Figure S1 Potential present distribution of Fagus sylvatica simulated by PHENOFIT using ATEAM climate data (left panel, AUC = 0.79) and observed present distribution according to the European Potential Natural Vegetation Map (right panel). Colours correspond to the different vegetation formation in which beech is recorded as present whatever its status and coverage (

Figure S2 Conceptual scheme of the Gibbs-based model. The initial spatial configuration of offspring (black dots) is progressively reorganized in function of the parents (black squares) until the final spatial configuration characterizing the given species is reached.

Figure S3 Method used to obtain the IPF of tree cohorts in a 25 km2 forest stand from the IPF of tree individuals in a 4 km2 forest stand. IPF parameter sets for tree individual are (1.5; −1.4), (6.8; −2.4), (17.9; −8.9), (25.8; −3.4) and (200; −1.4). IPF parameter sets for tree cohorts are (75; −60), (250; −30), (1000; 10), (1500; −80) and (3000; −90). The first value is the distance in meter and the second value is the interaction Φ.

Figure S4 Conceptual scheme of the IPF calibration. The IPF parameters are fitted to the spatial pattern of the forest stand which is described by the pair correlation function g(r) (Pommerening 2002). For each set of IPF parameters drawn during the optimization process, a point pattern is simulated according to a non-homogeneous Gibbs process and a g(r) function is calculated. This g(r) function is compared to the observed g(r) function. The fitting is achieved using a least square criteria and the simulated annealing algorithm of Metropolis et al. (1953). LSS expresses the least sum of square.

Figure S5 The cohort model. The 4 km2 beech forest stand was subdivided regularly (on the left panel) to obtain cohorts defined by their barycentre (middle panel) and mean density represented by the size of the circle symbolizing the cohort (right panel) and obtained with the histogram (middle panel).

Figure S6 Boxplot of differences of arrival date estimated by observation [using a Δ14C datating method, see detail in Brewer (2002)] and dates estimated by our simulation as a function of six colonization scenarios which differed by climatic influence, migration abilities of beech and potential refugia number and location.

Table S1 Parameters used in PHENOFIT. Note that the flowering date parameters are identical to the leaf unfolding date parameters except the F* parameter. This is because Fagus sylvatica has compound buds containing leaves and flowers, and flowers appear at the apex of the shoot a few days after leaf unfolding. Prov 201, 403, 602, 751 correspond to four French geographical provenances of beech as defined by the French Forest Inventory.

Table S2 Result of the regression analysis of variance. Row 1 to row 3 assess the agreement significance of one factor (climate, migration or refugia) on simulated beech distributions compared with observations (pollen and macrofossils), conditionally to the other two factors holding constant. The row 4 assesses the same agreement significance between model data, considering all of the three factors. The significance (P value) of the F-statistic was tested using a permutation (Nb permutations) of the residuals. ‘ Var’ is the variance explained by each of the three factors.

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