Influencing plantation stand structure through close-to-nature silviculture


New silvicultural practices to meet the requirements of ecosystem-based forest management are being adopted operationally, even if the long-term outcomes remain unknown. In eastern Quebec, Canada, the conversion of plantations from even-aged to irregular or uneven-aged stands is being carried out in 10% of commercial thinning operations. Existing growth and yield simulators cannot be used to forecast stand development. Here we apply a novel individual tree-level simulator to plantations characterized by high levels of natural regeneration ingrowth, such as those observed in Quebec. The simulator user can either choose distance-dependent or distance-independent competition indices, depending on user preference or simulation needs. Calibration statistics and validation results indicate that both versions perform very well. When applied to operational silvicultural scenarios, the simulator shows that thinning does not influence total stand yield; however, tree spatial aggregation does change. Moreover, the variability among the different simulation runs is greater for spatial statistics than for stand yield. Overall, thinning from below has the greatest effect on stand structure, whereas the smallest is from early crop tree release, used as the initial conversion step. This pattern implies that the first and second thinnings of the conversion process towards irregular or uneven-aged stands may not have a major effect on stand structure. In the case of the conversion process, the consequences for stand structure must thus be viewed as a longer-term issue. More importantly, the conversion process does not reduce stand yield, thereby reducing one of the key concerns of forest managers.

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The authors would like to underline the contribution of both anonymous reviewers. The authors would also like to thank Murray Hay for the linguistic review. The process was one of the most interesting they have gone through, with the impression that the revision was similar to having an interesting discussion around a cup of coffee. The development of the growth simulator was made possible by funding from the Québec Ministry of Forests, Wildlife and Parks (Ministère des Forêts, de la Faune et de Parcs du Québec), the Fonds de Recherche Québécois sur la Nature et les Technologies (FRQNT), the Natural Sciences and Engineering Research Council of Canada and the Lebel Group.

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Appendix: Development of the growth module

Appendix: Development of the growth module

The growth model comprises three components as described in Bérubé-Deschênes et al. (2017a, b):

$$\frac{{{\rm iBA}}_{ijk}}{{5\cdot {\rm BA}}_{ijk}}=f\left({{\rm SI}}_{i}\right)g\left({{D}}_{ijk}\right)h\left({{C}}_{ijk}\right)+{\varepsilon }_{ijk}$$

where iBAijk is the 5-year basal area increment of tree i in plot j of plantation k, BAijk is the basal area of that tree, Dijk is the tree’s DBH, \(f\left({{\rm SI}}_{i}\right)\) is the effect of site index on relative growth, \(g\left({{D}}_{ijk}\right)\) is the change in relative growth with tree size, \(h\left({{C}}_{ijk}\right)\) is the reduction in relative growth with the competition, and \({\varepsilon }_{ijk}\) is the random error of the model (\({\varepsilon }_{ijk}\sim N\left(0, {\sigma }^{2}\right))\). Random effects were tested and were not retained as signs of over-parameterization were observed. Moreover, the models having random effects had poorer fit statistics than the model presented in Eq. 18.

The effect of site fertility was entered linearly, i.e.:

$$f\left({{\rm SI}}_{i}\right)={b}_{0}+{b}_{1} \mathrm{SI}$$

Different forms for the effect of tree size on relative growth were tested:

$$g\left({{D}}_{ijk}\right)= \frac{1}{1+{d}_{1} {{\rm DBH}}_{ijk}}$$
$$g\left({{D}}_{ijk}\right)= \mathrm{exp}\left(-{d}_{1} {{\rm DBH}}_{ijk}\right)$$
$$g\left({{D}}_{ijk}\right)= \mathrm{exp}\left(-0.5 {\left(\frac{\mathrm{log}{{\rm DBH}}_{ijk}}{\left|{d}_{1}\right|}\right)}^{2}\right)$$
$$g\left({{D}}_{ijk}\right)= \frac{\mathrm{exp}\left({d}_{1} {{\rm DBH}}_{ijk}\right)}{1+\mathrm{exp}\left({d}_{1} {{\rm DBH}}_{ijk}\right)}$$

Alternative formulations of the effect of competition were also compared:

$$h\left({{C}}_{ijk}\right)= \frac{1}{1+{c}_{1} {{\rm CI}}_{ijk}}$$
$$h\left({{C}}_{ijk}\right)= 1-{{\rm exp}}\left(\frac{-{c}_{1}}{{{\rm CI}}_{ijk}}\right)$$
$$h\left({{C}}_{ijk}\right)= \frac{\mathrm{exp}\left({c}_{1} {{\rm CI}}_{ijk}\right)}{1+\mathrm{exp}\left({c}_{1} {{\rm CI}}_{ijk}\right)}$$

where \({{\rm CI}}_{ijk}\) was either the basal area of the trees larger than the target tree or the spatially explicit competition index proposed by Martin and Ek (1984):

$${{\rm CI}}_{n}=\sum_{n\ne m}\frac{{{\rm DBH}}_{m}}{{{\rm DBH}}_{n}}\mathrm{exp}\left(\frac{{{\rm dist}}_{nm}}{{{\rm DBH}}_{n}+{{\rm DBH}}_{m}}\right)$$

where CIn is the competition index of tree n, DBHm is the DBH of the competitor tree m, and distnm is the distance between the target tree n and competitor m. Other spatially explicit and nonspatial competition indices listed in Bérubé-Deschênes et al. (2017a, b) were tested, and the Martin–Ek (ME) and BAL were found to be the best spatially explicit and nonspatial competition indices, respectively (results not presented).

All possible combinations of \(f\left({{\rm SI}}_{i}\right)\), \(g\left({{\rm DBH}}_{ijk}\right)\) and \(h\left({{C}}_{ijk}\right)\) were tested, leading to 12 models being calibrated for each competition index using the white spruce trees found in the calibration database. The Akaike’s information criterion (AIC) for each combination is presented in Table

Table 5 Model AIC for each model calibrated for the BAL and ME competition indices

5. The best models are those having the lowest AIC. Model form for the other species or species groups was assumed to follow that of the white spruce forms.

Furthermore, the separation into clade-specific competition indices was also tested (Bérubé-Deschênes et al. 2017a, b). This implies that the competition indices were divided into either softwood or hardwood indices. For the Martin–Ek index, the CI are calculated as:

$${{\rm CI}}_{n, {{\rm softwood}}}=\sum_{n\ne m}\frac{{{\rm DBH}}_{m}}{{{\rm DBH}}_{n}}\mathrm{exp}\left(\frac{{{\rm dist}}_{nm}}{{{\rm DBH}}_{n}+{{\rm DBH}}_{m}}\right)$$

where m are softwood species, and

$${{\rm CI}}_{n, {{\rm hardwood}}}=\sum_{n\ne m}\frac{{{\rm DBH}}_{m}}{{{\rm DBH}}_{n}}\mathrm{exp}\left(\frac{{{\rm dist}}_{nm}}{{{\rm DBH}}_{n}+{{\rm DBH}}_{m}}\right)$$

where m are hardwood species.

The clade-specific BAL was calculated separately for softwood and hardwood species. The competition indices presented in Eqs. 2426 were then replaced by:

$${c}_{1} {{\rm CI}}_{ijk}={c}_{2} {{\rm CI}}_{ijk, {{\rm softwood}}}+{c}_{3} {{\rm CI}}_{ijk, {{\rm hardwood}}}$$

The models for each species group were then calibrated by differentiating (or not) the competition by clade. The AIC for each model and type of competition was then compared (Table

Table 6 AIC values for models with clade-specific and no differentiation between clades and for BAL and Martin–Ek competition indices


Finally, the search radius for identifying the competitors was varied between 3, 4 and 5 m. The minimum diameter of the neighbouring trees was also varied between using all trees and using trees with a DBH > 70–100% (by 5% increments) of the DBH of the target tree. The AIC of the white spruce spatially explicit model was compared (Fig.

Fig. 10

Model AIC for white spruce with varying search radius and minimum competitor DBH

10). The model having the lowest AIC was that where competitors were chosen within a 5-m radius and had a DBH of at least 85% of the DBH of the target tree.

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Schneider, R., Franceschini, T., Duchateau, E. et al. Influencing plantation stand structure through close-to-nature silviculture. Eur J Forest Res (2021).

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  • Ecosystem-based forest management
  • Growth and yield model
  • Silviculture
  • Conversion of even-aged stands