Maëlys Boënnec, Vasilis Dakos, Vincent Devictor

Aim.
Population dynamics are usually assessed through linear trend analysis, quantifying their general direction. However, linear trends may hide substantial variations in population dynamics that could reconcile apparent discrepancies when quantifying the extent of the biodiversity crisis. We seek to determine whether the use of non-linear methods and the quantification of temporal variability can add value to the linear approach by offering a more complete representation of global population changes. In addition, we seek to determine how these components are distributed among biogeographical regions and taxonomic groups.

Location.
Global.

Methods.
We analysed 6,437 population time series from 1,257 species from the Living Planet Database over the period 1950-2020. We modeled populations through the use of second order polynomials and classified trajectories according to their direction and acceleration. We modeled and classified these same populations using a more common linear trend analysis. We quantified temporal variability using three metrics, the coefficient of variation, the mean squared error and the consecutive disparity index. We then used chi-squared tests and linear mixed-effects models to test potential sources of heterogeneity in non-linear trajectories and temporal variability.

Results.
Non-linear models were a better fit for 44.8 % of the analyzed time series, and temporal variability was higher among trajectories classified as linear. Linear models missed meaningful information by misclassifying recent declines or recovery signals. Marine populations were highly variable, and all taxonomic groups or IUCN categories exhibited variability in their degree of non-linearity and temporal variability.

Main conclusions.
Non-linearity and temporal variability reveal usually overlooked dramatic declines or recovery signals in global population dynamics. Thus, moving beyond linearity can help reduce the risk of misleading conclusions and better inform conservation decisions. In particular, population usually classified as « stable » can hide informative non-linear and variable changes to integrate in more advanced global biodiversity assessment.