distinguished; birds, mammals, fish, reptiles and amphibians. Reptiles and amphibians can be merged into one group of herptiles. For the marine ecosystem there are 6 realms; Arctic, Atlantic North Temperate, Atlantic Tropical and Subtropical, Pacific North Temperate, Tropical and Subtropical Indo-Pacific, South Temperate and Antarctic. As there were weights for only 5 terrestrial/freshwater realms (Australasia and Indo-Malayan as one Indo-Pacific realm) and 3 and 4 taxa, respectively (reptiles and amphibians as herptiles), it was necessary to use the merged alternatives. Such a distinction of realm/taxon groups is established in the current LPD, but the latest two Living Planet Report 2020\u003csup\u003e14\u003c/sup\u003e and 2022\u003csup\u003e7\u003c/sup\u003e already state a different distinction for biogeographical realms, based on the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) regions; Africa, Europe and central Asia, North America, Latin Amerika and Caribbean, Asia Pacific. The LPD and Living Planet Report 2020\u003csup\u003e14\u003c/sup\u003e and 2022\u003csup\u003e7\u003c/sup\u003e regions thus do not fully overlap.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData of population time series stored within the Living Planet Database are managed and maintained by the Indicators \u0026amp; Assessments Unit at the Zoological Society of London (ZSL) and WWF International (WWF) and available on their website (https://livingplanetindex.org/data_portal).\u003c/p\u003e\n\u003cp\u003eThe values for weighting individual groups are available in Supplementary Tables S10-S13 from McRae et al. 2017.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe open-source code used to calculate the Living Planet Index using data from the LPD is available on the GitHub repository, maintained by the ZSL: https://github.com/Zoological-Society-of-London/rlpi.\u003c/p\u003e\n\u003cp\u003eR code and outputs (R scripts and RData files) for all analyses used for this study are available in Supplementary Data.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e\u003cspan\u003eLoh, J. et al. The Living Planet Index: using species population time series to track trends in biodiversity. Philos. Trans. R. Soc. B Biol. Sci. 360, 289\u0026ndash;295 (2005).\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eCollen, B. et al. Monitoring change in vertebrate abundance: the Living Planet Index. Conserv. Biol. 23, 317\u0026ndash;327 (2009).\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eMcRae, L., Deinet, S. \u0026amp; Freeman, R. The diversity-weighted Living Planet Index: controlling for taxonomic bias in a global biodiversity indicator. 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Change Biol. 22, 3948\u0026ndash;3959 (2016).\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eWestveer, J. et al. \u003cem\u003eA Deep Dive into the Living Planet Index: A Technical Report.\u003c/em\u003e (WWF, 2022); \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.livingplanetindex.org/documents/LPR_2022_TechnicalSupplement_DeepDiveLPI.pdf\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table","content":"\u003cp\u003e\u003cstrong\u003eTable 1:\u003c/strong\u003e The calculation of the global LPI and the LPI for each ecosystem adjusted (i) by increasing the number of records in individual populations included (time series with at least 5 records), (ii) by increasing the length of the population series included (time series at least 5 years long), (iii) by removing zeros from the population time series, (iv) by removing zeros from the population time series and including those with at least 5 records, (v) by removing zeros from the population time series and including those at least 5 years long, (vi) by not using the weights (compensating different species richness) for taxa and realms, (vii) and the unweighted LPI of the time series with at least 5 records, or (viii) at least 5 years long. (ix) The unweighted LPI without zeros in the population time series, (x) and unweighted without zeros in the population time series included with at least 5 records, or (xi) at least 5 years long. The values represent the final LPI values (the value of 1 was set for 1970). The green gradient shows the rate of decrease in the index decline (a positive difference between the adjusted and original value - the adjusted index declines less than the original). The red gradient shows the rate of increase in the index decline (a negative difference between the adjusted and original value - the adjusted index declines more than the original). Black colour refers to the rate of decrease in the index decline higher than 100%. For an extended version of the Table, see Extended Data Table 1.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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The LPI indicates that vertebrate populations have decreased by almost 70% over the last 50 years. This is in striking contrast with current studies based on the same population data that show that increasing and decreasing populations are balanced on average. We examined the methodological pipeline of calculating the LPI to search for the source of this discrepancy. We found that the calculation of the LPI is biased by several mathematical issues which impose an imbalance between detected increasing and decreasing trends and overestimate population declines. Rather than indicating that vertebrate populations do not substantially change, our findings imply that population time series used in the Living Planet Database are not suitable for a proper evaluation of current biodiversity changes.\u003c/p\u003e","manuscriptTitle":"Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-05-11 15:48:00","doi":"10.21203/rs.3.rs-2887653/v1","editorialEvents":[{"type":"communityComments","content":1}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c28ab5a9-8435-4f96-bcc6-b3162b8cc036","owner":[],"postedDate":"May 11th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":21191848,"name":"Biological sciences/Ecology/Biodiversity"},{"id":21191849,"name":"Earth and environmental sciences/Ecology/Population dynamics"}],"tags":[],"updatedAt":"2023-10-30T10:51:15+00:00","versionOfRecord":[],"versionCreatedAt":"2023-05-11 15:48:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2887653","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2887653","identity":"rs-2887653","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}