Predicting hardwood quality and its evolution over time in Quebec's forests

Predicting hardwood quality and its evolution over time in Quebec's forests Abstract Long-term success of forest management requires knowledge of standing tree characteristics and, an estimation of their evolution over time. In this study, hardwood stem quality was assessed using a specifically designed, non-destructive quality classification system that comprises four categorical output classes based on stem size and occurrence of external defects. We used data from national forest inventory sample plots distributed across Quebec (Canada) to predict hardwood stem quality and its evolution over time. We used ordinal logistic regression to model multiple stem quality classes. Hardwood stem quality was strongly related to stem harvest priority class and bioclimatic subdomain. Stem quality generally improved with d.b.h. and stand basal area. Changes in hardwood stem quality were strongly related to initial stem quality, with most trees retaining their initial quality over time. Stem quality evolution was also positively related to diameter growth. Overall, both initial and future stem quality were estimated with acceptable precision and minimal bias. Our results suggest that the equations could predict hardwood stem quality distribution and evolution among groups of forest stands. Introduction The long-term success of forest management requires appropriate knowledge of the characteristics of standing trees. Considering that quality and market value of North American hardwoods are related to the visual characteristics of the assortment of their various manufactured products, it is important to identify less vigorous stems which are expected to die or deteriorate before the next harvesting cycle, and to determine their potential uses for appearance wood products. In temperate deciduous forests of eastern North America, hardwood stem quality is generally assessed through a specifically designed quality classification system that uses a categorical output variable with two to four levels, each of which is related to a specific stem diameter threshold (Hanks, 1976; MFFP, 2014). The number of classes that are used in stem quality classification also varies among European countries (Bosela et al., 2015). Also, some classification systems consider tree vigour and quality simultaneously (e.g. Majcen et al., 1990; OMNR, 2004). Many defects located along the entire stem may affect both tree vigour and quality. However, most stem quality classification systems focus on the lower portion of the tree for the visual assessment of the presence, size and distribution of defects that might affect stem conversion into logs (Rast et al., 1973; Petro and Calvert, 1976) and lumber (NHLA, 2011). Stem quality classification has proven to be a good predictor of log grade occurrence and volume distribution (Fortin et al., 2009b) as well as value of standing trees (Cockwell and Caspersen, 2014; Havreljuk et al., 2014). Therefore, quality evaluation could improve marking decisions when selecting trees for either retention or harvest in hardwood stands (Webster et al., 2009; Fortin et al., 2009b; Pothier et al., 2013). Despite the usefulness of grading systems, exhaustive tree quality measurements are too costly to be systematically included in forest surveys. Consequently, some studies have used tree- and stand-level variables to predict tree grades, particularly for sugar maple (Acer saccharum Marsh.) (Lyon and Reed 1988; Webster et al., 2009), southern Appalachian species (Prestemon 1998), or European species (Sterba et al., 2006). Tree diameter is an important indicator of tree quality because it is related to its conversion to wood products. Several studies have shown a decrease in stem quality beyond a certain diameter threshold (e.g. Hansen and Nyland, 1987; Majcen et al., 1990; Prestemon, 1998; Pothier et al., 2013), which suggests a non-monotonic relationship between tree diameter and stem quality. Better predictions of standing tree value could be achieved when tree diameter is paired with the occurrence of certain specific tree defects (Bosela et al., 2015; Cecil-Cockwell and Caspersen, 2015). At the stand level, factors such as stand basal area (Belli et al., 1993; Mäkinen et al., 2003), site quality (Prestemon, 1998) and cutting methods (Erickson et al., 1990) were found to be related to tree quality. Yet, the effects of these variables on future tree quality still need to be addressed for northeastern hardwoods. To our knowledge, only a few studies have focused on dynamic models that project hardwood quality over time. Lyon and Reed (1988) developed linear discriminant functions to predict future tree grades from initial stem quality of sugar maple. However, their models included initial tree grade as a continuous variable, while in reality it is categorical. Lyon and Reed (1988) also assumed that the relationships in the study followed a linear trend, and did not establish thresholds that related stem diameter and grade. For their part, Fortin et al. (2009a), in order to predict future tree quality of hardwood species, considered it as a binary variable (i.e. presence/absence of sawlog potential) that was derived from a hybrid risk–product classification (Majcen et al., 1990). Model development of quality evolution over time requires long-term monitoring data. Longitudinal measurements of tree grades are necessary to fully evaluate the natural dynamics of stem quality (Pothier et al., 2013) but are generally limited by the lack of long-term field studies. From a statistical viewpoint, tree grade modelling is challenging, because the categorical nature of the response variable requires complex statistical approaches such as multinomial regressions (Agresti, 2013). Models using multinomial regressions have already been used to predict lumber product assortment for Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies [L.] Karst.) (Lyhykäinen et al., 2009; Hautamäki et al., 2010). Temporal structure must also be considered when projecting quality over time, in order to account for correlations that are induced by repeated measurements (Fox et al., 2001). The assessment of stem quality and its dynamics over time could (1) ensure more efficient allocation of the wood fibre supply, and (2) improve silvicultural strategies to meet management goals. Consequently, this study pursued three distinct objectives. First, we developed equations to predict stem quality of hardwood tree species in Quebec (Canada), based on the usual forest inventory variables. These equations could be used when stem quality is not measured directly. Second, we developed equations to estimate future stem quality. Third, we determined the main dendrometric and ecological variables that relate to stem quality and its evolution over time. These results will provide methods to estimate stem quality and it change over time, as a first step toward integrating these variables in forest growth simulators. Methods Stem quality Quebec's stem quality classification system aims to reflect lumber grade and volume recovery of hardwood trees (MFFP, 2014). The classification system has been consistent since its implementation in the 1985 provincial forest inventory. It was inspired by the USDA tree grading system (Hanks, 1976), and takes into account tree d.b.h. (diameter of the stem measured 1.3 m above ground level) and the presence of defects on the lowermost 5 m of the stem. Evaluation is based on visual assessment of defects that limit the clear wood (i.e. defect-free) length on the stem (e.g. branching, knots, bulges or other bark-covered defects), and those that reduce stem volume (e.g. cull, rot and sweep). Four grades are identified with letters A to D, in decreasing order of quality. Specific minimal d.b.h. thresholds of >39.0, >33.0 and >23.0 cm are required to achieve quality classes A, B, C or D, respectively. Trees with d.b.h. ≤ 23.0 cm are excluded from stem quality assessments since their d.b.h. is considered too small to produce logs that meet the minimum size requirements of standard sawlogs for factory lumber (Hanks et al., 1980). Although potential product recovery from small-diameter hardwoods could be improved with modern sawing techniques (Hamner et al., 2006; Nicholls and Bumgardner, 2015), most traditional hardwood mills in North America are adapted to process larger logs with sawing patterns that are designed to maximize grade recovery (Shmulsky and Jones, 2011). Sample datasets We used two distinct datasets from the provincial forest inventory of Quebec to predict stem quality (SQ) and stem quality evolution (SQE; i.e. change in stem quality over time) of hardwood tree species: (1) temporary sample plots (TSPs) and (2) permanent sample plots (PSPs). While the TSP dataset consists of a single measurement from each plot (measured between 2005 and 2012), the PSPs were established from 1975 to the 2000s and were monitored with repeated measurements at an average interval of 10 years. Hardwood species that were considered in this study are listed in Table 1. Plots of both datasets are well distributed over a 761 000-km2 forested area (Table 2), from the northern limit of the commercial forest to the southern border of the province (MFFP, 2015). Table 1 List of species included in each group Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Table 1 List of species included in each group Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Table 2 Number of observations by species and modelling groups for SQ and SQE Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) For the SQE model, the value in parentheses represents the number of individual trees that were included for the observed periods. Note: N/A is not applicable. Table 2 Number of observations by species and modelling groups for SQ and SQE Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) For the SQE model, the value in parentheses represents the number of individual trees that were included for the observed periods. Note: N/A is not applicable. Because the stem quality classification system is strongly related to d.b.h., we separated the data into three modelling groups, based on the highest quality class that a tree could achieve at a given d.b.h. (Table 2): modelling group I (>39.0 cm), modelling group II (33.1–39.0 cm) and modelling group III (23.1–33.0 cm). Statistical analysis Prediction of stem quality and stem quality evolution Preliminary data analysis, using descriptive statistics and correspondence analysis to investigate the association between species and actual and future stem quality, showed differences in stem quality distribution among species. Consequently, we developed separate models for SQ and SQE for each species. Some less abundant hardwood species were grouped, mostly by genus (Tables 1 and 2). One SQ and one SQE model were developed for each combination of species and modelling group. Stem quality of a tree from modelling group III can be considered as a binary variable, since its value is either grade C or grade D. We can assume that this variable follows a Bernoulli distribution with a probability π of being equal to C. We used a logit transformation to obtain predicted probabilities that were bounded by 0 and 1, and to linearize the relationship between the response and explanatory variables (Equation 1). For modelling groups I and II, we assumed that quality followed an ordinal multinomial distribution with a probability πk of being equal to quality grade k. A cumulative logit transformation was applied to equations of modelling groups I and II (Equation 2). g1(xij)=ln(π(xij)1−π(xij))=α+xijβ (1) g2(xij)=ln(πk(xij)1−πk−1(xij))=αk+xijβ (2) where g1 and g2 are the link functions, π is the probability of observing a given response value, α is the intercept, x is a vector of predictors, and β is a vector of parameters. The subscripts indicate the quality class k of tree i in plot j. The ordinal multinomial model (Equation 2) is a proportional odds model that assumes parameter vector β is constant among categories. For each predictor, we verified the assumption that the proportions followed an ordinal distribution by visually checking the parallelism among the slopes across different quality classes, for all continuous predictors of modelling groups I and II (Allison, 2012; Derr, 2013). In cases where this hypothesis was rejected, we added an interaction term between the predictor and the intercepts to fit the partial proportional odds model. This model was specified in the same manner as the proportional odds model with the Logistic procedure in the SAS statistical software (ver. 9.4, SAS Institute Inc., Cary, NC, USA), except that the ‘unequalslopes’ option was added for specific effects that did not satisfy the proportional odds assumption. This addition allowed parameters for each predictor in each response function to be estimated separately (Derr, 2013). Model development Prior to the analyses, we considered several types of variables as predictors of both SQ and SQE. Tree-level variables, such as d.b.h. (cm), d.b.h. increment (Δd.b.h., cm yr−1), harvest priority (HP) classification (Boulet 2007) and stem quality were included to represent initial tree characteristics. In both TSPs and PSPs, species and d.b.h. were recorded for every tree larger than 9.0 cm in d.b.h. within 400 m2 circular plots. Annual d.b.h. increments were computed from two consecutive PSP measurements, by subtracting the first d.b.h. measurement from the second then dividing the difference by the time interval between the two measurements (t, years). Tree vigour that was based on HP was recorded from a visual assessment of external defects and pathological symptoms along the stem (Hartmann et al., 2008). This system, which has been used since 2005 in Quebec's forest surveys, ranks trees based on their expected probability of surviving to the next scheduled cutting cycle (estimated at 20–25 years in the temperate forest zone of southern Quebec, Canada; Boulet, 2007). Trees are ranked according to four classes (M, S, C and R): (1) moribund trees (M), with the lowest survival probability; (2) defective, but surviving trees (S); (3) growing trees with minor defects (C); and reserve stock trees (R), with the highest survival probability. We expected that a tree changing modelling groups between two consecutive measurements because of an increase in d.b.h. would also have a greater probability of changing quality class, as it might also meet the minimal d.b.h. criteria of a better quality class. Consequently, we created a binary variable (Transition) to identify trees that had changed modelling groups between two measurements. Stand characteristics were described by stand basal area (G, m2 ha−1) and the occurrence of partial harvesting (Harvest) between two consecutive measurements. Stand basal area was derived from d.b.h. measurements of all trees with a d.b.h. >9.0 cm in the plot. We also considered ecological and climatic variables by including the bioclimatic subdomain in the models, together with mean annual temperature and total annual precipitation. Bioclimatic domains, which are based upon Quebec's ecological classification (MRN, 2013; Figure 1), refer to parts of the territory that, theoretically, support a similar type of vegetation (on mesic sites) at the end of the succession process. Mean annual temperature (˚C) and mean total precipitation (mm) for the 1980–2009 period were estimated with the BIOSIM climatic interpolation software (Régnière and St-Amant, 2007). Table 3 lists the explanatory variables that were used in the modelling process. Table 3 List of explanatory variables that were considered as predictors of SQ and SQE Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Table 3 List of explanatory variables that were considered as predictors of SQ and SQE Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Figure 1 View largeDownload slide Map of Quebec's bioclimatic subdomains (MRN, 2013). Figure 1 View largeDownload slide Map of Quebec's bioclimatic subdomains (MRN, 2013). We modelled SQ using measurements from 48 428 TSPs and 4 561 PSPs recorded from 2005 to 2012. Measurements prior to 2005 were excluded from the analyses because they did not include HP class. Consequently, the SQ dataset contains no repeated measurements. We first constructed a full model that included all the predictors (Table 3). For each combination of species and modelling group, a minimum threshold of 100 trees was set to consider a bioclimatic subdomain in the predictors. If this threshold was not reached, we grouped the bioclimatic subdomain with the nearest subdomain that reached the threshold. The list of bioclimatic subdomains and groups of bioclimatic subdomains (Appendix A: Tables A1 and A2) are included as supplementary material that is available online. A backward elimination procedure (Hosmer and Lemeshow, 2000), with a minimum P-value of 0.05 beginning with the full model, was used to select the variables that would be included in a reduced model. We also tested simple interactions between variables of the reduced model, and only retained those that were significant at a P-value of 0.05 or below. In order to make them useful and flexible, we attempted to parameterize the SQ equations without including tree harvest priority as a predictor. However, the value of the Akaike information criterion (AIC, Akaike, 1974) was considerably higher and precision was lower for models without HP. We therefore included this variable in the model fitting process. A plot level random effect was included in the reduced model to take into account the correlation between trees from the same plot and to avoid including non-significant fixed effects because of an underestimation of their standard error (Weiskittel et al., 2011). The random effect was added at the end of the model selection process to avoid problems of convergence that arise with larger models. We parameterized the model with the SAS Glimmix procedure, using the Laplace approximation method. When the inclusion of the random effect resulted in a lack of significance (P-value >0.05) of any of the fixed effects, we removed this fixed effect from the reduced model. Final model parameters were re-estimated with the Logistic procedure (i.e. without the plot random effect) to obtain non-biased population-level estimates of the coefficients, given that non-linear mixed models tend to be biased when they are applied at the population level (Meng et al., 2009; Groom et al., 2012; Fortin, 2013). Repeated stem quality measurements were needed to model SQE. Therefore, only data from 5 248 PSPs were used (Table 2). Growth intervals that were used to model SQE started between 1985 and 2007 and ended between 1989 and 2012. Seventeen per cent of SQE measurements consisted of repeated growth intervals from the same tree. We tried to include random effects to account for correlations between different measurements of the same tree, but could not obtain model convergence in most cases, partly because of the small proportion of trees with repeated measurements. Consequently, we only included the plot random effect in the Glimmix procedure, and applied the same method of model selection as for the SQ models. Model validation For both SQ and SQE equations, we evaluated model performance using a 10-fold cross-validation procedure (Efron and Gong 1983). For this purpose, each plot was randomly assigned to one of 10 groups. We withdrew groups one at a time from the calibration dataset and used the results to evaluate the withdrawn group. We computed mean bias for all SQ and SQE equations by calculating the difference between the sum of the observations of a given quality class and the sum of the predictions for this given quality class, and then dividing the difference by the number of observations (Equation 3). This bias statistic provides indications of model accuracy when used to predict SQ and SQE with an independent dataset. bk=∑yijk−∑ŷijkn (3) where bk is the estimated mean bias for quality class k, y is a binary variable that takes the value of 1 when the observed quality class of the tree is equal to k and of 0 when the observed quality class is different from k, ŷ is the predicted probability that a tree take the value k, n is the number of trees that are used to evaluate the equation; and the subscripts represent tree i in plot j . We assessed the predictive ability of the models by computing the rank correlation (Hosmer and Lemeshow, 2000) of observed responses and the predicted probabilities from the cross-validation results (Equation 4). This statistic is obtained by comparing all pairs of trees with different observed responses. If the tree from the pair with a better quality class has a higher predicted probability, the pair is considered concordant. Conversely, if the tree with a lower quality class has a higher predicted probability, the pair is classified as discordant. c=(nc+0.5(n−nc−nd))/n (4) where c is the rank correlation, nc is the number of concordant pairs, nd is the number of discordant pairs and n is the number of paired observations. We calculated standardized values of the parameters for each equation (Equation 5), to facilitate comparison of the parameters on the same scale when examining their influence on predictions of the outcome variables (Thompson, 2009). βis=3πβisi (5) where βis and βi are respectively the standardized and unstandardized coefficients of the ith explanatory variable model, and si is the standard deviation of the ith explanatory variable. Results Parameter estimates and explanatory variables varied among species and modelling groups (Appendix A: Tables A3 and A4), but a common pattern was found among species for SQ equations. Based on standardized values of the parameter estimates, HP, alone or in interaction with d.b.h., was the most important predictor for all models across species (Table A3). The importance of HP as a predictor of SQ can be clearly seen for sugar maple in Figure 2. For all equations, the increase in HP (i.e. from M to R), is associated with an increasing probability of observing high stem quality (Figure 2, Table A3). Two other important variables are stem d.b.h. and stand basal area, which were also included in most SQ equations. Stand basal area was also positively related to stem quality. Among the equations that included d.b.h., some parameters had an interaction with HP. In group I for sugar and red maple and in group III for other hardwood species, an increase in d.b.h. was associated with a decrease in quality class. The same pattern was observed in group III for poplars and white birch with harvest priority M, and in group III for red maple and in group I for white birch with harvest priorities M and S (Table A3). For the other equations, d.b.h. was positively associated with stem quality. Among the ecological and climatic variables, bioclimatic subdomain was the most frequent predictor of SQ, and was included in the majority of the equations. For most of the species where subdomain was used as a predictor, an increase in latitude of the subdomain was associated with a decrease of stem quality. However, for some combinations of species and modelling groups we found no latitudinal or longitudinal trend (group II for beech, paper birch or yellow birch, group III for sugar maple), or even a positive latitudinal trend (group I and II for other hardwood species). Figure 2 View largeDownload slide Example of predicted SQ for sugar maple as a function of modelling group, harvest priority class (shown in panel titles, M: moribund trees; S: defective but surviving trees, C: growing trees with minor defects, R: reserve stock trees) and stem d.b.h., in bioclimatic subdomain 3 west and stand with a basal area of 26 m2 ha−1. Figure 2 View largeDownload slide Example of predicted SQ for sugar maple as a function of modelling group, harvest priority class (shown in panel titles, M: moribund trees; S: defective but surviving trees, C: growing trees with minor defects, R: reserve stock trees) and stem d.b.h., in bioclimatic subdomain 3 west and stand with a basal area of 26 m2 ha−1. Just as SQ was strongly linked to tree HP, SQE was strongly linked to initial stem quality (e.g. Figures 3–5 for sugar maple). According to the standardized parameter estimates (Table A4), initial stem quality had the greatest influence on SQE. For each species and modelling group, initial quality tended to remain either unchanged or moved to the adjacent (i.e. higher or lower) class. Among the other variables that were used to predict SQE, Δd.b.h. was most frequently included in the final models, and showed a positive relationship with stem quality. Stem d.b.h. was often used to predict SQE in modelling group I, and was always negatively associated with stem quality (Figure 3). The ‘Transition’ variable was positively related to stem quality in five equations (Table A4), mostly in modelling group II. Bioclimatic subdomains were used less frequently to predict SQE compared with SQ. Mean annual temperature and total annual precipitation had a positive effect on SQE for six and five of the models, respectively. Figure 3 View largeDownload slide Example of predicted SQE for sugar maple group I as a function of initial stem quality class (shown in panel titles) and stem d.b.h. for a 10-years period between two measurements (t). For this example, mean annual temperature was fixed at 3.6 ˚C and d.b.h. increment (Δd.b.h.) at 0.24 cm yr−1. Figure 3 View largeDownload slide Example of predicted SQE for sugar maple group I as a function of initial stem quality class (shown in panel titles) and stem d.b.h. for a 10-years period between two measurements (t). For this example, mean annual temperature was fixed at 3.6 ˚C and d.b.h. increment (Δd.b.h.) at 0.24 cm yr−1. Figure 4 View largeDownload slide Example of predicted SQE for sugar maple group II as a function of initial stem quality class (shown in panel titles) and d.b.h. increment (Δd.b.h. for a 10-years period between two measurements (t)). The parameters representing the occurrence of partial harvest and the transition between two modelling groups during the growth period were fixed at 0 (absence of effect). Figure 4 View largeDownload slide Example of predicted SQE for sugar maple group II as a function of initial stem quality class (shown in panel titles) and d.b.h. increment (Δd.b.h. for a 10-years period between two measurements (t)). The parameters representing the occurrence of partial harvest and the transition between two modelling groups during the growth period were fixed at 0 (absence of effect). Figure 5 View largeDownload slide Example of predicted SQE for sugar maple group III as a function of initial stem quality class (shown in panel titles) and annual stem d.b.h. increment. For this example, d.b.h. was fixed at 24 cm, annual mean precipitations at 1100 mm and stand basal area at 26 m2 ha−1 for a 10-year period between two measurements (t). Figure 5 View largeDownload slide Example of predicted SQE for sugar maple group III as a function of initial stem quality class (shown in panel titles) and annual stem d.b.h. increment. For this example, d.b.h. was fixed at 24 cm, annual mean precipitations at 1100 mm and stand basal area at 26 m2 ha−1 for a 10-year period between two measurements (t). Cross-validation of SQ equations yielded reasonably unbiased results for all models (Table 4). In most instances, mean bias was less than 1 per cent. ‘Other hardwoods’ exhibited greater bias for the SQE equations (up to 3.7 per cent for quality class C in modelling group I) than for the SQ equations. Table 4 Mean bias and rank correlation from cross-validation for SQ and SQE equations Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Table 4 Mean bias and rank correlation from cross-validation for SQ and SQE equations Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Across models, rank correlations for SQ and SQE equations generally ranged from 0.7 to 0.8 (Table 4). For SQ, the only rank correlations lower than 0.7 were those of modelling groups I and II for paper birch and beech and the rank correlation of group I for poplars. For SQE equations, rank correlations were consistently >0.70, except for group III of other hardwood species. Discussion The results of this study confirm that forest survey variables can be used to reasonably accurately predict initial and projected stem quality. Cross-validation of SQ models showed that bias was minimal and that the models could adequately distinguish trees of different quality classes. With rank correlations generally ranging from 0.7 to 0.8, the capacity of models to differentiate tree outcome categories can be considered acceptable (Hosmer and Lemeshow, 2000). Among the variables that were used to predict SQ, HP explained the largest amount of variation. Likewise, SQE models showed minimal bias and even better rank correlation results, when evaluated by cross-validation. Not surprisingly, initial stem quality was the main predictor for these models and all species. Influence of tree and stand variables The strong relationship between SQ and HP can be explained by the fact that both are negatively affected by the same stem defects (Boulet, 2007). Consequently, SQ equations predicted an increase in stem quality as the probability of survival increased (i.e. from HP class M to class R). This is supported by the study of Drouin et al. (2010) who found that paper birch merchantable value was lower for low-vigour trees, i.e. those with lower survival probability according to the HP classification. In our study, stem d.b.h. was used in most SQ equations. Other studies also found a relationship between stem d.b.h. and stem quality (e.g. Belli et al., 1993; Prestemon, 1998), but they did not take into account the specific d.b.h. thresholds for quality classes that were tested. Consequently, the d.b.h. effect on stem quality was necessarily stronger in these studies to account for the dependency of stem quality classes on d.b.h.. Our results show that even within specific modelling groups, an increase in d.b.h. is generally associated with an increase in stem quality, except for the less vigorous trees (HP classes M and S). The presence of defects that threaten the survival of these trees also reduced their stem quality. Stand basal area was also positively associated with SQ for most species, which is consistent with other studies (e.g. Lyon and Reed, 1988; Prestemon, 1998; Pothier et al., 2013). The positive effect of stand basal area on SQ could be explained, in part, by an increase in inter-tree competition that possibly limits branch thickness (Mäkinen et al., 2003) and stimulates self-pruning (Prestemon, 1998), which favours the production of defect-free boles. However, we did not specifically consider the structural heterogeneity of stands, which may also affect wood quality (Pretzsch and Rais, 2016). In addition, many SQ equations included bioclimatic subdomain. The effect of this variable on SQ predictions (Table A3) was limited, but could reflect regional variations in stem quality. The effect of HP in each SQ equation could contribute to a reduction in the effect of bioclimatic subdomain on stem quality, and explain the relatively low influence of this variable on stem quality, according to the standardized coefficients (Appendix A). However, the inclusion of bioclimatic subdomain as a predictor could help ensure that regional predictions are not biased. As expected, initial stem quality was the best predictor of future stem quality in SQE equations. Over a 10-year period, sugar maple stem quality tended to remain constant or to change to an adjacent quality class, either better or worse (Figures 3–5). This finding was consistent with observations made by Lyon and Reed (1988) over a 5-year period. Thus, model predictions suggest that tree grade transition is a slow process, and that drastic changes are unlikely to occur over a 10-year timespan. As the risks of stem injury and of the appearance of defects increase with age, a longer time interval could increase the probability of detecting a decrease in quality class. The growth rate of d.b.h. was positively related to SQE for many species and modelling groups. Fast growing trees are generally vigorous (Hartmann et al., 2008) and free of major defects that could reduce stem quality. Rapid growth can also help to hide visual defects such as dead branch scars (Vasiliauskas, 2001). Since bioclimatic subdomain is correlated with d.b.h. increament, the effect of Δd.b.h., mean annual temperature and total annual precipitation in many SQE equations could also explain the rare inclusion of bioclimatic subdomain in SQE models, even though hardwood stem quality is known to vary at the regional scale (Hassegawa et al., 2015). Application of the equations To our knowledge, this study is one of the first to simulate hardwood stem quality with multinomial models, although the modelling approach described in this paper has been applied previously to predict lumber grades for some softwood species (Lyhykäinen et al., 2009; Hautamäki et al., 2010). The multinomial approach was chosen because it fully describes the changes among classes with no information loss, and therefore represents potential stem quality more accurately. This approach also allows direct links with the observed variable (Allison, 2012). Modelling stem quality without considering the inherent d.b.h. ranges that are associated with tree grades (Lyon and Reed, 1988; Belli et al., 1993) could result in inconsistent predictions (e.g. tree grade A predicted for a stem d.b.h. of 26 cm). Modelling of tree grades within specific d.b.h. ranges provided predictions that accurately reflected the current quality classification system (MFFP, 2014). The precision of the equations, as expressed by rank correlations, suggests that a substantial portion of variability was not accounted for by the model, as is often observed in stem quality models (e.g. Pothier et al., 2013). However, the small biases suggest that over a relatively large population, the proportion of stems in each quality class and their changes over time can be predicted accurately. Given the large area covered by the databases used to parameterize them, the SQ and SQE equations should be applied over large territories (e.g. a management unit of several thousand square kilometres) or groups of interest (e.g. species). As the number of trees used in predictions increases, the uncertainty around the proportion of trees in each quality class should decrease. Consequently, the equations should be used carefully for predictions on a small number of individuals (see also Yaussy, 1993). These equations can be implemented in forest growth simulators such as Artemis (Fortin and Langevin, 2010), a tree–level growth simulator used to estimate annual allowable cuts on public forest lands in the province of Quebec. The application of wood quality models is challenging, given that standing tree assessment and stem quality-related parameters vary between different studies and countries (Bosela et al., 2015; Defo et al., 2015). The application of the SQ models requires tree HP classification data (Boulet, 2007) in addition to usual inventory data. This additional requirement could be a factor limiting the use of SQ equations, particularly where this classification is not available (McRoberts et al., 2012). For SQ models to be more generalizable (Mäkelä et al., 2010) and useful in other areas, they need to be calibrated with additional data or with different classification systems of harvest priority or tree vigour. Predictions from SQ equations can be used as input data for SQE equations when current stem quality is missing. In this case, one should expect predictions from SQE equations to be less precise because of error propagation (Mowrer and Frayer, 1986). Future tree grade model uncertainties could also be increased over periods of simulation by the use of predicted variables, such as tree d.b.h., in SQE equations and by a lack of independence of predictors between models. However, given that trees were sorted by d.b.h. threshold (i.e. modelling groups) and constrained to a specific range, the risk of large cumulative errors in SQE models is relatively limited (Houllier et al., 1995). Preferably, SQE equations should be used with stem quality data obtained from forest surveys, whenever this information is available (Bosela et al., 2015). The major limitation of SQE models was the small size of datasets for some less-represented species that had to be grouped. The small number of observations implies that these equations may not entirely capture the effect of growing conditions that affect stem quality or the regional patterns of stem quality. Consequently, they may be less reliable than other equations that are based on a larger sample. Management implications Results from SQE models provide useful insights for forest management, by defining the optimal d.b.h. for tree harvest, that maximizes stem quality and optimizes stand structure (Majcen et al., 1990; Leak et al., 2014). The influence of d.b.h. on SQE followed a negative trend for the larger trees of most species (modelling group I). This result is consistent with the work of Pothier et al. (2013) and Havreljuk et al. (2014), who noted a reduction in hardwood stem quality for the 40–70 cm d.b.h. range. Large trees are usually older and may have accumulated defects over their lifespan (Havreljuk et al., 2013). Identifying trees that would likely decrease in quality and value over time may also improve marking decisions. This is particularly important in uneven-aged stands of the North American temperate deciduous forest, where a selection cutting (i.e. periodical removal of stems that are expected to degrade or die before the next harvesting cycle) silvicultural system is applied (Arbogast, 1957; Nyland, 1998). In the Great Lakes region of North America, Webster et al. (2009) found no advantage in retaining sugar maple stems that were likely to degrade before the next cutting cycle, since a reduction in tree grades was associated with lower future financial returns. Buongiorno and Hseu (1993) obtained similar results for maple–birch stands in Wisconsin, USA. Although tree grade evolution could guide silvicultural decisions, an efficient management strategy should also consider price trends that are associated with tree quality, in order to ensure that net risks of stem retention provide satisfactory additional net stem value. Conclusion The equations that were developed in this study allow stem quality and its evolution over time to be predicted with reasonable accuracy for the commercially important hardwoods of Eastern Canada. Such tools are important to support sustainable forest management, since the use of hardwood trees for appearance wood products largely depends on their quality. Our findings suggest that hardwood quality can be modelled with tree-level variables, and, to a lesser extent, with stand- and regional-level variables. Thus, stem quality is closely related to tree vigour, assessed by the harvest priority classification, while its variation over time mainly depends on tree growth. In order to improve knowledge of the wood resources in a given territory and to improve forest management and silvicultural decisions that take into account hardwood stem quality, further work will focus on product recovery based on tree stem quality. Supplementary data Supplementary data are available at Forestry Online. Acknowledgements The authors would like to thank Isabelle Auger, Steve Bédard, Josianne DeBlois, François Guillemette and Denise Tousignant (Direction de la recherche forestière, Ministère des Forêts, de la Faune et des Parcs du Québec) for helpful advice and revision of previous versions of the manuscript, Dr. William F. J. Parsons for reviewing the latest version of the manuscript and Carl Bergeron (Direction des inventaires forestiers, Ministère des Forêts, de la Faune et des Parcs du Québec) for providing data for this study. We also thank the Associate Editor and two anonymous reviewers for their helpful comments on a previous version of the manuscript. Conflict of interest statement None declared Funding Ministère des Forêts, de la Faune et des Parcs, Gouvernement du Québec (project number 1420564-142332123). References Akaike , H. 1974 A new look at the statistical model identification . IEEE Trans. Autom. 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Google Scholar CrossRef Search ADS Yaussy , D.A. 1993 Method for Estimating Potential Tree-grade Distributions for Northeastern Forest Species . USDA, Forest Service, Northeastern Forest Experiment Station, Radnor, PA. Res. Pap. NE-670, 12 pp . © Institute of Chartered Foresters, 2016. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forestry: An International Journal Of Forest Research Oxford University Press

Predicting hardwood quality and its evolution over time in Quebec's forests

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Institute of Chartered Foresters
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Abstract

Abstract Long-term success of forest management requires knowledge of standing tree characteristics and, an estimation of their evolution over time. In this study, hardwood stem quality was assessed using a specifically designed, non-destructive quality classification system that comprises four categorical output classes based on stem size and occurrence of external defects. We used data from national forest inventory sample plots distributed across Quebec (Canada) to predict hardwood stem quality and its evolution over time. We used ordinal logistic regression to model multiple stem quality classes. Hardwood stem quality was strongly related to stem harvest priority class and bioclimatic subdomain. Stem quality generally improved with d.b.h. and stand basal area. Changes in hardwood stem quality were strongly related to initial stem quality, with most trees retaining their initial quality over time. Stem quality evolution was also positively related to diameter growth. Overall, both initial and future stem quality were estimated with acceptable precision and minimal bias. Our results suggest that the equations could predict hardwood stem quality distribution and evolution among groups of forest stands. Introduction The long-term success of forest management requires appropriate knowledge of the characteristics of standing trees. Considering that quality and market value of North American hardwoods are related to the visual characteristics of the assortment of their various manufactured products, it is important to identify less vigorous stems which are expected to die or deteriorate before the next harvesting cycle, and to determine their potential uses for appearance wood products. In temperate deciduous forests of eastern North America, hardwood stem quality is generally assessed through a specifically designed quality classification system that uses a categorical output variable with two to four levels, each of which is related to a specific stem diameter threshold (Hanks, 1976; MFFP, 2014). The number of classes that are used in stem quality classification also varies among European countries (Bosela et al., 2015). Also, some classification systems consider tree vigour and quality simultaneously (e.g. Majcen et al., 1990; OMNR, 2004). Many defects located along the entire stem may affect both tree vigour and quality. However, most stem quality classification systems focus on the lower portion of the tree for the visual assessment of the presence, size and distribution of defects that might affect stem conversion into logs (Rast et al., 1973; Petro and Calvert, 1976) and lumber (NHLA, 2011). Stem quality classification has proven to be a good predictor of log grade occurrence and volume distribution (Fortin et al., 2009b) as well as value of standing trees (Cockwell and Caspersen, 2014; Havreljuk et al., 2014). Therefore, quality evaluation could improve marking decisions when selecting trees for either retention or harvest in hardwood stands (Webster et al., 2009; Fortin et al., 2009b; Pothier et al., 2013). Despite the usefulness of grading systems, exhaustive tree quality measurements are too costly to be systematically included in forest surveys. Consequently, some studies have used tree- and stand-level variables to predict tree grades, particularly for sugar maple (Acer saccharum Marsh.) (Lyon and Reed 1988; Webster et al., 2009), southern Appalachian species (Prestemon 1998), or European species (Sterba et al., 2006). Tree diameter is an important indicator of tree quality because it is related to its conversion to wood products. Several studies have shown a decrease in stem quality beyond a certain diameter threshold (e.g. Hansen and Nyland, 1987; Majcen et al., 1990; Prestemon, 1998; Pothier et al., 2013), which suggests a non-monotonic relationship between tree diameter and stem quality. Better predictions of standing tree value could be achieved when tree diameter is paired with the occurrence of certain specific tree defects (Bosela et al., 2015; Cecil-Cockwell and Caspersen, 2015). At the stand level, factors such as stand basal area (Belli et al., 1993; Mäkinen et al., 2003), site quality (Prestemon, 1998) and cutting methods (Erickson et al., 1990) were found to be related to tree quality. Yet, the effects of these variables on future tree quality still need to be addressed for northeastern hardwoods. To our knowledge, only a few studies have focused on dynamic models that project hardwood quality over time. Lyon and Reed (1988) developed linear discriminant functions to predict future tree grades from initial stem quality of sugar maple. However, their models included initial tree grade as a continuous variable, while in reality it is categorical. Lyon and Reed (1988) also assumed that the relationships in the study followed a linear trend, and did not establish thresholds that related stem diameter and grade. For their part, Fortin et al. (2009a), in order to predict future tree quality of hardwood species, considered it as a binary variable (i.e. presence/absence of sawlog potential) that was derived from a hybrid risk–product classification (Majcen et al., 1990). Model development of quality evolution over time requires long-term monitoring data. Longitudinal measurements of tree grades are necessary to fully evaluate the natural dynamics of stem quality (Pothier et al., 2013) but are generally limited by the lack of long-term field studies. From a statistical viewpoint, tree grade modelling is challenging, because the categorical nature of the response variable requires complex statistical approaches such as multinomial regressions (Agresti, 2013). Models using multinomial regressions have already been used to predict lumber product assortment for Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies [L.] Karst.) (Lyhykäinen et al., 2009; Hautamäki et al., 2010). Temporal structure must also be considered when projecting quality over time, in order to account for correlations that are induced by repeated measurements (Fox et al., 2001). The assessment of stem quality and its dynamics over time could (1) ensure more efficient allocation of the wood fibre supply, and (2) improve silvicultural strategies to meet management goals. Consequently, this study pursued three distinct objectives. First, we developed equations to predict stem quality of hardwood tree species in Quebec (Canada), based on the usual forest inventory variables. These equations could be used when stem quality is not measured directly. Second, we developed equations to estimate future stem quality. Third, we determined the main dendrometric and ecological variables that relate to stem quality and its evolution over time. These results will provide methods to estimate stem quality and it change over time, as a first step toward integrating these variables in forest growth simulators. Methods Stem quality Quebec's stem quality classification system aims to reflect lumber grade and volume recovery of hardwood trees (MFFP, 2014). The classification system has been consistent since its implementation in the 1985 provincial forest inventory. It was inspired by the USDA tree grading system (Hanks, 1976), and takes into account tree d.b.h. (diameter of the stem measured 1.3 m above ground level) and the presence of defects on the lowermost 5 m of the stem. Evaluation is based on visual assessment of defects that limit the clear wood (i.e. defect-free) length on the stem (e.g. branching, knots, bulges or other bark-covered defects), and those that reduce stem volume (e.g. cull, rot and sweep). Four grades are identified with letters A to D, in decreasing order of quality. Specific minimal d.b.h. thresholds of >39.0, >33.0 and >23.0 cm are required to achieve quality classes A, B, C or D, respectively. Trees with d.b.h. ≤ 23.0 cm are excluded from stem quality assessments since their d.b.h. is considered too small to produce logs that meet the minimum size requirements of standard sawlogs for factory lumber (Hanks et al., 1980). Although potential product recovery from small-diameter hardwoods could be improved with modern sawing techniques (Hamner et al., 2006; Nicholls and Bumgardner, 2015), most traditional hardwood mills in North America are adapted to process larger logs with sawing patterns that are designed to maximize grade recovery (Shmulsky and Jones, 2011). Sample datasets We used two distinct datasets from the provincial forest inventory of Quebec to predict stem quality (SQ) and stem quality evolution (SQE; i.e. change in stem quality over time) of hardwood tree species: (1) temporary sample plots (TSPs) and (2) permanent sample plots (PSPs). While the TSP dataset consists of a single measurement from each plot (measured between 2005 and 2012), the PSPs were established from 1975 to the 2000s and were monitored with repeated measurements at an average interval of 10 years. Hardwood species that were considered in this study are listed in Table 1. Plots of both datasets are well distributed over a 761 000-km2 forested area (Table 2), from the northern limit of the commercial forest to the southern border of the province (MFFP, 2015). Table 1 List of species included in each group Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Table 1 List of species included in each group Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Group Species Beech American beech (Fagus grandifolia Ehrh.) Oaks Bur oak (Quercus macrocarpa Michx.), northern red oak (Quercus rubra L.), swamp white oak (Quercus bicolor Wild.), white oak (Quercus alba L.) Paper birch Paper birch (Betula papyrifera Marsh.) Poplar Balsam poplar (Populus balsamifera L.), large-toothed aspen (Populus grandidentata Michx.), eastern cottonwood (Populus deltoides W. Bartram ex Marsh.), trembling aspen (Populus tremuloides Michx.) Red maple Red maple (Acer rubrum L.), silver maple (Acer saccharinum L.) Sugar maple Sugar maple (Acer saccharum Marsh.) Yellow birch Yellow birch (Betula alleghaniensis Britt.) Other hardwoods White elm (Ulmus americana L.), basswood (Tilia americana L.), bitternut hickory (Carya cordiformis [Wang.] K. Koch.), black ash (Fraxinus nigra Marsh.), black cherry (Prunus serotina Ehrh.), butternut (Juglans cinerea L.), eastern hop-hornbeam (Ostrya virginiana [Mill.] K. Koch.), red ash (Fraxinus pennsylvanica Marsh.), rock elm (Ulmus thomasii Sarg.), slippery elm (Ulmus rubra Mühl.), white ash (Fraxinus americana L.) Table 2 Number of observations by species and modelling groups for SQ and SQE Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) For the SQE model, the value in parentheses represents the number of individual trees that were included for the observed periods. Note: N/A is not applicable. Table 2 Number of observations by species and modelling groups for SQ and SQE Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) Species group SQ SQE Group I Group II Group III Group I Group II Group III Beech 1633 2333 5577 251 (196) 290 (259) 544 (439) Oaks 1489 1839 4470 N/A N/A 394 (355) Paper birch 3397 6923 37 424 245 (210) 522 (450) 2975 (2535) Poplars 2389 2706 6584 557 (479) 899 (822) 2301 (2036) Red maple 2893 5298 24 096 305 (243) 525(456) 1721 (1435) Sugar maple 11 993 13 261 34 038 1647 (1191) 1352 (1106) 3690 (2846) Yellow birch 16 886 12 633 24 463 1168 (906) 849 (733) 1667 (1369) Other hardwoods 1210 1649 4676 160 (130) 314 (289) 524 (461) For the SQE model, the value in parentheses represents the number of individual trees that were included for the observed periods. Note: N/A is not applicable. Because the stem quality classification system is strongly related to d.b.h., we separated the data into three modelling groups, based on the highest quality class that a tree could achieve at a given d.b.h. (Table 2): modelling group I (>39.0 cm), modelling group II (33.1–39.0 cm) and modelling group III (23.1–33.0 cm). Statistical analysis Prediction of stem quality and stem quality evolution Preliminary data analysis, using descriptive statistics and correspondence analysis to investigate the association between species and actual and future stem quality, showed differences in stem quality distribution among species. Consequently, we developed separate models for SQ and SQE for each species. Some less abundant hardwood species were grouped, mostly by genus (Tables 1 and 2). One SQ and one SQE model were developed for each combination of species and modelling group. Stem quality of a tree from modelling group III can be considered as a binary variable, since its value is either grade C or grade D. We can assume that this variable follows a Bernoulli distribution with a probability π of being equal to C. We used a logit transformation to obtain predicted probabilities that were bounded by 0 and 1, and to linearize the relationship between the response and explanatory variables (Equation 1). For modelling groups I and II, we assumed that quality followed an ordinal multinomial distribution with a probability πk of being equal to quality grade k. A cumulative logit transformation was applied to equations of modelling groups I and II (Equation 2). g1(xij)=ln(π(xij)1−π(xij))=α+xijβ (1) g2(xij)=ln(πk(xij)1−πk−1(xij))=αk+xijβ (2) where g1 and g2 are the link functions, π is the probability of observing a given response value, α is the intercept, x is a vector of predictors, and β is a vector of parameters. The subscripts indicate the quality class k of tree i in plot j. The ordinal multinomial model (Equation 2) is a proportional odds model that assumes parameter vector β is constant among categories. For each predictor, we verified the assumption that the proportions followed an ordinal distribution by visually checking the parallelism among the slopes across different quality classes, for all continuous predictors of modelling groups I and II (Allison, 2012; Derr, 2013). In cases where this hypothesis was rejected, we added an interaction term between the predictor and the intercepts to fit the partial proportional odds model. This model was specified in the same manner as the proportional odds model with the Logistic procedure in the SAS statistical software (ver. 9.4, SAS Institute Inc., Cary, NC, USA), except that the ‘unequalslopes’ option was added for specific effects that did not satisfy the proportional odds assumption. This addition allowed parameters for each predictor in each response function to be estimated separately (Derr, 2013). Model development Prior to the analyses, we considered several types of variables as predictors of both SQ and SQE. Tree-level variables, such as d.b.h. (cm), d.b.h. increment (Δd.b.h., cm yr−1), harvest priority (HP) classification (Boulet 2007) and stem quality were included to represent initial tree characteristics. In both TSPs and PSPs, species and d.b.h. were recorded for every tree larger than 9.0 cm in d.b.h. within 400 m2 circular plots. Annual d.b.h. increments were computed from two consecutive PSP measurements, by subtracting the first d.b.h. measurement from the second then dividing the difference by the time interval between the two measurements (t, years). Tree vigour that was based on HP was recorded from a visual assessment of external defects and pathological symptoms along the stem (Hartmann et al., 2008). This system, which has been used since 2005 in Quebec's forest surveys, ranks trees based on their expected probability of surviving to the next scheduled cutting cycle (estimated at 20–25 years in the temperate forest zone of southern Quebec, Canada; Boulet, 2007). Trees are ranked according to four classes (M, S, C and R): (1) moribund trees (M), with the lowest survival probability; (2) defective, but surviving trees (S); (3) growing trees with minor defects (C); and reserve stock trees (R), with the highest survival probability. We expected that a tree changing modelling groups between two consecutive measurements because of an increase in d.b.h. would also have a greater probability of changing quality class, as it might also meet the minimal d.b.h. criteria of a better quality class. Consequently, we created a binary variable (Transition) to identify trees that had changed modelling groups between two measurements. Stand characteristics were described by stand basal area (G, m2 ha−1) and the occurrence of partial harvesting (Harvest) between two consecutive measurements. Stand basal area was derived from d.b.h. measurements of all trees with a d.b.h. >9.0 cm in the plot. We also considered ecological and climatic variables by including the bioclimatic subdomain in the models, together with mean annual temperature and total annual precipitation. Bioclimatic domains, which are based upon Quebec's ecological classification (MRN, 2013; Figure 1), refer to parts of the territory that, theoretically, support a similar type of vegetation (on mesic sites) at the end of the succession process. Mean annual temperature (˚C) and mean total precipitation (mm) for the 1980–2009 period were estimated with the BIOSIM climatic interpolation software (Régnière and St-Amant, 2007). Table 3 lists the explanatory variables that were used in the modelling process. Table 3 List of explanatory variables that were considered as predictors of SQ and SQE Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Table 3 List of explanatory variables that were considered as predictors of SQ and SQE Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Explanatory variables SQ SQE Bioclimatic subdomain x x Diameter at breast height (d.b.h., cm) x x d.b.h. increment (Δd.b.h., cm yr−1) x Stem quality (SQ) x Occurrence of partial harvest (Harvest) x x Stand basal area (G, m2 ha−1) x x Time between two measurements (t, years) x Mean annual temperature (Temp., ˚C) x x Total annual precipitation (Prec., mm) x x Transition between two modelling groups during the growth period (Transition) x Harvest priority (HP) x Figure 1 View largeDownload slide Map of Quebec's bioclimatic subdomains (MRN, 2013). Figure 1 View largeDownload slide Map of Quebec's bioclimatic subdomains (MRN, 2013). We modelled SQ using measurements from 48 428 TSPs and 4 561 PSPs recorded from 2005 to 2012. Measurements prior to 2005 were excluded from the analyses because they did not include HP class. Consequently, the SQ dataset contains no repeated measurements. We first constructed a full model that included all the predictors (Table 3). For each combination of species and modelling group, a minimum threshold of 100 trees was set to consider a bioclimatic subdomain in the predictors. If this threshold was not reached, we grouped the bioclimatic subdomain with the nearest subdomain that reached the threshold. The list of bioclimatic subdomains and groups of bioclimatic subdomains (Appendix A: Tables A1 and A2) are included as supplementary material that is available online. A backward elimination procedure (Hosmer and Lemeshow, 2000), with a minimum P-value of 0.05 beginning with the full model, was used to select the variables that would be included in a reduced model. We also tested simple interactions between variables of the reduced model, and only retained those that were significant at a P-value of 0.05 or below. In order to make them useful and flexible, we attempted to parameterize the SQ equations without including tree harvest priority as a predictor. However, the value of the Akaike information criterion (AIC, Akaike, 1974) was considerably higher and precision was lower for models without HP. We therefore included this variable in the model fitting process. A plot level random effect was included in the reduced model to take into account the correlation between trees from the same plot and to avoid including non-significant fixed effects because of an underestimation of their standard error (Weiskittel et al., 2011). The random effect was added at the end of the model selection process to avoid problems of convergence that arise with larger models. We parameterized the model with the SAS Glimmix procedure, using the Laplace approximation method. When the inclusion of the random effect resulted in a lack of significance (P-value >0.05) of any of the fixed effects, we removed this fixed effect from the reduced model. Final model parameters were re-estimated with the Logistic procedure (i.e. without the plot random effect) to obtain non-biased population-level estimates of the coefficients, given that non-linear mixed models tend to be biased when they are applied at the population level (Meng et al., 2009; Groom et al., 2012; Fortin, 2013). Repeated stem quality measurements were needed to model SQE. Therefore, only data from 5 248 PSPs were used (Table 2). Growth intervals that were used to model SQE started between 1985 and 2007 and ended between 1989 and 2012. Seventeen per cent of SQE measurements consisted of repeated growth intervals from the same tree. We tried to include random effects to account for correlations between different measurements of the same tree, but could not obtain model convergence in most cases, partly because of the small proportion of trees with repeated measurements. Consequently, we only included the plot random effect in the Glimmix procedure, and applied the same method of model selection as for the SQ models. Model validation For both SQ and SQE equations, we evaluated model performance using a 10-fold cross-validation procedure (Efron and Gong 1983). For this purpose, each plot was randomly assigned to one of 10 groups. We withdrew groups one at a time from the calibration dataset and used the results to evaluate the withdrawn group. We computed mean bias for all SQ and SQE equations by calculating the difference between the sum of the observations of a given quality class and the sum of the predictions for this given quality class, and then dividing the difference by the number of observations (Equation 3). This bias statistic provides indications of model accuracy when used to predict SQ and SQE with an independent dataset. bk=∑yijk−∑ŷijkn (3) where bk is the estimated mean bias for quality class k, y is a binary variable that takes the value of 1 when the observed quality class of the tree is equal to k and of 0 when the observed quality class is different from k, ŷ is the predicted probability that a tree take the value k, n is the number of trees that are used to evaluate the equation; and the subscripts represent tree i in plot j . We assessed the predictive ability of the models by computing the rank correlation (Hosmer and Lemeshow, 2000) of observed responses and the predicted probabilities from the cross-validation results (Equation 4). This statistic is obtained by comparing all pairs of trees with different observed responses. If the tree from the pair with a better quality class has a higher predicted probability, the pair is considered concordant. Conversely, if the tree with a lower quality class has a higher predicted probability, the pair is classified as discordant. c=(nc+0.5(n−nc−nd))/n (4) where c is the rank correlation, nc is the number of concordant pairs, nd is the number of discordant pairs and n is the number of paired observations. We calculated standardized values of the parameters for each equation (Equation 5), to facilitate comparison of the parameters on the same scale when examining their influence on predictions of the outcome variables (Thompson, 2009). βis=3πβisi (5) where βis and βi are respectively the standardized and unstandardized coefficients of the ith explanatory variable model, and si is the standard deviation of the ith explanatory variable. Results Parameter estimates and explanatory variables varied among species and modelling groups (Appendix A: Tables A3 and A4), but a common pattern was found among species for SQ equations. Based on standardized values of the parameter estimates, HP, alone or in interaction with d.b.h., was the most important predictor for all models across species (Table A3). The importance of HP as a predictor of SQ can be clearly seen for sugar maple in Figure 2. For all equations, the increase in HP (i.e. from M to R), is associated with an increasing probability of observing high stem quality (Figure 2, Table A3). Two other important variables are stem d.b.h. and stand basal area, which were also included in most SQ equations. Stand basal area was also positively related to stem quality. Among the equations that included d.b.h., some parameters had an interaction with HP. In group I for sugar and red maple and in group III for other hardwood species, an increase in d.b.h. was associated with a decrease in quality class. The same pattern was observed in group III for poplars and white birch with harvest priority M, and in group III for red maple and in group I for white birch with harvest priorities M and S (Table A3). For the other equations, d.b.h. was positively associated with stem quality. Among the ecological and climatic variables, bioclimatic subdomain was the most frequent predictor of SQ, and was included in the majority of the equations. For most of the species where subdomain was used as a predictor, an increase in latitude of the subdomain was associated with a decrease of stem quality. However, for some combinations of species and modelling groups we found no latitudinal or longitudinal trend (group II for beech, paper birch or yellow birch, group III for sugar maple), or even a positive latitudinal trend (group I and II for other hardwood species). Figure 2 View largeDownload slide Example of predicted SQ for sugar maple as a function of modelling group, harvest priority class (shown in panel titles, M: moribund trees; S: defective but surviving trees, C: growing trees with minor defects, R: reserve stock trees) and stem d.b.h., in bioclimatic subdomain 3 west and stand with a basal area of 26 m2 ha−1. Figure 2 View largeDownload slide Example of predicted SQ for sugar maple as a function of modelling group, harvest priority class (shown in panel titles, M: moribund trees; S: defective but surviving trees, C: growing trees with minor defects, R: reserve stock trees) and stem d.b.h., in bioclimatic subdomain 3 west and stand with a basal area of 26 m2 ha−1. Just as SQ was strongly linked to tree HP, SQE was strongly linked to initial stem quality (e.g. Figures 3–5 for sugar maple). According to the standardized parameter estimates (Table A4), initial stem quality had the greatest influence on SQE. For each species and modelling group, initial quality tended to remain either unchanged or moved to the adjacent (i.e. higher or lower) class. Among the other variables that were used to predict SQE, Δd.b.h. was most frequently included in the final models, and showed a positive relationship with stem quality. Stem d.b.h. was often used to predict SQE in modelling group I, and was always negatively associated with stem quality (Figure 3). The ‘Transition’ variable was positively related to stem quality in five equations (Table A4), mostly in modelling group II. Bioclimatic subdomains were used less frequently to predict SQE compared with SQ. Mean annual temperature and total annual precipitation had a positive effect on SQE for six and five of the models, respectively. Figure 3 View largeDownload slide Example of predicted SQE for sugar maple group I as a function of initial stem quality class (shown in panel titles) and stem d.b.h. for a 10-years period between two measurements (t). For this example, mean annual temperature was fixed at 3.6 ˚C and d.b.h. increment (Δd.b.h.) at 0.24 cm yr−1. Figure 3 View largeDownload slide Example of predicted SQE for sugar maple group I as a function of initial stem quality class (shown in panel titles) and stem d.b.h. for a 10-years period between two measurements (t). For this example, mean annual temperature was fixed at 3.6 ˚C and d.b.h. increment (Δd.b.h.) at 0.24 cm yr−1. Figure 4 View largeDownload slide Example of predicted SQE for sugar maple group II as a function of initial stem quality class (shown in panel titles) and d.b.h. increment (Δd.b.h. for a 10-years period between two measurements (t)). The parameters representing the occurrence of partial harvest and the transition between two modelling groups during the growth period were fixed at 0 (absence of effect). Figure 4 View largeDownload slide Example of predicted SQE for sugar maple group II as a function of initial stem quality class (shown in panel titles) and d.b.h. increment (Δd.b.h. for a 10-years period between two measurements (t)). The parameters representing the occurrence of partial harvest and the transition between two modelling groups during the growth period were fixed at 0 (absence of effect). Figure 5 View largeDownload slide Example of predicted SQE for sugar maple group III as a function of initial stem quality class (shown in panel titles) and annual stem d.b.h. increment. For this example, d.b.h. was fixed at 24 cm, annual mean precipitations at 1100 mm and stand basal area at 26 m2 ha−1 for a 10-year period between two measurements (t). Figure 5 View largeDownload slide Example of predicted SQE for sugar maple group III as a function of initial stem quality class (shown in panel titles) and annual stem d.b.h. increment. For this example, d.b.h. was fixed at 24 cm, annual mean precipitations at 1100 mm and stand basal area at 26 m2 ha−1 for a 10-year period between two measurements (t). Cross-validation of SQ equations yielded reasonably unbiased results for all models (Table 4). In most instances, mean bias was less than 1 per cent. ‘Other hardwoods’ exhibited greater bias for the SQE equations (up to 3.7 per cent for quality class C in modelling group I) than for the SQ equations. Table 4 Mean bias and rank correlation from cross-validation for SQ and SQE equations Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Table 4 Mean bias and rank correlation from cross-validation for SQ and SQE equations Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Species group Equation Modelling group Mean bias (Equation 3) by quality class Rank correlation (Equation 4) A B C D Beech SQ I 0.0001 0.0024 0.0017 −0.0042 0.649 II N/A 0.0005 0.0002 −0.0007 0.683 III N/A N/A 0.0000 0.0000 0.704 SQE I 0.0004 −0.0013 −0.0027 0.0036 0.750 II N/A −0.0009 −0.0021 0.0029 0.768 III N/A N/A −0.0008 0.0008 0.832 Oaks SQ I 0.0095 0.0012 −0.0082 −0.0025 0.737 II N/A 0.0046 −0.0024 −0.0022 0.753 III N/A N/A 0.0000 0.0000 0.836 SQE III N/A N/A 0.0003 −0.0003 0.705 Paper birch SQ I 0.0047 0.0030 −0.0044 −0.0033 0.652 II N/A 0.0048 −0.0024 −0.0025 0.671 III N/A N/A 0.0000 0.0000 0.705 SQE I 0.0012 −0.0128 0.0089 0.0027 0.868 II N/A −0.0008 0.0006 0.0002 0.796 III N/A N/A 0.0000 0.0000 0.811 Poplar SQ I 0.0071 −0.0003 −0.0054 −0.0014 0.693 II N/A 0.0006 −0.0030 −0.0030 0.730 III N/A N/A 0.0000 0.0000 0.798 SQE I −0.0068 −0.0060 0.0120 0.0007 0.828 II N/A −0.0055 0.0028 0.0027 0.746 III N/A N/A 0.0000 0.0000 0.793 Red maple SQ I 0.0017 0.0023 −0.0012 −0.0028 0.732 II N/A 0.0031 −0.0007 −0.0025 0.721 III N/A N/A 0.0000 0.0000 0.768 SQE I −0.0056 −0.0048 0.0073 0.0031 0.800 II N/A −0.0141 0.0063 0.0079 0.793 III N/A N/A 0.0003 −0.0003 0.800 Sugar maple SQ I 0.0035 0.0037 −0.0038 −0.0035 0.746 II N/A 0.0032 −0.0016 −0.0016 0.758 III N/A N/A 0.0001 −0.0001 0.796 SQE I −0.0025 −0.0029 0.0047 0.0007 0.814 II N/A −0.0010 0.0002 0.0007 0.798 III N/A N/A 0.0001 −0.0001 0.813 Yellow birch SQ I 0.0057 0.0056 −0.0061 −0.0052 0.728 II N/A 0.0050 −0.0022 −0.0028 0.739 III N/A N/A 0.0000 0.0000 0.774 SQE I −0.0050 −0.0034 0.0076 0.0008 0.863 II N/A −0.0020 −0.0025 0.0045 0.794 III N/A N/A 0.0000 0.0000 0.846 Other hardwoods SQ I 0.0053 0.0001 −0.0039 −0.0015 0.750 II N/A 0.0029 −0.0018 −0.0012 0.734 III N/A N/A 0.0000 0.0000 0.773 SQE I 0.0111 −0.0128 0.0369 −0.0352 0.851 II N/A −0.0085 −0.0019 0.0104 0.732 III N/A N/A 0.0000 0.0000 0.696 Across models, rank correlations for SQ and SQE equations generally ranged from 0.7 to 0.8 (Table 4). For SQ, the only rank correlations lower than 0.7 were those of modelling groups I and II for paper birch and beech and the rank correlation of group I for poplars. For SQE equations, rank correlations were consistently >0.70, except for group III of other hardwood species. Discussion The results of this study confirm that forest survey variables can be used to reasonably accurately predict initial and projected stem quality. Cross-validation of SQ models showed that bias was minimal and that the models could adequately distinguish trees of different quality classes. With rank correlations generally ranging from 0.7 to 0.8, the capacity of models to differentiate tree outcome categories can be considered acceptable (Hosmer and Lemeshow, 2000). Among the variables that were used to predict SQ, HP explained the largest amount of variation. Likewise, SQE models showed minimal bias and even better rank correlation results, when evaluated by cross-validation. Not surprisingly, initial stem quality was the main predictor for these models and all species. Influence of tree and stand variables The strong relationship between SQ and HP can be explained by the fact that both are negatively affected by the same stem defects (Boulet, 2007). Consequently, SQ equations predicted an increase in stem quality as the probability of survival increased (i.e. from HP class M to class R). This is supported by the study of Drouin et al. (2010) who found that paper birch merchantable value was lower for low-vigour trees, i.e. those with lower survival probability according to the HP classification. In our study, stem d.b.h. was used in most SQ equations. Other studies also found a relationship between stem d.b.h. and stem quality (e.g. Belli et al., 1993; Prestemon, 1998), but they did not take into account the specific d.b.h. thresholds for quality classes that were tested. Consequently, the d.b.h. effect on stem quality was necessarily stronger in these studies to account for the dependency of stem quality classes on d.b.h.. Our results show that even within specific modelling groups, an increase in d.b.h. is generally associated with an increase in stem quality, except for the less vigorous trees (HP classes M and S). The presence of defects that threaten the survival of these trees also reduced their stem quality. Stand basal area was also positively associated with SQ for most species, which is consistent with other studies (e.g. Lyon and Reed, 1988; Prestemon, 1998; Pothier et al., 2013). The positive effect of stand basal area on SQ could be explained, in part, by an increase in inter-tree competition that possibly limits branch thickness (Mäkinen et al., 2003) and stimulates self-pruning (Prestemon, 1998), which favours the production of defect-free boles. However, we did not specifically consider the structural heterogeneity of stands, which may also affect wood quality (Pretzsch and Rais, 2016). In addition, many SQ equations included bioclimatic subdomain. The effect of this variable on SQ predictions (Table A3) was limited, but could reflect regional variations in stem quality. The effect of HP in each SQ equation could contribute to a reduction in the effect of bioclimatic subdomain on stem quality, and explain the relatively low influence of this variable on stem quality, according to the standardized coefficients (Appendix A). However, the inclusion of bioclimatic subdomain as a predictor could help ensure that regional predictions are not biased. As expected, initial stem quality was the best predictor of future stem quality in SQE equations. Over a 10-year period, sugar maple stem quality tended to remain constant or to change to an adjacent quality class, either better or worse (Figures 3–5). This finding was consistent with observations made by Lyon and Reed (1988) over a 5-year period. Thus, model predictions suggest that tree grade transition is a slow process, and that drastic changes are unlikely to occur over a 10-year timespan. As the risks of stem injury and of the appearance of defects increase with age, a longer time interval could increase the probability of detecting a decrease in quality class. The growth rate of d.b.h. was positively related to SQE for many species and modelling groups. Fast growing trees are generally vigorous (Hartmann et al., 2008) and free of major defects that could reduce stem quality. Rapid growth can also help to hide visual defects such as dead branch scars (Vasiliauskas, 2001). Since bioclimatic subdomain is correlated with d.b.h. increament, the effect of Δd.b.h., mean annual temperature and total annual precipitation in many SQE equations could also explain the rare inclusion of bioclimatic subdomain in SQE models, even though hardwood stem quality is known to vary at the regional scale (Hassegawa et al., 2015). Application of the equations To our knowledge, this study is one of the first to simulate hardwood stem quality with multinomial models, although the modelling approach described in this paper has been applied previously to predict lumber grades for some softwood species (Lyhykäinen et al., 2009; Hautamäki et al., 2010). The multinomial approach was chosen because it fully describes the changes among classes with no information loss, and therefore represents potential stem quality more accurately. This approach also allows direct links with the observed variable (Allison, 2012). Modelling stem quality without considering the inherent d.b.h. ranges that are associated with tree grades (Lyon and Reed, 1988; Belli et al., 1993) could result in inconsistent predictions (e.g. tree grade A predicted for a stem d.b.h. of 26 cm). Modelling of tree grades within specific d.b.h. ranges provided predictions that accurately reflected the current quality classification system (MFFP, 2014). The precision of the equations, as expressed by rank correlations, suggests that a substantial portion of variability was not accounted for by the model, as is often observed in stem quality models (e.g. Pothier et al., 2013). However, the small biases suggest that over a relatively large population, the proportion of stems in each quality class and their changes over time can be predicted accurately. Given the large area covered by the databases used to parameterize them, the SQ and SQE equations should be applied over large territories (e.g. a management unit of several thousand square kilometres) or groups of interest (e.g. species). As the number of trees used in predictions increases, the uncertainty around the proportion of trees in each quality class should decrease. Consequently, the equations should be used carefully for predictions on a small number of individuals (see also Yaussy, 1993). These equations can be implemented in forest growth simulators such as Artemis (Fortin and Langevin, 2010), a tree–level growth simulator used to estimate annual allowable cuts on public forest lands in the province of Quebec. The application of wood quality models is challenging, given that standing tree assessment and stem quality-related parameters vary between different studies and countries (Bosela et al., 2015; Defo et al., 2015). The application of the SQ models requires tree HP classification data (Boulet, 2007) in addition to usual inventory data. This additional requirement could be a factor limiting the use of SQ equations, particularly where this classification is not available (McRoberts et al., 2012). For SQ models to be more generalizable (Mäkelä et al., 2010) and useful in other areas, they need to be calibrated with additional data or with different classification systems of harvest priority or tree vigour. Predictions from SQ equations can be used as input data for SQE equations when current stem quality is missing. In this case, one should expect predictions from SQE equations to be less precise because of error propagation (Mowrer and Frayer, 1986). Future tree grade model uncertainties could also be increased over periods of simulation by the use of predicted variables, such as tree d.b.h., in SQE equations and by a lack of independence of predictors between models. However, given that trees were sorted by d.b.h. threshold (i.e. modelling groups) and constrained to a specific range, the risk of large cumulative errors in SQE models is relatively limited (Houllier et al., 1995). Preferably, SQE equations should be used with stem quality data obtained from forest surveys, whenever this information is available (Bosela et al., 2015). The major limitation of SQE models was the small size of datasets for some less-represented species that had to be grouped. The small number of observations implies that these equations may not entirely capture the effect of growing conditions that affect stem quality or the regional patterns of stem quality. Consequently, they may be less reliable than other equations that are based on a larger sample. Management implications Results from SQE models provide useful insights for forest management, by defining the optimal d.b.h. for tree harvest, that maximizes stem quality and optimizes stand structure (Majcen et al., 1990; Leak et al., 2014). The influence of d.b.h. on SQE followed a negative trend for the larger trees of most species (modelling group I). This result is consistent with the work of Pothier et al. (2013) and Havreljuk et al. (2014), who noted a reduction in hardwood stem quality for the 40–70 cm d.b.h. range. Large trees are usually older and may have accumulated defects over their lifespan (Havreljuk et al., 2013). Identifying trees that would likely decrease in quality and value over time may also improve marking decisions. This is particularly important in uneven-aged stands of the North American temperate deciduous forest, where a selection cutting (i.e. periodical removal of stems that are expected to degrade or die before the next harvesting cycle) silvicultural system is applied (Arbogast, 1957; Nyland, 1998). In the Great Lakes region of North America, Webster et al. (2009) found no advantage in retaining sugar maple stems that were likely to degrade before the next cutting cycle, since a reduction in tree grades was associated with lower future financial returns. Buongiorno and Hseu (1993) obtained similar results for maple–birch stands in Wisconsin, USA. Although tree grade evolution could guide silvicultural decisions, an efficient management strategy should also consider price trends that are associated with tree quality, in order to ensure that net risks of stem retention provide satisfactory additional net stem value. Conclusion The equations that were developed in this study allow stem quality and its evolution over time to be predicted with reasonable accuracy for the commercially important hardwoods of Eastern Canada. Such tools are important to support sustainable forest management, since the use of hardwood trees for appearance wood products largely depends on their quality. Our findings suggest that hardwood quality can be modelled with tree-level variables, and, to a lesser extent, with stand- and regional-level variables. Thus, stem quality is closely related to tree vigour, assessed by the harvest priority classification, while its variation over time mainly depends on tree growth. In order to improve knowledge of the wood resources in a given territory and to improve forest management and silvicultural decisions that take into account hardwood stem quality, further work will focus on product recovery based on tree stem quality. Supplementary data Supplementary data are available at Forestry Online. Acknowledgements The authors would like to thank Isabelle Auger, Steve Bédard, Josianne DeBlois, François Guillemette and Denise Tousignant (Direction de la recherche forestière, Ministère des Forêts, de la Faune et des Parcs du Québec) for helpful advice and revision of previous versions of the manuscript, Dr. William F. J. Parsons for reviewing the latest version of the manuscript and Carl Bergeron (Direction des inventaires forestiers, Ministère des Forêts, de la Faune et des Parcs du Québec) for providing data for this study. We also thank the Associate Editor and two anonymous reviewers for their helpful comments on a previous version of the manuscript. Conflict of interest statement None declared Funding Ministère des Forêts, de la Faune et des Parcs, Gouvernement du Québec (project number 1420564-142332123). References Akaike , H. 1974 A new look at the statistical model identification . IEEE Trans. Autom. 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Journal

Forestry: An International Journal Of Forest ResearchOxford University Press

Published: Nov 9, 2016

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