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, Moran's I correlation coefficient

, Supporting Information Table S1.1. Statistics of the spatial autocorrelation of vertical growth (VG), radial growth (RG), young tree survival (YTS) and leaf flushing (LF)

, Ex: expected value of I under the null hypothesis; Sd: standard deviation of I under the null hypothesis

, Moran's I correlograms

, Supporting Information Figure S1.1. Correlograms of Moran's I correlation coefficient (y-axis) and the distance classes (x-axis) for vertical (a) and radial (b) growth, young tree survival (c), and leaf flushing (d)

, Moran's correlation coefficient ranges between 1 and -1. Distance classes are Euclidian and in degrees

, AIC: Akaike information criterion; CP: climate of the provenance; CT: climate of the trial; BIO1: annual mean temperature; BIO5: max temperature of warmest month; BIO6: min temperature of coldest month; BIO12: annual precipitation; BIO13: precipitation of wettest month; BIO14: precipitation of driest month; PET Max: maximal monthly potential evapotranspiration

. December, MTson: mean temperature of September

, MTdjfmam: mean temperature of December

, Obs: number of trait measurements; Variance: variance explained by the random effects; SD: standard deviation of each level of random effects; Estimate: coefficient of the regression shown in logarithmic scale; SE: standard error of each fixed variable; t: Wald statistical test that measures the point estimate divided by the estimate of its SE, assuming a Gaussian distribution of observations conditional on fixed and random effects. Coefficients of the fixed effects of the model: Cov: trait covariate; CP: climate of the provenance origin; CT: climate of the trial; CP 2 : quadratic effect of the climate of the provenance. Coefficients of the interactions: Age x CP, Supporting Information Table S1.5. Statistics of random and fixed effects from linear mixed-effect models of the vertical growth-radial growth and vertical growth-leaf flushing two-trait models

, Conditional variance); r: Pearson correlation. The trait co-variate (Cov) for growth-radial growth is radial growth and for vertical growth-leaf flushing is leaf flushing. The climate variable of the trial (CT) for the two-trait models is precipitation of the wettest month (BIO13). The climate variable of the provenance (CP) for the two-trait model is maximal potential evapotranspiration, R 2 C: percentage of the variance explained by the random and fixed effects

, Supporting Information Figure S1.3. Differences in predictions between future (2070) and contemporary (2000-2014) climate for one-trait models in beech range: (a) vertical growth of 12 year-old trees

, (b) radial growth of 12 year-old trees (in mm); (c) probability of young tree survival of 6 year-old trees; (d) leaf flushing of 12 year-old trees (difference in Julian days); and for two-trait models: (e) vertical growth (in cm; co-variate radial growth) and (f) vertical growth (in cm; co-variate leaf flushing). The color gradient depicts the clinal variation from low