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The Living Planet Index (LPI) is a standardized indicator for tracking population trends through time. Due to its ability to aggregate many time series in a single metric, the LPI has been proposed as an indicator for the Convention on Biological Diversity's post-2020 Global Biodiversity Strategy. However, here we show that random population fluctuations introduce biases when calculating the LPI. By combining simulated and empirical data, we show how random fluctuations lead to a declining LPI even when overall population trends are sta