Modelling Growth and Yield Response to Thinning in Quercus robur L. Stands in NW Spain

Abstract

Thinning is a key silvicultural practice for managing forests; however, its effects on stand growth and yield remain debated. This study evaluated the growth and yield responses to thinning in even-aged Quercus robur stands in Galicia (NW Spain) using data from three long-term thinning trials established between 1998 and 1999. A randomised complete block design was applied with four thinning intensities from below: control (C, 0% basal area removal), light (L, 15%), moderate (M, 35%), and heavy (H, 55%). Two complementary analytical approaches were implemented using linear mixed-effects models: a state-space approach examining post-thinning stand dynamics and a thinning-effect approach assessing the cumulative stand growth and yield, accounting for both standing and harvested components. The state-space analysis confirmed that thinning produced distinct stand structures in moderate and heavy treatments (M and H), with the largest differences observed in the stand basal area and trees per hectare, while the dominant height remained unaffected. In the thinning-effect approach, the cumulative basal area and volume—excluding and including mortality—followed the pattern L > C > M > H. Overall, the results indicate that light or moderate thinning intensities maintain stand yield and enable intermediate harvests. At the same time, although the mean diameter increased under more intensive thinning, differences in the dominant diameter—approximating potential future crop trees—were not significant, indicating that stronger thinning from below did not necessarily enhance the development of the dominant trees.

1. Introduction

The pedunculate oak (Quercus robur L.) is the most widespread species of the genus Quercus, extending across the majority of Europe as well as large parts of Asia Minor and the Caucasus [1]. This species can naturally hybridise with the sessile oak (Quercus petraea Matt. Liebl.), which is regarded as the second most prevalent oak in Europe. Given the similarities in their silvicultural practices, many specialised references address them jointly [2,3,4]. From ancient times, these oak species have been integral to European culture, supplying firewood, acorns for animal feed, bark for leather tanning, and timber for building purposes. Moreover, oaks often serve as national or regional emblems throughout Europe [4]. The Iberian Peninsula represents the southwestern limit of the distribution of Q. robur, where it predominates in the Cantabrian and Atlantic regions [1]. In the region of Galicia (north-western Spain), pedunculate oak is the dominant species in native forests, covering approximately 125,000 ha in pure stands [5]. In this region, depending on site quality, 110–145 years are required to maximise the stem volume production in pedunculate oak even-aged stands [6].

Successful oak silviculture in even-aged stands requires attention, and in addition to regeneration felling, thinning is the most widely applied silvicultural practice. Since the emergence of forestry as a discipline over two centuries ago, perceptions of thinning have undergone substantial changes, ranging from the rejection of thinning to the adoption of heavy thinning, encompassing different aims including maintaining growth, increasing growth, or redistributing growth [7]. According to Langsaeter’s curve [8], the total stand production is largely independent of the thinning intensity within a wide range of intermediate densities, while only at very low or very high densities does production decrease markedly. Thinning modifies the stand density, mean tree size, and stand structure, and the response of trees and stands to thinning is influenced by the species, site conditions, stand age, and the intensity and type of thinning applied [9]. Various thinning types have been defined [10,11], including thinning from below, crown thinning, selection thinning, mechanical thinning, and free thinning. Although all of these thinning types can be applied to even-aged oak stands, thinning from below is one of the most commonly used methods [11]. In thinning from below, also referred to as low thinning, trees in the lower crown positions and smaller diameter classes are removed. However, some trees in the upper classes may also be removed to achieve the desired density or to eliminate poorly formed or weak trees [11].

To properly understand the dynamics of stand development under different thinning intensities, long-term replicated experiments that include unmanaged reference plots are essential [12]. Without such data, analyses of the density–growth relationship risk remain case-specific and may reinforce circular assumptions rather than yield generalisable insights [13]. Thinning and its effects on growth have been a longstanding focus of forest science, with numerous experiments conducted, including some with long-term observations. Despite this, the impact of thinning on tree growth and stand yield continues to be debated, including in Quercus stands [14]. There is no clear consensus on how and when thinning should be implemented in oak stands; however, it should not compromise the stand quality or growth potential [11].

The overall objective of the present study was to test the growth and yield response to thinning in Quercus robur L. even-aged stands in Galicia under different thinning intensities from below. To achieve this, the following specific objectives were addressed: (i) to determine the approach to be carried out; (ii) to select which stand variables would be analysed in each approach; and (iii) to develop a statistical analysis appropriate for the structure of the data.

2. Materials and Methods

2.1. Data

The data come from a thinning experiment established between 1998 and 1999 by the Lourizán Forestry Research Centre in monospecific even-aged stands of Q. robur in Galicia. Three sites representing the main types of Galician pedunculate oak forest [15] were selected to establish 3 thinning trials (Figure 1): Boimente and Labio (Lugo province, 1998) and Cotobade (Pontevedra province, 1999). The soils are deep (>70 cm) and granitic. The climate is humid oceanic in Boimente, continental oceanic in Labio, and humid oceanic with a tendency to summer aridity in Cotobade [16]. The site indices (

Table 1. Summary statistics of the trial stands in the year of installation before thinning. Standard deviations between plots are in brackets.

Trial	Year	Age	N	G	Dm	Dg	Hm	H0	SI
Boimente	1998	60	797 (168)	16.90 (2.07)	15.97 (1.84)	16.64 (1.95)	13.27 (1.76)	13.81 (1.89)	13.81
Cotobade	1999	32	1013 (422)	21.23 (4.69)	15.78 (3.47)	17.12 (3.56)	11.63 (1.38)	14.84 (1.86)	23.09
Labio	1998	38	1044 (136)	15.58 (1.59)	13.57 (1.05)	13.85 (1.08)	12.29 (1.06)	12.54 (1.03)	17.77

Year: year of trial installation; Age: stand age (years); N: number of trees per hectare; G: basal area (m² ha⁻¹); D_m: mean diameter (cm); D_g: quadratic mean diameter (cm); H_m: mean tree height (m); H₀: dominant height (m) defined as the mean height of the 100 largest diameter trees per hectare; SI: site index (m) defined as H₀ at a stand age of 60 years according to Gómez-García et al. [6] was estimated for Cotobade and Labio using the transition equation developed by the cited authors.

) indicate that the site quality in the trial stands is medium to high [6]. The thinning experimental design was identical across trials: randomised complete blocks with four thinning treatments (control, 15%, 35%, and 55% basal area removal), yielding 12 plots per trial. The plot size was 1600 m² (40 × 40 m), except in Cotobade (900 m², 30 × 30 m).

All living trees with a diameter at breast height (DBH, measured at 1.3 m above ground level) larger than 5 cm were labelled. DBH was measured with millimetric precision using tree callipers, taking two perpendicular readings and calculating their arithmetic mean. The tree height was recorded in a subsample with a Blume-Leiss or Vertex III hypsometer. Thinning was from below, removing suppressed trees but also some dominant trees when they were growing very close to each other. The treatments correspond to light (15% basal area removal), moderate (35%), and heavy (55%) thinning, in line with the average ranges reported in the literature (<20%, 20–35%, >35%; [17]). After thinning, the stands were remeasured at ~3-year intervals for DBH (all trees) and height (subsample), using callipers and a Vertex IV hypsometer. In the final inventory (2024), all tree heights were measured. The stand volumes were estimated from the individual tree volumes using the species-specific volume equation developed for the region [18]. Because this equation requires DBH and height as independent variables, and the total height was not measured for all individuals until the last inventory, we estimated the missing heights by fitting local DBH–height equations, following the model of Burkhart and Strub [19], for each trial and inventory [20].

For this study, three post-thinning remeasurements from the Cotobade trial were used; subsequent measurements were excluded, because a non-experimental thinning was applied by the forest owners. The Cotobade trial is no longer active. Boimente and Labio remain active, with seven post-thinning remeasurements each.

2.2. Analysis Approach

Two complementary approaches were used to analyse the data. In the first approach, we examined the evolution of the stand variables without accounting for the initial state (starting from inventory 1, after thinning). This analysis focused on the absolute change in stand variables following thinning, aiming to assess whether the treatments resulted in divergent stand structures. The approach is framed within the state-space concept [21], which provides a dynamic framework for representing forest stand development. In this framework, the state of a stand at a given time is defined as the minimal set of variables necessary to characterise its current condition and to predict its subsequent evolution. Typical state variables in forest modelling include the dominant height, basal area, and number of trees per hectare, which together summarise the structural and competitive status of the stand.

In the second approach, the thinning-effect, we analysed the changes in stand variables derived from the thinning treatment. To control for the initial differences among plots, all models included the corresponding pre-treatment measurement of the response variable as a covariate [22]. Including baseline values allows the models to isolate the effects of treatment and time on the subsequent response while accounting for potential confounding due to the initial variation. To improve the interpretability and reduce the collinearity with other predictors, the baseline covariates were mean-centred by subtracting their overall mean across all plots. This approach is consistent with guidelines that recommend adjusting for baseline covariates to enhance the precision of the treatment effect estimates in ecological studies [23]. Additionally, mean centring is a common practice in statistical modelling to facilitate the interpretation of the interaction terms and to mitigate issues related to multicollinearity [24].

2.3. Dependent Variables

In the state-space approach, we analysed the evolution of the basal area (G), number of trees per hectare (N), and dominant height (H₀) after thinning, considering the different intensities of thinning. These are the typical state variables in the state-space approach and are the state variables used in the current dynamic growth model for even-aged Q. robur stands in Galicia [6], which can be classified as a statistical, disaggregated, non-spatial, and deterministic stand model [25].

In the thinning-effect approach, the pre-thinning stand is taken as the starting point, and we analysed the variables related to the yield as well as the average tree attributes. Therefore, we analysed the cumulative basal area (G_c, m² ha⁻¹) (current G plus G removed in the thinning), cumulative total G (G_tc, m² ha⁻¹, G_c plus G loss in dead trees), cumulative volume (V_c, m³ ha⁻¹, current V plus V removed in the thinning), cumulative total volume (V_tc, m³ ha⁻¹, V_c plus V loss in dead trees), mean diameter (D_m, cm), and dominant diameter (D₀, cm, defined as the mean diameter at breast height of the 100 largest diameter trees per hectare). The inclusion of dead trees as part of the ‘removed stand’ has also been adopted in other thinning studies [12,26,27] to represent the total yield, whereas V_c and G_c represent the usable yield. The dominant diameter (D₀) was included among the analysed variables as an indicator of the potential future crop trees, because they are the largest individuals in the stand, although not necessarily the best-formed or most valuable ones. Therefore, D₀ provides an approximate measure of the growth potential of dominant trees that are likely to persist until the end of the rotation, allowing the evaluation of whether the thinning intensity influences the development of the stand’s dominant component beyond the average response. This value approximates the 125 trees per hectare at final harvest reported by Barrio-Anta [28] for the production of high-quality Q. robur timber in the region.

2.4. Statistical Analysis

The correlation structure among observations can be addressed by formulating a multilevel mixed model [29,30,31]. For the first approach (state-space), we propose mixed model (1), and for the second (thinning-effect), we propose mixed model (2):

$$y_{ijsbp}=f\left({treat}_i,t_j\right)+{trial}_s+{block\left(trial\right)}_b+{plot\left(block\left(trial\right)\right)}_p+{\epsilon }_{ijsbp}$$

(1)

$$y_{ijsbp}=f\left({treat}_i,t_j,y_{0ic}\right)+{trial}_s+{block\left(trial\right)}_b+{plot\left(block\left(trial\right)\right)}_p+{\epsilon }_{ijsbp}$$

(2)

where y_ijsbp indicates the observation for the variable y taken in a plot p with treatment i repeatedly measured at time since thinning j, located in block b within trial s; f(treat_i, t_j) and f(treat_i, t_j, y_0ic) represent the fixed components of the models, which depend on the treatment effect and the time-dependent covariate, time since thinning (t_j), and, additionally, in model (2), the baseline covariate mean-centred variable y (y_0ic); trial_s, block(trial)_b and plot(block(trial))_p are random effects, following a normal distribution with mean zero and variance ${\sigma }_s^2$, ${\sigma }_b^2$, and ${\sigma }_p^2$ respectively; ε_ijsbp represents independent and identically distributed residual terms of error, with mean zero and residual variance ${\sigma }_e^2$. Model (1) shows similarities to that of del Rio et al. [27], but it replaces age with time since thinning, including the plot as a random effect, and does not include other interactions in the random effects. Time since thinning was chosen instead of age because the age ranges in the trials do not completely overlap, and the effects could otherwise be attributed to age when they actually arise from differences between the trial sites. Model (2) is similar to that of Mäkinen and Isomäki [22] but also includes the time-dependent covariate (time since thinning, t_j) as a fixed-effect component.

Linear mixed models were fitted using the lmer function in the lme4 package [31] for the R programming language [32]. For each dependent variable, the fitting process was the same. The appropriate model structure was evaluated by testing the interaction between treatment and time since thinning. A maximum likelihood (ML) procedure or a restricted maximum likelihood (REML) procedure can be used to fit the model. The former was used in comparing models that differ in their fixed effects [31,33], i.e., whether or not they included the treatment × time interaction (treat_i × t_j). The model selection was based on the significance of the parameters, and Akaike’s information criterion (AIC) and Schwarz’s Bayesian information criterion (BIC) were applied to avoid overparameterization. When AIC and BIC diverged, we retained the model including the treatment × time interaction. However, the ML estimates of the variance components do not consider the degrees of freedom lost in estimating the fixed-effects parameters and are therefore biased downwards, in contrast to the REML estimates [34]. Therefore, the REML procedure was used to obtain the final parameter estimates in the selected models. The normality and homogeneity of variance of residuals were checked in the selected models. The fixed effects were tested using t-tests with Satterthwaite’s method for degrees of freedom, implemented in the R package lmerTest (Version 3.1-3) [35]. To assess pairwise differences among treatment levels, we used the R package emmeans (Version 1.11.2-8) [36], which computes the estimated marginal means (previously known as least-squares means) and allows for multiple comparisons adjusted using the Tukey method [37]. For models that included the treatment × time interaction, treatment comparisons were performed at specific time points (0, 5, 10, 15, 20, and 25 years).

3. Results

3.1. The State-Space Approach

According to the AIC and BIC criteria (Table S1 in the Supplementary Material), including the treatment × time interaction significantly improved the model fit for the variable N; therefore, this interaction term was retained in the final model. In contrast, the interaction was excluded from the final models for G and H₀.

3.1.1. G Variable

Treatment had a significant effect on G (

Table 2. Fixed effects of treatment and time from the linear mixed-effects model for G. Time refers to time after thinning. All treatment coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	18.71	1.871	2.57	10.00	0.0040
Treatment L	−2.428	1.034	23.28	−2.35	0.0277
Treatment M	−6.924	1.034	23.28	−6.70	<0.0001
Treatment H	−10.62	1.034	23.28	−10.27	<0.0001
Time	0.3683	0.013	199.4	28.96	<0.0001

), with lower mean values in the thinned plots compared with the control. In particular, the H and M treatments showed significantly lower G values than the control (p < 0.001), while the L treatment presented an intermediate response, differing from the control only marginally. Time had a strong positive effect on G (p < 0.001), indicating consistent growth across all treatments throughout the study period. Fixed effects from the mixed model indicated that treatment L had a moderate negative effect compared with the control (p = 0.0277). However, Tukey’s post hoc comparisons among treatments showed that this difference was not significant after adjustment for multiple testing (p = 0.115). Therefore, only treatments H and M significantly reduced G relative to the control, creating three statistically distinct groups (C–L, M, and H) that remained stable over time (Figure 2).

3.1.2. N Variable

As expected, time had a negative effect on N (p < 0.001) due to mortality (

Table 3. Fixed effects of treatment, time, and treatment × time from the linear mixed-effects model for N. Time refers to time after thinning. All treatment and treatment × time coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	827.6	83.29	3.49	9.936	0.0011
Treatment L	−76.56	67.10	25.04	−1.141	0.2646
Treatment M	−317.2	67.10	25.04	−4.727	<0.0001
Treatment H	−439.0	67.10	25.04	−6.543	<0.0001
Time	−6.489	0.785	197.86	−8.270	<0.0001
Treatment L × Time	2.076	1.071	197.94	1.939	0.0540
Treatment M × Time	3.978	1.071	197.94	3.715	0.0003
Treatment H × Time	5.874	1.071	197.94	5.485	<0.0001

). However, the mortality was higher in control plots and decreased in L, then in M, and then in H. In the H treatment, the variable N was almost constant over time. Tukey’s post hoc comparisons among treatments showed that treatment L did not differ from the control, and there were no differences between treatments M and H, but these differed from L and the control (Figure 3).

3.1.3. H₀ Variable

The value of H₀ was influenced by the thinning applied, as some dominant trees were removed when they were growing very close to each other, although the differences between treatments were not significant (

Table 4. Fixed effects of treatment and time from the linear mixed-effects model for H₀. Time refers to time after thinning. All treatment coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	14.46	0.826	3.26	17.50	0.0002
Treatment L	−0.482	0.613	24.06	−0.79	0.4394
Treatment M	−1.234	0.613	24.09	−2.01	0.0555
Treatment H	−1.097	0.613	24.09	−1.79	0.0861
Time	0.149	0.010	179.9	15.25	<0.0001

, Figure 4). Lower H₀ values were observed in the M and H treatments. Time had a strong positive effect on H₀ (p < 0.001), indicating consistent growth across all treatments throughout the study period.

In summary, the results from the state-space approach indicated that thinning produced differentiated stand structures under the moderate and heavy treatments (M and H), mainly expressed through differences in stand basal area and trees per hectare, whereas the dominant height remained unaffected.

3.2. Thinning-Effect Approach

The AIC and BIC provided concordant criteria for model selection, supporting the inclusion of the treatment × time interaction for the variable V_tc and its exclusion from the final models for G_c and D₀ (Table S1 in the Supplementary Material). In contrast, the AIC and BIC diverged for model selection in G_tc, V_c, and D_m, and we therefore retained the model including the treatment × time interaction. For all variables studied, the resulting models indicated strong positive effects of both time after thinning (time) and the baseline values.

3.2.1. G_c Variable

Among the treatments, only treatment L showed a marginally significant increase relative to the control (C) (p = 0.041), whereas treatments H and M did not differ significantly from the control (

Table 5. Fixed effects of treatment, time, and baseline value from the linear mixed-effects model for G_c. Time refers to time after thinning, and the baseline value is G pre-treatment centred (G pre-treat. cent.). All treatment coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	17.47	1.066	2.32	16.38	0.0019
Treatment L	0.8912	0.414	25.22	2.15	0.0411
Treatment M	0.0848	0.419	25.88	0.20	0.8412
Treatment H	−0.2411	0.421	25.72	−0.57	0.5715
Time	0.3678	0.013	203.4	29.08	<0.0001
G pre-treat. cent.	0.8580	0.055	28.02	15.74	<0.0001

). However, pairwise comparisons using Tukey’s test of estimated marginal means revealed no statistically significant differences among treatments (p > 0.05), indicating that the effect of treatment L was weak (Figure 5).

3.2.2. G_tc Variable

A significant negative interaction between treatment H and time (p = 0.005) revealed that the growth rate under treatment H decreased over time relative to the control (

Table 6. Fixed effects of treatment, time, baseline value, and treatment × time from the linear mixed-effects model for G_tc. Time refers to time after thinning, and the baseline value is G pre-treatment centred (G pre-treat. cent.). All treatment and treatment × time coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	17.243	0.896	2.759	19.25	0.0005
Treatment L	0.4521	0.509	84.44	0.888	0.3771
Treatment M	−0.1424	0.513	84.07	−0.277	0.7822
Treatment H	0.0601	0.517	84.78	0.116	0.9077
Time	0.4989	0.026	217.25	19.42	<0.0001
G pre-treat. cent.	0.9422	0.056	37.61	16.97	<0.0001
Treatment L × Time	0.0062	0.035	218.47	0.178	0.8588
Treatment M × Time	−0.0224	0.035	218.53	−0.642	0.5215
Treatment H × Time	−0.0989	0.035	218.43	−2.83	0.0051

). No significant interactions were detected for treatments L or M. Pairwise comparisons of the estimated marginal means showed that treatment H differed significantly from the control (C) at the last predefined time points (≥15 years after thinning; p < 0.01), while treatments L and M did not differ significantly from C at any time (Figure 6). Differences between treatments H and L were also significant at 10, 15, 20, and 25 years (p < 0.01), indicating a consistently lower growth trajectory under treatment H.

3.2.3. V_c Variable

A significant negative interaction between treatment H and time (p = 0.008) revealed that the rate of volume accumulation under treatment H decreased over time relative to the control (

Table 7. Fixed effects of treatment, time, baseline value, and treatment × time from the linear mixed-effects model for V_c. Time refers to time after thinning, and the baseline value is V pre-treatment centred (V pre-treat. cent.). All treatment and treatment × time coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	93.76	8.056	2.519	11.64	0.0030
Treatment L	4.047	3.839	94.49	1.05	0.2945
Treatment M	2.106	3.855	93.93	0.55	0.5862
Treatment H	1.357	3.906	95.07	0.347	0.7290
Time	3.390	0.198	218.46	17.12	<0.0001
V pre-treat. cent.	0.9309	0.060	33.51	15.62	<0.0001
Treatment L × Time	−0.0705	0.269	219.69	−0.26	0.7934
Treatment M × Time	−0.5339	0.269	219.68	−1.99	0.0480
Treatment H × Time	−0.7204	0.269	219.70	−2.68	0.0080

). A smaller but significant negative interaction was also found for treatment M (p = 0.048), whereas no significant interaction was detected for treatment L. Pairwise comparisons of the estimated marginal means showed that treatment H produced a significantly lower cumulative volume than the control (C) at the last predefined time points (≥15 years after thinning; p < 0.01), while treatments L and M did not differ significantly from C at any time (Figure 7). Differences between treatments H and L were highly significant from 10 years onward (p < 0.01), indicating a consistently lower growth trajectory under treatment H.

3.2.4. V_tc Variable

A significant negative interaction between treatment H and time (p = 0.0003,

Table 8. Fixed effects of treatment, time, baseline value, and treatment × time from the linear mixed-effects model for V_tc. Time refers to time after thinning, and the baseline value is V pre-treatment centred (V pre-treat. cent.). All treatment and treatment × time coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	93.07	7.076	2.666	13.15	0.0017
Treatment L	2.759	3.794	93.44	0.73	0.4690
Treatment M	−0.2352	3.813	92.64	−0.06	0.9510
Treatment H	0.7910	3.871	93.46	0.20	0.8386
Time	4.014	0.195	218.07	20.62	<0.0001
V pre-treat. cent.	0.9938	0.064	39.22	15.59	<0.0001
Treatment L × Time	−0.1355	0.264	219.21	−0.51	0.6088
Treatment M × Time	−0.5357	0.264	219.21	−2.03	0.0437
Treatment H × Time	−0.9706	0.264	219.22	−3.67	0.0003

) indicated that the cumulative total volume growth rate under treatment H declined over time relative to the control, while treatment M also showed a weaker but significant negative interaction (p = 0.044). No significant interaction was detected for treatment L. Pairwise comparisons of the estimated marginal means indicated that treatments H and M had a significantly lower cumulative total volume than both C and L at the final predefined time points (p < 0.01), with significant differences observed from 10 years onward for treatment H and from 15 years onward for treatment M (Figure 8).

3.2.5. D_m Variable

The significant positive interaction between treatment H and time (p = 0.0017) indicated that the rate of diameter increase under treatment H was higher than that of the control over time, whereas treatments L and M did not differ significantly from the control in their temporal response (

Table 9. Fixed effects of treatment, time, baseline value, and treatment × time from the linear mixed-effects model for D_m. Time refers to time after thinning, and the baseline value is D_m pre-treatment centred (D_m pre-treat. cent.). All treatment and treatment × time coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	14.57	0.810	3.185	17.99	0.0002
Treatment L	1.409	0.571	38.41	2.47	0.0182
Treatment M	1.587	0.557	38.85	2.85	0.0070
Treatment H	2.691	0.578	38.05	4.66	<0.0001
Time	0.2547	0.0196	241.0	13.00	<0.0001
Dm pre-treat. cent.	1.235	0.0855	30.12	14.44	<0.0001
Treatment L × Time	0.00403	0.0263	240.9	0.15	0.8786
Treatment M × Time	0.03723	0.0264	240.9	1.41	0.1590
Treatment H × Time	0.08351	0.0263	240.9	3.17	0.0017

). Pairwise comparisons of estimated marginal means showed that treatment H had consistently higher adjusted mean D_m values than the control from the beginning (p < 0.01), higher than treatment L from 5 years onward, and higher than treatment M from 10 years onward (Figure 9). Treatment M also exhibited higher adjusted mean D_m values than the control from the beginning, whereas treatment L did not differ significantly from either C or M at any evaluated time.

3.2.6. D₀ Variable

The treatment effects were not significant (p > 0.05,

Table 10. Fixed effects of treatment, time, and baseline value from the linear mixed-effects model for D₀. Time refers to time after thinning, and the baseline value is D₀ pre-treatment centred (D₀ pre-treat. cent.). All treatment coefficients represent differences from the control level (reference). Treatments are C (control), L (light thinning), M (moderate thinning), and H (heavy thinning).

Term	Estimate	Std. Error	df	t Value	p Value
(Intercept)	22.71	0.469	2.70	48.44	<0.0001
Treatment L	0.3596	0.237	22.72	1.52	0.1428
Treatment M	0.4950	0.245	24.18	2.02	0.0549
Treatment H	0.1701	0.257	24.50	0.66	0.5140
Time	0.3808	0.00735	234.6	51.82	<0.0001
D0 pre-treat. cent.	0.9962	0.0344	34.13	28.93	<0.0001

), suggesting that the dominant diameter growth followed a similar pattern across all treatments. Pairwise comparisons of the estimated marginal means confirmed that none of the treatments differed significantly from the control or from each other (Figure 10).

In summary, the results from the thinning-effect approach indicated that the cumulative stand basal area and volume—both excluding mortality (G_c and V_c) and including it (G_tc and V_tc)—followed the pattern L > C > M > H, although the differences between L and C were not statistically significant. Differences between the M and C treatments were also not significant, except for V_tc at the last predefined time point (≥15 years after thinning). Statistically significant differences between the H and C treatments occurred in G_tc, V_c, and V_tc, but only from 10 to 15 years onward, depending on the variable considered. For the mean diameter (D_m), treatments M and H showed significantly higher values than the control from the beginning, whereas differences in the dominant diameter (D₀) were not significant among treatments.

4. Discussion

The results of this long-term thinning experiment provide valuable insights into the growth dynamics of pedunculate oak (Quercus robur L.) stands under different thinning from below intensities in Galicia (NW Spain). The combination of two complementary analytical frameworks—the state-space and thinning-effect approaches—proved crucial for distinguishing structural from productive responses and for capturing both standing growth and harvested yield. Accounting for the baseline conditions and using time since thinning rather than stand age as a temporal covariate allowed for a clearer separation of treatment effects from inherent trial differences, which is particularly important in long-term multi-site studies.

In relation to the state-space approach, this study provides valuable empirical information for evaluating and refining existing growth models for Q. robur in Galicia [6]. The observed stability of the dominant height among treatments supports its use as a reliable state variable, while the differentiated responses of stand basal area and trees per hectare offer reference points for calibrating dynamic models that incorporate thinning effects.

Consistent with classical stand density–growth relationships [7,8,12], the cumulative basal area (G_c, G_tc) and volume (V_c, V_tc) were only moderately affected by the thinning intensity except for heavy thinning. Both G_c and V_c (harvested yield) and their total counterparts G_tc and V_tc (including mortality) followed the pattern L > C > M > H, indicating that light thinning maintained or slightly enhanced the total yield compared with unthinned stands, whereas heavy thinning reduced the long-term production. This outcome supports the notion that stand productivity is relatively insensitive to density within an intermediate range, as expressed by Langsaeter’s curve, and that excessive density reduction leads to yield losses. Similar findings were reported for other Iberian species such as Quercus pyrenaica [26] and Pinus sylvestris [27], as well as in long-term experiments across Europe [12,22].

The fact that light or moderate thinning maintained cumulative yield while reducing competition suggests a favourable trade-off between growth and utilisation efficiency. This is particularly relevant from a management perspective, as it implies that part of the total yield can be harvested during stand development without significant loss of overall productivity. The results thus highlight the importance of considering both standing and harvested components when evaluating thinning effects, rather than focusing solely on the final stand volume.

Temporal patterns in G and V confirmed that the short-term growth benefits following thinning may not persist over longer periods, as previously observed by Pretzsch [12] and Lhotka [14]. In the early post-thinning years, plots under heavier thinning exhibited accelerated diameter growth and apparent increases in periodic increment. However, as the stands aged, these advantages diminished and ultimately translated into lower cumulative yields. This behaviour reflects the well-documented contrast between short- and long-term thinning responses: early growth acceleration is compensated by later slowdowns as the total growing stock declines. Our findings reinforce that only multi-decade monitoring with unthinned reference plots can reveal the true long-term balance of thinning effects.

Regarding tree size, the mean diameter (D_m) increased markedly with the thinning intensity, both due to the immediate effect of removing smaller trees (technical increment) and the subsequent acceleration of the average diameter growth. However, differences in the dominant diameter (D₀)—representing potential future crop trees—were not significant across treatments. This indicates that, although heavier thinning enhances average diameter growth, it does not necessarily promote the superior development of the dominant cohort. Similar patterns have been observed in other oak and pine species [26,27,38], where thinning increased the quadratic mean diameter but had limited or no effect on the dominant diameter. In Mäkinen and Isomäki [22], thinning increased the mean diameter and, to a lesser extent, the diameter of the 400 largest trees per hectare. The absence of significant differences in D₀ suggests that the largest and most competitive trees maintain similar growth trajectories regardless of the thinning from below intensity, while diameter gains mainly occur among suppressed and intermediate individuals released from competition. This may be because thinning from below does not affect the crown growth of dominant trees, and there is a positive relationship between the crown size and tree diameter [39,40,41].

These results have important implications for silvicultural decision-making. Under the medium-to-high site quality conditions, light to moderate thinning appears to offer an optimal balance between maintaining stand-level yield, ensuring periodic harvests, and removing weak trees. Heavy thinning, by contrast, may compromise the long-term volume yield and carbon sequestration and should therefore be avoided when the management objective is the maximum total production. Moreover, excessive reductions in stand density may increase the occurrence of epicormic branching, thereby reducing the stem quality [42,43] or increasing the cost of its control through pruning [40], in either case decreasing the economic value of oak. Nevertheless, in stands managed for aesthetic and ecological reasons, more intensive thinning could still be justified.

Although this study provides useful information for the management of oak stands, several important factors could not be directly evaluated. As previously noted by Lhotka [14], further research is required to consider oak stands established on low-quality sites, since the thinning response varies with site quality [12,22]. However, Barrio-Anta [28] indicated that the development of productive silviculture for Quercus robur in Galicia can only be considered on sites of medium to high quality. It would be valuable to clarify the effects within the range between light and moderate thinning intensities. In addition to thinning from below, different thinning types should be investigated, especially those that promote large well-formed trees. Finally, it remains to be determined whether thinning costs are economically compensated at the time of thinning and/or over the entire rotation [11,22]. An economic assessment linked to the thinning regime is therefore recommended to optimise management strategies and maximise economic returns [40,44].

5. Conclusions

In summary, long-term experimental results show that thinning from below alters the stand structure in Q. robur even-aged stands under moderate and heavy treatments, mainly through differences in stand basal area and trees per hectare, while dominant height remains unchanged. Overall, light to moderate thinning intensities do not significantly reduce stand yield and at the same time permit intermediate harvests and/or the removal of weak trees. Mean diameter increased under more intensive thinning, but differences in dominant diameter—representing potential future crop trees—were not significant, suggesting that stronger thinning from below does not necessarily improve the development of the dominant trees.