The Living Planet Index (LPI), developed by the World Wildlife Fund (WWF) and the World Conservation Monitoring Centre, is a crucial indicator of biodiversity change, adopted by several international organizations and frequently reported in the media. It utilizes population time series data to calculate the average trend in vertebrate populations across terrestrial, freshwater, and marine ecosystems. The LPI's consistently reported significant decline in vertebrate populations—a 69% decrease between 1970 and 2018—is a major concern. However, this alarming trend contrasts with findings from other studies using similar data, which show a more balanced picture of population increases and decreases. This discrepancy raises questions about potential biases within the LPI's calculation methodology. Several potential biases have been identified in previous studies, including the weighted averaging procedure that gives disproportionate weight to poorly represented species-rich regions (typically tropical ones), the use of many short time series prone to high measurement errors, and the Generalized Additive Model (GAM) smoothing method that misestimates marginal values. This paper delves into a detailed examination of the LPI's calculation pipeline to identify and quantify these biases, aiming to clarify the discrepancies between the LPI and other assessments of biodiversity trends and to propose improvements for future calculations.

Existing literature highlights several potential biases in the LPI calculation. Buschke et al. (2021) demonstrated that the index can decline even with stable average population trends due to an asymmetry in the calculation, particularly when population fluctuations are symmetric on an arithmetic scale rather than a logarithmic scale. Puurtinen et al. (2022) questioned the appropriateness of geometric averaging used in the LPI, arguing it's only suitable for interdependent values within a single population, not for averaging trends across multiple populations. Other studies have pointed to the influence of short time series, susceptible to high measurement errors, and the impact of weighting by species richness, which might overemphasize poorly represented regions. Dove et al. (2023) investigated the reliability and data deficiency in global vertebrate population trends using the Living Planet Index, further highlighting the complexities and challenges in accurately capturing biodiversity change.

The authors examined the R code from the `rlpi` package (version 0.1.0), which is used to calculate the LPI. The methodology involves several steps: (1) adding a constant (1% of the mean) to time series with zeros; (2) estimating population values using GAM (for series ≥ 6 records) or a chain method (otherwise); (3) log-transforming population values; (4) calculating annual population growth (λ); (5-9) hierarchical averaging of λ across populations, species, taxa, realms, and ecosystems; (10) calculating the LPI (I_t = I_t-1 × 10^λ); (11) bootstrap confidence interval calculation. The analysis involved recalculating the LPI using various modifications to the methodology, including different minimum time series lengths (number of records and years), removing zeros, removing the effect of single population representatives and comparing weighted vs. unweighted forms of the index. The data came from the Living Planet Database (LPD), comprising population time series for various vertebrate species. The authors identified and corrected several errors in the original code. They then re-ran the LPI calculations with various adjustments to the parameters and data inclusion criteria to assess the impact on the overall trend.

The study revealed significant sensitivity of the LPI to various methodological choices and data characteristics. The number of records in the time series had a strong effect; including only time series with at least 5 records reduced the index decline substantially. The presence of zeros in the population time series significantly biased the LPI towards a decline; removing zeros substantially reduced the overall decline, although it also widened confidence intervals in some cases. The LPI was found to be extremely sensitive to initial population declines, especially due to the hierarchical averaging procedure which can magnify the influence of a few poorly represented taxa or regions. A single declining population at the start of a time series could disproportionately affect the overall index. Weighting by species richness also played a considerable role; the weighted LPI showed a much greater decline than the unweighted version. Corrections in the R code produced negligible changes in the global LPI, but showed detectable effects for smaller subsets of data. The simulations showed that the LPI accurately reflects the stationarity of the system under certain conditions of population fluctuations (symmetric fluctuations on a logarithmic scale or stationary distribution of population abundances). The authors found that the non-stationary system with symmetric fluctuations on an arithmetic scale (such as the Poisson distribution used by Buschke et al.) causes a decreasing LPI even when the mean community abundance is stable. In such systems, the declining LPI properly reflects the non-stationarity of the system.

The findings challenge the interpretation of the LPI's dramatic decline in vertebrate populations. The identified biases suggest that the reported decline is an overestimation, at least partially due to methodological flaws and data limitations. The high sensitivity of the LPI to subjective choices in data handling and calculation parameters casts doubt on its robustness as a reliable indicator of biodiversity trends. The need for standardized, systematic surveys, independent of specific purposes or locations, is highlighted to overcome the geographical and temporal biases present in current data. The paper demonstrates the importance of carefully considering the mathematical assumptions and potential biases in biodiversity indices. While the corrected LPI shows a less severe decline, it remains likely that the current LPI still under- or overestimates the true extent of vertebrate population changes, owing to the complexities of sampling and the incomplete nature of the available data.

This study demonstrates that mathematical biases within the Living Planet Index calculation lead to an overestimation of vertebrate population decline. Straightforward corrections, such as removing zeros and using longer time series, significantly alter the index trend. The study emphasizes the need for more robust methodologies, rigorous sensitivity analyses, and standardized data collection to improve the accuracy and reliability of global biodiversity indicators. Future work should focus on developing indices less sensitive to subjective decisions and data limitations, and address the challenges posed by the heterogeneous nature of existing biodiversity data.

The study's analysis relied on a specific version of the `rlpi` R package. While the authors identified and corrected errors in the code, it is possible that newer versions incorporate improvements or that other unforeseen biases exist. The reliance on the Living Planet Database, with its inherent biases in data collection and geographic coverage, limits the generalizability of the findings. The proposed improvements to the LPI may introduce new limitations or biases. Further research is needed to rigorously validate the corrected index and to explore alternative approaches to measuring biodiversity trends.