In Mexico, coniferous forests occur from 150 to 4000 meters above sea level (m a.s.l.), predominantly in mountainous regions where annual temperatures range from 6˚C to 28˚C and annual precipitation varies between 350 and more than 1000 mm ([41]). According to [14], these forests are found on seven principal soil types—Leptosol, Regosol, Luvisol, Phaeozem, Cambisol, Umbrisol, and Andosol—which have developed from igneous, sedimentary, and metamorphic parent materials.

For this study, twelve species were selected—six pines and six oaks: Pinusdevoniana Lindl. (hereafter referred to as Pdev), Pinusdouglasiana Martínez (Pdou), Pinusleiophylla Schiede ex Schltdl. & Cham. (Plei), Pinusoocarpa Schiede ex Schltdl. (Pooc), Pinuspatula Schiede ex Schltdl. & Cham. (Ppat), Pinuspseudostrobus Lindl. (Ppse), Quercuscrassifolia Bonpl. (Qcra), Quercuslaurina Humb. & Bonpl. (Qlau), Quercusmagnoliifolia Née (Qmag), Quercusradiata Trel. (Qrad), Quercusresinosa Liebm. (Qres), and Quercusrugosa Née (Qrug).

The original data from the National Forest and Soil Inventory of Mexico (INFyS, 2015-2020) were preprocessed to produce a database structured by species and plot (ID). Each record contains geographic coordinates (longitude, latitude; datum WGS84) and the number of subplots sampled (sites). The variables considered were: n (number of individuals measured), DBH (mean diameter at breast height measured at 1.30 m; cm), HT (mean total height; m), BA (basal area; m² ha⁻¹), AGB (total aboveground biomass; Mg ha⁻¹), and cdAGB (carbon density in aboveground biomass; Mg C ha⁻¹).

The 19 bioclimatic variables were obtained from the WorldClim database, version 2.0 ([21]), at a spatial resolution of 30 arc-seconds for the period 1970-2000. Values for each of the 19 bioclimatic variables (Bios) at each site (ID) and for each species were extracted from the WorldClim raster layers using the terra package ([21]).

To assess the correlation between cdAGB and each bioclimatic variable, and owing to the violation of the assumption of bivariate normality, the variables were rank-transformed and a Bayesian Spearman correlation coefficient (ρBayes) was estimated using the BayesFactor package ([31]). This approach was chosen for its robustness to non-normal distributions and because Bayesian inference provides more flexible estimates and an explicit probabilistic framework for hypothesis comparison. In addition to the posterior median, we calculated credible intervals (CrI), the probability of direction (pd), the percentage in the region of practical equivalence (% in ROPE), and the Bayes factor (BF).

In this study, climatic sensitivity was defined as the magnitude and direction of the statistical response of cdAGB to bioclimatic gradients, with rank-based Bayesian correlations and segmented regression slopes serving as functional proxies. Vulnerability was defined functionally as a statistically significant reduction in cdAGB associated with adverse climatic conditions or bioclimatic thresholds, reflecting climate-driven constraints on carbon accumulation capacity rather than direct physiological failure, mortality, or demographic risk.

Predictor variables were selected using a two-step framework integrating multicollinearity control (VIF < 10) and Random Forest-derived importance metrics ([24]). The dataset was partitioned into training (80%) and testing (20%) subsets via stratified random sampling to preserve cdAGB distributions. Model performance and generalizability were evaluated using 5-fold cross-validation and independent testing, with predictive accuracy quantified by RMSE, R², and MAE. The relative importance of bioclimatic predictors for estimating cdAGB was determined by comparing model-internal importance with permutation-based importance derived from the testing set.

We applied a segmented regression model to statistically identify the presence of a breakpoint (ψ) in the response of aboveground biomass carbon density (cdAGB) to a previously derived bioclimatic predictor (Z). This model introduces a piecewise linear relationship by adding a nonlinear term to the Generalized Linear Model (GLM) linear predictor. The fundamental equation for the segmented relationship is as follows:

where:

E|cdAGB_i|: Is the expected value of Aboveground Biomass Carbon Density (cdAGB) for observation i.

Z: Is the independent bioclimatic variable (segmented variable).

ψ: Is the estimated change-point (or breakpoint), representing the bioclimatic threshold value.

β₁: Is the left slope (the initial rate of change before ψ.

β₂: Is the difference-in-slopes. The slope after the threshold is β₁ + β₂.

β₀: Is the intercept term.

(z_i − ψ)₊: Is the segmentation term, defined as ( z i − ψ ) × ( z i > ψ ) .

I(·): Is the indicator function (equal to 1 if z_i > ψ, and 0 otherwise).

The estimation of the breakpoint and model parameters was performed using the iterative algorithm implemented in the R package segmented ([32]) which translates the nonlinear problem into an approximate standard linear framework. To test whether the relationship is truly segmented versus a simple straight line (i.e., whether the breakpoint exists), the Davies Test was employed for the null hypothesis H 0 : β 2 ( ψ ) = 0 .

If H 0 was rejected, the data for the bioclimatic variable (Z) were classified into two categories: (a) Vulnerable (V), representing sites where x < ψ, and (b) Non-vulnerable (N-V), representing sites where Z > ψ, based on the statistical significance (p < 0.05) of the slope in the segmented regression.

Breakpoint robustness and uncertainty (ψ) were quantified using a non-parametric bootstrap approach (1000 resamples) applied to the segmented regression model, with percentile-based confidence intervals providing an empirical, assumption-independent measure of breakpoint stability. Breakpoint-based classifications and spatial analyses were performed only when the Davies test indicated a statistically significant segmented relationship (p < 0.05); otherwise, relationships were treated as linear and all sites were conservatively classified as Non-vulnerable. When segmentation was supported, pre- and post-threshold slopes were estimated, and slope-change significance was assessed via the segmented-term t-statistic, enabling a quantitative evaluation of the magnitude and direction of climate sensitivity shifts across the breakpoint.

Partial correlation analyses were conducted to quantify associations between cdAGB and bioclimatic variables while controlling for latitude and longitude, thereby accounting for spatial structure. Altitude was excluded to avoid overcontrol of climate-driven signals, and Spearman’s rank correlation was employed to ensure robustness against non-normality and outliers.

Residual spatial dependence was evaluated using Moran’s I computed on segmented-regression residuals with a k-nearest neighbor weighting scheme (k = 5), where non-significant values indicated adequate control of spatial autocorrelation.

Subsequently, the sites were spatialized through a Vulnerability Map in a Geographic Information System (GIS) using the ggplot2 ([50]) and sf ([35]) r libraries. The spatial vulnerability of cdAGB for each species was assessed as a binary outcome (Vulnerable vs. Non-vulnerable sites) using binomial generalized additive models (GAMs) with a logit link function, with the objective of estimating the spatial probability of cdAGB vulnerability. The models incorporated a two-dimensional spatial smoother (longitude-latitude) together with a one-dimensional elevation smoother, both estimated using restricted maximum likelihood (REML) and penalization to prevent overfitting. All statistical analyses were performed in R version 4.3.1 ([37]).

The response of cdAGB to bioclimatic variables was complex, exhibiting both positive and negative relationships and varying across species (Figure 1).

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Figure 1. Bayesian correlation between 19 bioclimatic variables and the carbon density of aboveground live biomass (cdAGB) for 12 temperate-forest species in Mexico. The vertical line separates temperature-related bioclimatic variables (left) from precipitation-related variables (right). Blue bars denote negative correlations and green bars denote positive correlations. The value above each bar indicates the percentage in the ROPE (Region of Practical Equivalence). Panels: (a) P.devoniana; (b) P.douglasiana; (c) P.leiophylla; (d) P.oocarpa; (e) P.patula; (f) P.pseudostrobus; (g) Q.crassifolia; (h) Q.laurina; (i) Q.magnoliifolia; (j) Q.radiata; (k) Q.resinosa; (l) Q.rugosa.

The three species showing the highest mean absolute Bayesian correlations (|ρ^Bayes|) between cdAGB and all bioclimatic variables were P.douglasiana (ρ = 0.24 ± 0.17, pd = 0.91, BF₁₀ > 10⁶), Q.resinosa (ρ = 0.23, pd = 0.90, BF₁₀ > 10⁵), and Q.rugosa (ρ = 0.17, pd = 0.99, BF₁₀ > 10⁸).

In contrast, the lowest absolute correlations were found in P.devoniana (ρ = 0.06, pd = 0.70, BF₁₀ = 0.34), P.leiophylla and P.oocarpa (ρ = 0.11, pd = 0.92, BF₁₀ > 10⁵), and Q.laurina (ρ = 0.13, pd = 0.91, BF₁₀ = 2.40).

The analysis indicates that thermal variables predominate over precipitation variables. Temperature seasonality (bio4) was the most important predictor of cdAGB, exhibiting 100% relative importance in four of the 12 species (P.douglasiana, P.leiophylla, Q.crassifolia and Q.resinosa). Annual temperature range (bio7) was the second most important variable, showing 100% relative importance for three species (P.oocarpa, P.patula and Q.resinosa) (Figure 2).

By contrast, precipitation of the driest month (bio14) showed the lowest importance (0%) in 8 of the 12 species (four Pinus and four Quercus) (Figure 2).

Based on the average importance of the variables, the species showing the greatest climatic dependence were Q.magnoliifolia (67.2%), Q.rugosa (64.8%), P.oocarpa (63.3%), and P.pseudostrobus (61.1%), whereas the least sensitive species were Q.radiata (17.8%), P.patula (22.7%), and P.devoniana (36.4%).

Figure 2. Relative importance of 19 bioclimatic variables for predicting the carbon density of aboveground live biomass (cdAGB) for 12 temperate-forest species in Mexico. Each cell indicates the importance value estimated by a Random Forest model. From left to right: P.patula, P.devoniana, Q.radiata, Q.crassifolia, P.douglasiana, P.leiophylla, Q.resinosa, Q.laurina, P.oocarpa, Q.rugosa, P.pseudostrobus, and Q.magnoliifolia.

Statistically significant thresholds or breakpoint (ψ) were detected in 41.6% of the analyzed species, corresponding to those explicitly denoted by the † symbol (Table 2). Species-level segmented regression analyses indicated that five taxa (P.leiophylla, P. oocarpa, P. patula, Q. magnoliifolia, and Q. rugosa) exhibit statistically significant nonlinear responses of cdAGB across bioclimatic gradients, as evidenced by the Davies test (p ≤ 0.05).

Table 2. Species-level segmented regression analyses of carbon density in aboveground biomass as a function of bioclimatic variables, integrating collinearity, threshold detection, segment-specific slopes, and spatial autocorrelation.

VIF: variance inflation factor; Bio+: bioclimatic predictor with the highest relative importance; Davies-p: p-value from the Davies test used to detect a breakpoint; ψ: estimated bioclimatic threshold (breakpoint) of the segmented regression model; CI ψ: 95% confidence interval for ψ; U1.x − t: t statistic associated with the post-threshold change in slope; β₁ and β₂: slopes of the first and second segments of the model, respectively (Mg ha⁻¹); β₁ − t and β₂ − t: t statistics associated with β₁ and β₂; Corp-p: p-value of the partial correlation; IM: Moran’s I; p(IM): p-value of Moran’s I test; †: statistically significant breakpoint (Davies test, p < 0.05). BIO1, annual mean temperature (˚C); BIO2, mean diurnal temperature range (˚C); BIO4, temperature seasonality (SD ×100, unitless); BIO7, annual temperature range (˚C); BIO15, precipitation seasonality (coefficient of variation, unitless); and BIO19, precipitation of the coldest quarter (mm).

Multicollinearity was controlled using variance inflation factors (VIF), which remained below 10 across all species-specific models (maximum in Quercuslaurina, VIF = 9.14; minimum in Quercusmagnoliifolia, VIF = 1.49). The U1.x−t statistic approached and exceeded the critical threshold (|t| > 3) in species exhibiting a breakpoint, most notably Pinuspatula (t = 3.96) and Quercusrugosa (t = 3.87), providing strong evidence of highly significant slope shifts following the threshold.

In Pinusoocarpa, cdAGB exhibited a pronounced asymmetric response across the thermal threshold identified by segmented regression (ψ = 13.28; p < 0.05). CdAGB remained stable below ψ but declined significantly beyond this threshold (β₂ = −3.209 Mg ha⁻¹ ˚C⁻¹), indicating increased vulnerability to thermal variability (Table 2; Figure 3(a)).

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Figure 3. Segmented regression relationships between aboveground live biomass carbon density (cdAGB; Mg ha⁻¹) and the most influential bioclimatic predictor. Only species exhibiting statistically significant bioclimatic thresholds according to the Davies test (p ≤ 0.05) are shown. Points represent INFyS sampling sites. Red points indicate the range of the predictor in which significant changes in cdAGB are detected according to the segmented regression model (i.e., a threshold-driven response), whereas green points indicate ranges where no significant changes in cdAGB are detected. Solid black lines represent the fitted segmented regression, and shaded areas correspond to the 95% confidence intervals. Panels correspond to Pinusleiophylla (a) Pinusoocarpa (b), Pinuspatula (c), Quercusmagnoliifolia (d), and Quercusrugosa (e).

In Pinuspatula, threshold effects manifested prior to ψ = 16.80, with a sharp pre-threshold decline in cdAGB (β₁ = −43.470 Mg ha⁻¹ ˚C⁻¹), followed by a comparatively stable response after ψ was exceeded (Table 2; Figure 3(b)).

In Quercusmagnoliifolia and Q.rugosa, cdAGB responses were limited to the pre-threshold segment, with thresholds at ψ = 20.04 and ψ = 90.00, respectively Table 2;Figure 3(c), Figure 3(d). CdAGB increased in Q.magnoliifolia (β₁ = 2.206 Mg ha⁻¹˚C⁻¹), whereas Q.rugosa showed a weak decline (β₁ = −0.154 Mg ha⁻¹ mm⁻¹). The absence of post-threshold effects suggests stabilization of cdAGB beyond ψ.

Significant partial correlations (Corp-p ≤ 0.05) in three of the five species with identified breakpoints indicate an independent influence of the dominant bioclimatic variable on cdAGB. Low Moran’s I values (IM ≈ 0.001-0.212; Table 2) confirm the absence of residual spatial autocorrelation, supporting the robustness of the spatial model specification.

Segmented regression revealed breakpoints between the 30.3rd (P.patula) and 59.9th (Q.rugosa) percentiles of the predictor gradient, indicating that thresholds occur within the central portion of the data distribution and are not driven by outliers.

According to the GAM-based models, the spatial component was highly significant for all species (p < 0.01) and was characterized by elevated estimated degrees of freedom (EDF > 1), indicating complex nonlinear spatial patterns in vulnerability probability across the geographic landscape (Table 3). By contrast, the effect

Table 3. Summary of species-specific binomial generalized additive models (GAMs) evaluating spatial and altitudinal effects on vulnerability status, reporting smooth-term penalization, inferential statistics, model discrimination (AUC), dispersion, and deviance explained.

EDF: Effective degrees of freedom of smooth terms (values > 1 indicate non-linear relationships, whereas values < 1 reflect penalized, near-linear effects); Statistic (χ²): Wald-type chi-square test statistic assessing the significance of smooth terms; p-value: Statistical significance of smooth effects; AUC: Area Under the Receiver Operating Characteristic (ROC) Curve, measuring the model’s discriminative performance; Dispersion (φ): Estimated dispersion parameter of the binomial GAM; values well below 1 indicate no evidence of overdispersion and reflect strong penalization and well-regularized model fit; Dev. Expl. (%): Proportion of deviance explained by the model relative to a null model. Only species exhibiting statistically significant bioclimatic thresholds according to the Davies test (p ≤ 0.05) are shown.

of elevation was weak or non-significant for most species (p > 0.05), with EDF values below 1 and only marginal levels of significance. A notable exception was Quercusmagnoliifolia, for which elevation exerted a strong, significant, and nonlinear effect (p < 2 × 10⁻¹⁶).

The models exhibited excellent discriminative ability, with AUC values ranging from 0.94 to 0.99, and explained a substantial proportion of the deviance (63-93%), indicating a robust and reliable fit. Low dispersion parameter values (φ < 0.6) confirmed the absence of overdispersion and appropriate model regularization.

Figure 4. Spatial distribution of sites from the National Forest and Soil Inventory (2015-2020) for the genus Pinus and their vulnerability status. In this analysis, N-V represents non-vulnerable sites (green symbols), and V indicates vulnerable sites (red symbols). Circle size represents carbon density (Mg ha⁻¹), while the color gradient denotes the level of vulnerability.

Based on the GAM results, spatial patterns of vulnerable and non-vulnerable cdAGB sites relative to the dominant bioclimatic predictor are illustrated in Figure 4 (pine species) and Figure 5 (Quercus species). These patterns demonstrate a clear geographic segregation between vulnerable and non-vulnerable sites, underscoring the dominant role of spatial structure (latitude and longitude) over simple elevational gradients. In Pinus species, vulnerable sites predominantly occur at lower latitudes (Figure 4), whereas in Quercus species, vulnerability is mainly associated with lower longitudes (Figure 5).

The proportion of vulnerable sites was highest for Q.magnoliifolia (61.5%) and Q.rugosa (59.9%), and lower for P.patula (30.3%) and P.oocarpa (40.8%).

Figure 5. Spatial distribution of sites from the National Forest and Soil Inventory (2015-2020) for the genus Quercus and their vulnerability status. In this analysis, N-V represents non-vulnerable sites (green symbols), and V indicates vulnerable sites (red symbols). Circle size represents carbon density (Mg ha⁻¹), while the color gradient denotes the level of vulnerability.