Maximum height of mountain forests abruptly decreases above an elevation breakpoint

Figures & data

Figure 1. Location of the study area and distribution of the main species along elevation gradients (a) Distribution of the main forest species across the Spanish Pyrenees; (b) Location of the study area within Southern Europe; (c) Detail of the distribution of the main species along elevation gradients in a valley in the Central Pyrenees; (d) Violin plots showing the overall distribution of the main species across the elevation gradient in the Pyrenees, as observed using PNOA LiDAR data and the Spanish Forest Map

Table 1. Summary of the results for the fitted models of maximum canopy height as a function of elevation

	Breakpoint (m)		β1		β2		R^2		ΔR^2
	Mean	sd	mean	sd	mean	sd	mean	sd	mean	sd
General model	1623.3	4.7	7.9 · 10^−06	7.4 · 10^−06	−7.8 · 10^−4	6.5 · 10^−06	0.63	0.004	0.18	0.003
Per aspect classes
North-facing	1657.1	9.1	4.2 · 10^−5	1.4 · 10^−5	−1.0 · 10^−3	1.9 · 10^−5	0.66	0.008	0.21	0.007
South-facing	1674.0	92.9	−5.2 · 10^−5	7.9 · 10^−5	−6.4 · 10^−4	7.5 · 10^−5	0.40	0.011	0.07	0.005
Per species
Pinus uncinata	1782.9	9.1	−1.3 · 10^−4	2.0 · 10^−5	−7.8 · 10^−4	1.2 · 10^−5	0.59	0.008	0.14	0.006
Abies alba	1722.3	20.5	−1.8 · 10^−4	2.6 · 10^−5	−1.4 · 10^−3	9.9 · 10^−5	0.87	0.012	0.25	0.023
Pinus sylvetris	1915.2	32.4	−1.8 · 10^−4	5.9 · 10^−6	−1.2 · 10^−3	1.9 · 10^−4	0.17	0.007	0.01	0.002
Fagus sylvatica	1696.9	135.35	−1.5 · 10^−4	4.3 · 10^−5	−1.1 · 10^−3	5.8 · 10^−4	0.24	0.033	0.04	0.015

The parameter estimates correspond to a segmented log-linear model in the form: log(max_height) = α₁+ ß1·Elevation for elevation < breakpoint; and log(max_height) = α₂+ ß2·Elevation for elevation > breakpoint. The results are presented for the general model, for a model fitted for each species separately, and for a model fitted for each aspect class separately. Values are average predictions of parameters estimates for 1,000 models fitted to random subsets of the dataset (5,000 points for training and 5,000 for validation). R² for each model is calculated as the coefficient of determination of the relationship between the observed data and the predicted data using the validation dataset. ΔR² refers to the average increase in R² of the segmented model as compared to a log-linear model.

Figure 2. High-resolution (20 m) canopy height grid of the Spanish Pyrenees as derived from the Spanish Airborn LiDAR plan (PNOA). Canopy height was higher at both ends of the Pyrenees, where the sea influence softens the climate and allows the presence of tree species such as fir or beech

Figure 3. Relationship between terrain elevation and maximum canopy height across the Spanish Pyrenees, as determined from airborne LiDAR data. Orange lines represent the predictions according to a segmented log-linear regression model, and dashed line represents the breakpoint identified by the same model. Values indicate the approximate rate of change in maximum canopy height for a 100 m change in elevation below and above the breakpoint. The segmented log-linear model is the average prediction of 1,000 models fitted to random subsets of the original dataset. R² is calculated as the coefficient of determination of the relationship between the observed data and the predicted data using the validation dataset

Table 2. Mean and sd of r-squared and RMSE of the 1000 tested models for each realization. Model name refers to the variable included as predictor of maximum canopy height, whereas Full Model refers to a multivariate model including all the possible predictors

Model	Mean R^2	SD R^2	Mean RMSE	SD RMSE
Elevation	0.63	0.00613	2.25	0.0220
Mean anual temperature	0.358	0.00873	2.94	0.0254
Annual rainfall	0.182	0.00817	3.33	0.0256
Soil depth	0.139	0.00718	3.41	0.0243
Northness	0.030	0.00447	3.62	0.0247
Distance to sea	0.027	0.00379	3.63	0.0258
Sand %	0.023	0.00435	3.63	0.0268
Clay %	0.016	0.00416	3.65	0.0260
Silt %	−1.2 · 10^−4	0.00305	3.68	0.0246
Slope	−0.0012	0.00277	3.68	0.0257
Eastness	−7.7 · 10^−3	0.00248	3.69	0.0248
Full model	0.653	0.00570	2.17	0.0208

R² for each model is calculated as the coefficient of determination of the relationship between the observed and predicted data, using randomly chosen independent datasets for training (5,000 points) and validation (5,000).

Figure 4. Variation of maximum canopy height with elevation and climatic variables. Maximum canopy height increases with increasing temperature (A) and decreasing precipitation (B) but this relationship is explained by the covariation between elevation and climate variables (see Table 2). Elevation breakpoint is indicated by the dashed gray line

Figure 5. Relationship between terrain elevation and maximum canopy height in the Spanish Pyrenees, split for north-facing and south-facing slopes. Orange lines represent the predictions according to a segmented log-linear regression model, and dashed line represents the breakpoint identified by the same model. Values indicate the approximate rate of change in maximum canopy height for a 100 m change in elevation below and above the breakpoint. The segmented log-linear model is the average prediction of 1,000 models fitted to random subsets of the original dataset. R2 for each model is calculated as the coefficient of determination of the relationship between the observed data and the predicted data using the validation dataset

Figure 6. Relationship between terrain elevation and maximum canopy height in the Spanish Pyrenees, split across the main dominant species. Orange lines represent the predictions according to a segmented log-linear regression model, and dashed line represents the breakpoint identified by the same model. Values indicate the approximate rate of change in maximum canopy height for a 100 m change in elevation below and above the breakpoint. The segmented log-linear model is the average prediction of 1,000 models fitted to random subsets of the original dataset. R2 for each model is calculated as the coefficient of determination of the relationship between the observed data and the predicted data using the validation dataset

Data and codes availability statement

The data that supports the findings of this study is available in FigShare at https://doi.org/10.6084/m9.figshare.13213823