Figure S1 Map showing the location of Spain within Europe (A), and of the study area (Andalusia, (B)). Appendix S1 Analytical methods _ Analysis of tree survival To analyze tree survival as a function of several environmental and biotic variables we used adult census data for the two times, N1 and N2 in a binomial likelihood where trees survived between censuses with probability Ѳ. Then for stand i: N2i ~Binomial(N1i, Ѳi) And process model: logit(Ѳi) = αregion(i) + βXi + bi where α is the intercept (estimated for each region, wet and dry), β represents the vector of fixed effect coefficients associated with each of the exploratory variables included, Xi is the matrix of explanatory variables (the final model included: winter precipitation, winter temperature, slope, topographic radiation index, sand content, sand*winter precipitation and heterospecific basal area, Table 1), and bi is a spatially explicit random effect. Appendix S2 Analytical methods _ Analysis of the seedling group In the analysis of the seedling group, we defined the likelihood using a zero inflated Poisson distribution (Zuur et al. 2009) with mean parameter µ, due to the excess zerocounts in the data. We tried other types of models, i.e. zero inflated negative binomial, and approaches to the ordinal data, through inclusion of a latent variable for each count (Table S5). For the final model, the probability of a zero count was given by . The likelihood in stand i with count yi was: Pr(yi = 0) ( + (1 − ) × − ) Pr(Yi=yi | yi > 0) ((1 − ) × − × ( ! )) And process model: ln( ) = () + × Χi + ϵi + i with an intercept γ for each region, fixed effect coefficients φ and a matrix of explanatory variables, Xi that for the final model included: winter precipitation, winter temperature, their interaction, slope and heterospecific basal area (Table 2). We also included individual error term per stand, εi, and spatial random effects, bi. References Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A. & Smith, G.M. (2009) Zero-truncated and zero-inflated models for count data (ed. by Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A., Smith, G.M.). Mixed effects models and extensions in ecology with R, 261-293.. Springer, New York, New York Appendix S3 Analytical methods _ Analysis of the sapling group For the analysis of the sapling group we evaluated the abundance of saplings in those stands where they were present (71 stands in total). We used a Poisson likelihood (with parameter µ) to model the abundance of saplings recorded in the second census (SFNI3): Pr(Yi = yi) ( − × ( ! )) And process model similar to the model used for seedlings: ln( ) = () + × Χi + ϵi + i In this case the explanatory variables included in Xi for the best model were annual temperature and precipitation in spring, but none of them were significant (Table 2, Table S7). Appendix S4 Analytical methods _ Parameter estimation We followed a Bayesian approach to estimate the parameters of the adult tree survival and recruitment models, α, β, γ, φ, ω, є and b. Bayesian modeling allowed us to track the different sources of uncertainty inherent in the analysis, i.e., the data, the process and the parameters (McCarthy, 2007). Parameters were estimated from non-informative prior distributions, α, β, γ and φ ~Normal(0,1000), єi ~Normal (0, 2) with 1/2 ~Gamma(0.01,0.01) and ωi~Beta(1,1). The spatial random effects bi were estimated using Bayesian Gaussian kriging models, where the spatial random effects were estimated separately for each region as: bi|bj, j≠i~Normal(exp(-(ρdij)κ), b2) where dij is the distance between two stands, ρ is the rate of decay estimated from ρ~Gamma(1,1), the smoothing parameter, , was set up to 1, and 1/b2~Gamma(0.1,0.1). Posterior densities of the parameters were obtained by Gibbs sampling (Geman & Geman, 1984) using OpenBUGS 3.1.2. (Thomass et al. 2006). Models were run until convergence of the parameters was reached (~150,000 iterations) and parameters and their confidence intervals were estimated after discarding pre-converge “burn-in” iterations (~10000). Plots of predicted versus observed values were also used to evaluate the fit of the model (unbiased model having a slope of unity). R2 of observed vs predicted values was used as a measure of goodness-of-fit. Fixed effects coefficients, and φ parameters, whose 95% credible intervals did not include zero, were considered statistically significant. References Geman, S. & Geman, D. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. Ieee Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741. McCarthy M. A. (2007) Bayesian Methods for Ecology, Cambridge University Press, Cambridge. Thomas, A., O'Hara, R., Ligges, U. & Sturts, S. (2006) Making BUGS Open. In: R News, 6, 12-17. Table S1 Number of stands and number of Q. suber trees (total and dead between SFNI2 and SFNI3) considered for the analysis of tree survival. Number of stands where seedlings and saplings were present considered in the analysis of recruitment. Analysis of tree survival Total Stands in SNFI2 Q. suber trees Mean trees/stand Tree Mortality Number of stands (Percentage total stands) Trees (Percentage total trees) Maximum (tree/stand) Mean (tree/stand in stands were mortality was recorded) Analysis of recruitment Seedling Stands (with present individuals) Sapling Stands (with present individuals) Andalusia Wet region Dry region 755 4964 6.6 408 3541 8.7 347 1423 4.1 170 22.5 347 7.0 28 114 27.9 271 7.7 28 56 16.1 76 5.3 6 2.0 2.4 1.4 396/736 254/405 142/331 71/736 35/405 36/331 Table S2 Mean (± sd) and minimum and maximum values of the exploratory variables for each region. Variables Climatic Topographic Edaphic* Biotic Annual temperature (ºC) Spring temperature (ºC) Summer temperature (ºC) Fall temperature (ºC) Winter temperature (ºC) Annual precipitation (mm) Spring precipitation (mm) Summer precipitation (mm) Fall precipitation (mm) Winter precipitation (mm) Slope % Sand content % Silt content % Clay content % Soil bulk density (g/cc) Organic matter % Soil water content (g/100g) Available water capacity (g/100g) pH Conspecific basal area3 (m2/ha) Heterospecific basal area3 (m2/ha) Wet region mean±sd 16.8±1.1 14.8±1.2 23.4±1.0 18.1±1.1 10.9±1.3 1031.8±172.5 237.4±42.4 30.1±9.7 280.3±46.8 484.0±82.5 3.3±2.2 36.3±9.6 23.7±4.3 39.4±8.6 1.5±0.1 1.2±0.1 28.4±5.7 18.3±6.2 min 12.8 10.5 20.5 13.2 6.8 472.0 116.0 8.0 121.0 214.0 0.1 31.7 5.6 19.4 1.05 0.6 12.1 3.0 max 18.7 16.9 25.5 19.9 13.3 1756.0 390.0 57.0 506.0 812.0 11.3 70.1 33.8 56.7 1.7 1.4 36.3 21.4 Dry region mean±sd 16.0±1.0 14.0±1.0 24.2±0.9 17.0±1.0 8.8±1.1 767.3±96.6 196.6±23.1 38.3±7.7 216.0±29.07 315.9±47.4 2.0±1.4 44.2±7.5 27.3±6.1 27.2±4.1 1.5±0.2 1.2±0.2 20.9±3.3 9.7±5.1 min 13.1 10.7 21.8 13.8 5.4 532.0 131.0 20.0 133.0 204.0 0.2 30.2 15.6 19.6 1.1 0.8 12.1 5.9 max 18.6 16.7 26.6 20.0 11.7 1092.0 257 62.0 314.0 468.0 5.3 63.5 34.8 35.8 1.7 1.4 24.7 31.6 6.7±1.0 11.5±6.8 6.1 0.4 7.0 42.1 6.4±0.3 5.5±4.9 6.1 0.4 7.1 25.8 3.8±6.3 0.0 38.0 4.7±6.6 0.0 54.2 * For soil bulk density, soil water content and available water capacity the spatial resolution was 1:400.000. The other soil variables were estimated by the SEISnet system. The estimates come from three levels of information: regional level, landscape levels and field soil profiles. Average values of the soil properties of interest were estimated by using a model based on three main information sources: (1) a Geological Mining map and (2) a FAO soil-classes map, both at 1:400.000 scale; and (3) a wide array of detailed soil data stored in a soil profile database of the study area (SDBm Plus, de la Rosa et al 2002). Using pedotransfer functions (de la Rosa et al 2001) and interpolation techniques for spatial data, average values of several soil properties of interest, for a given geo-edaphic unit and location, were estimated (Monge et al. 2008). For a more detailed description see: De la Rosa, D., Mayol, F., Moreno, F., Cabrera, F., Diaz-Pereira, E. & Antoine, J. (2002) A multilingual soil profile database (SDBm Plus) as an essential part of land resources information systems. Environmental Modelling & Software, 17, 721-730 Monge, G., Rodríguez, J.A., Anaya-Romero, M. & de la Rosa, D. (2008) Generación de Mapas Lito-Edafológicos de Andalucía. Mapping Interactivo. Revista Internacional de Ciencias de la Tierra, 124, 38-45. Table S3 Factor loadings of varimax-rotated factors for the soil variables. The most representative variables for each axis are shown in bold. Variables pH Clay content Silt content Sand content Organic matter Soil water content Soil bulk density Available water capacity Importance of components Standard deviation Proportion of variance Cumulative proportion Factor 1 0.48 0.92 -0.06 -0.93 0.30 0.92 0.60 0.92 Factor 2 -0.03 -0.07 0.32 -0.23 -0.14 -0.18 0.94 -0.16 Factor 3 -0.01 0.20 0.11 -0.05 0.94 0.17 -0.21 0.17 3.82 0.42 0.42 1.49 0.17 0.59 1.09 0.12 0.71 Table S4 Selected models to evaluate the probability of mature tree survival. Predictive loss (D) and description of the best models in each group of variables (smallest value of D). We included only the interactions that were significant. To account for spatial autocorrelation we added a spatially random effect bi. Temperature and precipitation in the models including topographic, soil and biotic variables correspond to temperature in spring and precipitation in winter. αi are the intercepts for each region, βi are the parameters of the covariates Xi. Model description Hierarchical A model with the form P(Y| y)= αjs + βjs x Xj where αjs and βjs are the parameters for each X1 to Xj covariates in each s region, allowed us to combine data from the two regions to estimate the overall response of cork oak to the climatic variables while allowing for variation in this response among the two regions. Parameter estimation for one region was informed by data from the other region through the hyperparameters aj and bj. αjs and βjs were estimated from prior distributions αjs~Normal(a,σa2) and βjs~Normal(b,σb2) respectively. Prior parameters for this distributions were estimated from un-informative distributions: a~Normal(0,1000), σa~Uniform(0,1000), b~Normal(0,1000), σb~Uniform(0,1000). Simple Bayes Climate Climate+Topography Climate+Soils Climate+Biotic variables Process model D logit(pi)= α1,S+α2,S*Winter Precipitationi+α3,S*Spring Temperaturei Observations: high values of the standard deviation of the hypermarameters leaded us to discard the hierarchical model and work with the two regions independently. 1402 logit(pi)= α[regionS]+α2* Precipitationi+α3* Temperaturei Annual temperature 1733 Winter temperature 1878 Spring temperature 1560 Summer temperature 1771 Fall temperature 2185 Spring temperature-annual precipitation 1560 Spring temperature-winter precipitation (selected) 1511 Spring temperature-spring precipitation 2087 Spring temperature-summer precipitation 1827 Spring temperature-fall precipitation 1964 logit(pi)= α[regionS]+α2*Winter Precipitationi+α3*Spring Temperaturei+α4*Slopei+α5*Topographic radiation indexi logit(pi)= α[regionS]+α2* Winter Precipitationi+α3*Spring Temperaturei+α4*Sand contenti+α5*Soil bulk densityi+α6*Organic matteri logit(pi)= α[regionS]+α2*Winter Precipitationi+α3*Spring Temperaturei+α4*Slopei+α5*Topographic radiation indexi+α6*Sandi+α7*Sandi*Winter Precipitationi+α8*Heterospecific basal areai 1387 1461 1496 Climate + Topographic + Soils + Biotic variables Model accounting for spatial autocorrelation Climate + Topographic + Soils + Biotic variables+spatially random effect logit(pi)= α[regionS]+α2*Winter Precipitationi+α3*Spring Temperaturei+α4*Slopei+α5*Topographic radiation indexi+α6*Sandi+α7*Sandi* Winter Precipitationi+α8*Heterospecific basal areai logit(pi)= α[regionS]+α2*Winter Precipitationi+α3*Spring Temperaturei+α4*Slopei+α5*Topographic radiation indexi+α6*Sandi+α7*Sandi*Winter Precipitationi+α8*Heterospecific basal areai+bi 1269 493 Table S5 Selected models to evaluate the number of Q. suber seedlings less than 1.30 m tall. We included only the interactions that were significant. Temperature and precipitation in the models including topographic, soil and biotic variables correspond to temperature in winter and precipitation in winter. Mean μi of the positive count data is calculated as a function of the covariates. γi are the intercepts for each region, φi are the parameters of the covariates Xi. ωi was estimated with a prior distribution Beta(1,1). ki is a parameter from the negative binomial distribution and it represents the number of failures until a certain number of successes. D: predictive loss calculated for each model. To account for spatial autocorrelation we added to the best models a spatially random effect bi. To account for the overdispersion of the non-zero data we tried two different approximations: in a first approach, we added a stand level random effect є into the linear predictor for the Poisson intensity, µ. As a second approach, we specified a negative binomial (ZINB) distribution that is overdispersed relative to the Poisson (Kéry 2010). Zero-inflated Poisson distributions (ZIP) resulted in a better fit to the data compared with ZINB and accordingly we used the ZIP model. We also considered the number of counts, yi as a latent variable, where the true value of counts was estimated from a normal distribution with mean yi and a variance constrained to reflect the maximum and minimum values of that ordinal level (e.g., the low ranged from 1 to 4, we used a mean of 2 and a variance of (4-1)2/12, variance of the uniform distribution). We tried several model structures and combination of explanatory variables, and once the best model was selected we accounted for spatial autocorrelation by adding a spatially explicit random effect, defined above. References Kéry, M. (2010) Introduction to WinBUGS for Ecologists: A Bayesian Approach to Regression, ANOVA and Related Analyses. Academic Press. Burlington, MA. Model description Process model Selection of the likelihood distribution Zero-inflated negative Pr(yi = 0) ωi+(1-ωi )*(ki/(μi+ki))ki binomial (explanatory variables Pr(Yi=yi | yi > 0) annual precipitation and (1-ωi)*(Γ(yi+ki)/(Γ(ki)*Γ(yi+1))*(ki/(μi+ki))ki*(1-ki/(μi+ki))yi temperature) μi = exp(α0+α1*X1i+…..+αn*Xni+εi) Zero-inflated Poisson Pr(yi = 0) ωi+(1-ωi )*exp(-μi) number of Pr(Yi=yi | yi > 0) (1-ωi)*exp(-μi)*(μiylatenti/ylatenti!) seedlings/saplings as a latent variable μi = exp( γ0+φ1*X1i+…..+φn*Xni+εi) (explanatory variables annual precipitation and temperature) Zero-inflated Poisson number of Pr(yi = 0) ωi+(1-ωi )*exp(-μi) seedlings/saplings as a fix Pr(Yi=yi | yi > 0) (1-ωi)*e-μi*(μiyi/yi!) variable (explanatory variables μi = exp( γ0+φ1*X1i+…..+φn*Xni+εi) annual precipitation and temperature) Alternative groups of models with a Zero Inflated Poisson likelihood Hierarchical A model with the form P(Y| y)= α1s + βjs x Xj where αjs and βjs are the parameters for each X2 to Xj covariates in each s region, allowed us to combine data from the two regions to estimate the overall response of cork oak to the climatic variables while allowing for variation in this response among the two regions. Parameter estimation for one region Pr(yi = 0) ωi+(1-ωi )*exp(-μi) was informed by data Pr(Yi=yi | yi > 0) (1-ωi)*e-μi*(μiyi/yi!) from the other region through the μi = exp( γ1,S+γ2,S*Winter Precipitationi+φ1,S*Winter hyperparameters aj and Temperaturei+εi) bj. αjs and βjs were estimated from prior distributions αjs~Normal(a,σa2) and βjs~Normal(b,σb2) respectively. Prior parameters for these distributions were estimated from uninformative distributions: a~Normal(0,1000), σa~Uniform(0,1000), b~Normal(0,1000), σb~Uniform(0,1000). Simple Bayes Annual temperature D 215100 30270 15070 14950 15070 Climate+topography Climate + edaphic variables Climate+ biotic variables Climate + Topography + Biotic variables Model accounting for spatial autocorrelation Climate + Topographic + Biotic variables+spatially random effect Winter temperature 15030 Spring temperature 15210 Summer temperature 15080 Fall temperature 15040 Spring temperature-annual precipitation 15030 Winter temperature-winter precipitation (selected) 14980 Winter temperature-spring precipitation 15040 Winter temperature-summer precipitation 15050 Winter temperature-fall precipitation 15000 μi = exp(γ [regionS]+φ1* Winter Precipitationi+φ2*Winter Temperaturei+φ3* Winter Precipitationi* Winter Temperaturei+εi) μi = exp(γ[regionS]+ φ1* Winter Precipitationi+ φ2* Winter Temperaturei+ φ3* Winter Precipitationi* Winter Temperaturei+ φ4*Slopei+φ 5*Top radiation indexi+εi) μi = exp(γ[regionS]+φ1* Winter Precipitationi+φ2* Winter Temperaturei+φ3* Winter Precipitationi* Winter Temperaturei+φ4*Sand contenti+φ5*Soil bulk densityi+φ6*Organic matteri+εi) μi = exp(γ[regionS]+φ1* Winter Precipitationi+φ2* Winter Temperaturei+φ3* Winter Precipitationi* Winter Temperaturei+φ4*Conspecific basal areai+φ5*Heterospecific basal areai+εi) μi = exp(γ[regionS]+φ1* Winter Precipitationi+φ2* Winter Temperaturei+φ3* Winter Precipitationi* Winter Temperaturei+φ4*Slopei+φ5*Heterospecific basal areai+εi) μi = exp(γ[regionS]+φ1* Winter Precipitationi+φ2* Winter Temperaturei+φ3* Winter Precipitationi* Winter Temperaturei+φ4*Slopei+φ5*Heterospecific basal areai+εi +bi) 14980 14960 15130 14950 14890 14680 Table S6 Classification of small seedlings (height < 0.30 m), large seedlings (height between 0.30 m and 1.30 m), small saplings (height > 1.30 m and dbh < 2.5 cm) and large saplings (height >1.30 m and 2.5<dbh<7.5 cm) in SFNI2 and SFNI3. The semiquantitative scale corresponds to low: 1-4 seedlings or saplings, medium: 5-15 seedlings or saplings, or high: >15 seedlings or saplings. To make a unique category of saplings we add the exact number of saplings in category 4 of the SIFN3 and the average count for each of the ordinal categories for category 3 in the SIFN3 (low = 2, medium = 10, and high = 20). The corresponding recruitment stage group column shows the two different groups (seedlings and saplings) considered in the analysis. corresponding recruitment Height dbh quantification SIFN2 SIFN3 stage group for the analysis < 0.30 m - semi-quantitative scale category 1 category 1 seedlings 0.30-1.30 m - semi-quantitative scale category 1 category 2 seedlings >1.30 m <2.5 cm semi-quantitative scale category 1 category 3 saplings category 2 category 4 saplings >1.30 m 2.5-7.5 cm exact number of saplings Table S7 Predictive loss (D) for the models run in the analysis of saplings (>1.30 m high). Alternative models Climate D Annual temperature 849.5 Winter temperature 857.4 Spring temperature 855.8 Summer temperature 850.9 Fall temperature 850.8 Annual temperature-annual precipitation 849.6 Annual temperature-winter precipitation 851.3 Annual temperature-spring precipitation 847.9 Annual temperature-summer precipitation 853.9 Annual temperature-fall precipitation 851.4 Topography 853.2 Soil 850.5 Biotic 852.8 Previous recruitment census 857.1 Soil, biotic 854.5 Soil, biotic + spatially explicit random effect 850.1

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# ddi12193-sup-0001-FigS1_AppS1-S4_TabS1-S7