Climate and water-table levels regulate peat accumulation rates across Europe

PLOS One | https://doi.org/10.1371/journal.pone.0327422 July 23, 2025 12 / 16 Statistical analysis Relationships between site-based aPAR (average, highest, lowest), climate variables and reconstructed WTD were explored for each site using Theil-Sen robust regression in the R package deming v.1.4 [64]. Theil-Sen regression coefficients were then standardised to produce beta coefficients. Spearman’s rank correlation was used to further clarify relationships among variables because it is a non-parametric method that does not assume a linear relationship or normally distributed data. This makes it particularly suitable for exploring monotonic associations between ecological and climatic variables, especially when dealing with reconstructed or heterogeneous datasets that may include outliers or non-linear trends. The climatic variables analysed for each site included both contemporary (NOAA-CIRES-DOE 20th Century Reanalysis V3) and palaeo-climate (CHELSA-TraCE21k) datasets. These comprised annual and summer (JJA) temperature, annual and summer (JJA) precipi- tation, and growing degree days above 0°C (GDD0) and 5°C (GDD5). Water table depth (WTD) variables were represented by average, maximum, and minimum values from each reconstruction, based on bootstrapped error estimations. To determine relationships between aPAR and WTD, a Loess Smoothing Model [65,66], a Gaussian Response Model [67], and a Generalized Additive Model (GAM) [68] were utilised. The GRM calculates an initial estimation of optimum and

tolerance based on the weighted average, followed by a nonlinear optimization by the Levenberg-Marquardt method. All statistical analyses were carried out in either PAST v.4 [69] or R v.4.2.1 [70]. Graphics were produced using the ggplot2 R package v.3.4.4 [71]. The GAM was calculated using the mgcv R package v.1.9.0 [72]. Supporting information S1 File. Supporting Information 1 (Figure): Bayesian age-depth models. Supporting Information 2 (Table): Spearman’s rank correlation information (Rs (bottom left) and p-values (top right) are shown). Supporting Information 3 (Figure): Boxplot showing aPAR for each region (Britain and Ireland, Continental Europe; Scandinavia and Baltics).Supporting Information 4 (Figure): Boxplot showing aPAR across different climate phases including the Little Ice Age (LIA: 1500–1850 CE), Medieval Warm Period (MWP: 950–1250 CE) and Roman Warm Period (RWP: 1–400 CE). All data points are shows as well as the non-Little Ice Age data points (nLIA). Supporting Information 5 (Figure): Theil–Sen robust regression scatterplot of aPAR versus modern climatic data (NOAA–CIRES–DOE 20th Century Reanalysis Version 3). Supporting Information 6 (Figure): Theil–Sen robust regression scatterplot of aPAR versus palaeo-climatic data (CHELSA-TraCE21k). Supporting Information 7 (Table): Site-based data for aPAR, WTD, contemporary climate and palaeo-climate. Supporting Information 8 (Table): Theil–Sen robust regression information for aPAR regressions with WTD, contemporary climate, and palaeo-climate. Supporting Information 9 (Dataset). All data. (ZIP) Acknowledgments

We thank the two reviewers for their constructive comments on an earlier version of this manuscript. JMGs contribution represents NRCan contribution number/Numéro de contribution de RNCan: 20230392. This paper is a contribution to the PAGES C-PEAT group. Author contributions Conceptualization: Graeme Swindles, Richard E. Fewster, Mariusz Lamentowicz, Evelyn M. Keaveney, Michelle M. McKeown. Data curation: Graeme Swindles, Angela Gallego-Sala, Mariusz Lamentowicz, Matthew J. Amesbury, Antony Blundell, Frank M. Chambers, Dan J. Charman, Angelica Feurdean, Mariusz Galka, Edgar Karofeld, Atte Korhola, Lukasz Lamentowicz, Peter Langdon, Dmitri Mauquoy, Edward A. D. Mitchell, Gill Plunkett, Helen M. Roe, T. Edward Turner, Ulle Sillasoo, Minna Valiranta, Marjolein van der Linden, Barry Warner.