Stem deformation in young plantations of black spruce (Picea mariana (Mill.) B.S.P.) and jack pine (Pinus banksiana Lamb.) in the boreal forest of Quebec,Canada

Stem deformation has often been observed in young black spruce (Picea mariana (Mill.) B.S.P.) and jack pine (Pinus banksiana Lamb.) plantations. Whenever important stem deformations are observed at the time of harvesting, timber value is negatively affected especially during the wood transformation process. The present work was undertaken to quantify and qualify the importance of stem deformation of black spruce and jack pine in the boreal forest of central Quebec at the stand and tree levels. In 30 black spruce and jack pine plantations, approximately 22% of spruce trees and 27% of pine trees exhibited stem deformation. The proportion of deformed trees was higher in the youngest plantations and decreased with the age of the plantations. Stem deformation caused the formation of compression wood which is another factor that can reduce the value of wood products. Thirty-nine black spruces and 34 jack pines were analysed at the tree level. On average, compression wood represented 14% and 20% of stem volume in 7- and 10-year old black spruce plantations, respectively. These proportions ranged from 18% in the youngest jack pine plantation to 26% in the oldest one. Stems of both species classified as normal contained a lower volume of compression wood than stems classified as deformed or very deformed. Annual percentages of compression wood and annual shoot length increased significantly with tree age (p < 0.0001 for both variables). Statistically significant correlations were also found between the range of displacement of the stem and the percentage of compression wood. The fewer number of trees with deformed stems in older plantations combined with high compression wood formation suggests that, over time, a deformed tree can become normal and straight in appearance.     

Long-term effects of superphosphate fertilization on stem form, taper and stem volume estimation of Pinus radiata

The long term effects of superphosphate fertilization on stem form, taper and stem volume estimation of Pinus radiata on a phosphorus-deficient site was examined using data from a fertilizer experiment which had been maintained for 30 years. The application of superphosphate resulted in long term and statistically significant changes in stem form. Mean cylindrical form factor ranged from 0.33 for the control trees up to 0.40 for trees fertilized with 100 kg P ha⁻¹. Stem form was also examined through taper curves which provided detailed depiction of average relative stem profiles. The increase in cylindrical form factor of fertilized trees was largely attributed to a significantly broader profile of the lower third of the stem. In comparison with the control trees, the fertilized trees also had a broader, although not statistically significant, profile of upper and middle stem which could also contribute to the increase in their cylindrical form factor. With increased form factor a greater proportion of the stem became merchantable because of increased log length to tree height ratio. Mean average taper of trees did not show a consistent trend with increasing lelevels of superphosphate application. It largely reflected the differential response of DBH and height growth to the treatments. The volume equation based on control trees underestimated the underbark stem volume of fertilized trees by 5–12% on average. Developing separate volume equations for the fertilized trees is warranted.     

Models for predicting lumber bending MOR and MOE based on tree and stand characteristics in black spruce

In this study, a stepwise method was introduced to identify the best variables for predicting lumber static bending modulus of elasticity (MOE) and modulus of rupture (MOR) based on stand and tree characteristics in black spruce (Picea mariana). In the initial development of the technique, the two equations were fitted independently using ordinary least squares (OLS). A test for cross-equation correlation using black spruce data showed highly significant correlation between the two equations. Since the cross-equation correlation exists between the two equations, more efficient parameter estimation can be achieved through joint-generalized least squares, better known as seemingly unrelated regression (SUR). A simultaneous system of two equations was derived for black spruce. The two methods were evaluated and compared for some statistical parameters. The results indicated that there is a small difference between the two methods, but parameter estimates from seemingly unrelated regression estimation had smaller standard errors in all cases as compared to those from ordinary least squares estimates. Therefore, the system estimation methods theoretically perform better for simultaneously interdependent systems of equations and the appropriate system estimation approaches are recommended for estimating coefficients in simultaneously interdependent systems of forestry equations.     

Quality of growth substrates of post-disturbed lowland black spruce sites for black spruce (<Emphasis Type="Italic">Picea mariana</Emphasis>) seedling growth

Black spruce (Picea mariana (Mill.) BSP) is the most important commercial tree species in the eastern boreal forest of Canada. Only limited work has been conducted to assess the quality of the various substrates that are found on post-disturbed sites prone to paludification having an effect on black spruce seedling growth. The objectives of this study were (1) to use a pot test to assess black spruce seedling performance on substrates found at the soil surface, in the rooting zone of undisturbed soil, at depths that become available to spruce roots after soil disturbance by wildfire or through management; and (2) to determine the nutritional quality of these substrates when constraints of poor drainage are artificially removed. Black spruce growth was greatest with fibric Pleurozium in the rooting zone, and with burned fibric Pleurozium and living Sphagnum at the soil surface. Good seedling growth on different substrates found in the rooting zone was associated with higher N and P foliar concentrations. Based on these results, we recommend targeted planting of black spruce seedlings in substrates of Pleurozium origin and the development of management techniques that promote Pleurozium schreberi. The Canadian Crown’s right to retain a non-exclusive royalty-free licence in and to any copyright is acknowledged.     

Changes in stem taper for birch plants growing in tree shelters

Plantings with pendula (Betula pendula Roth) and pubescent (Betula pubescens Ehrh.) birches were studied on five localities (Lat. 57–60 ° N) in Sweden. Seedlings were planted in 1988 or 1989. The experiment contained 50 plants per parcel and five replications per treatment. Among treatments harrowed area and birches covered with tree shelter were included. In spring 1993 five plants growing on harrowed area, with and without tree shelter, respectively were randomly chosen on each parcel. A total of 25 birches per treatment, species and locality were used. The trial was replicated in 1994 and 1995. The plant height was estimated and diameter at 20 and 60% of tree height was measured each year for 4 yr. The stem taper was calculated by the quotient D₆₀/D₂₀. The stem taper for birches without tree shelter was 0.5 for both species on all localities. The quotients for birches, which have grown in tree shelter, were 0.6–0.75 the first years of the trial. Then the quotients decreased and 2–3 years later they were on the same level as for birches planted without tree shelters. The results of the studies indicate that tree shelters should be removed two to three years after the plant has reached the top of the shelter. The height of the tree shelter might be shortened to 0.8–1.0 m to stabilise the plant earlier than with the conventional shelter height of 1.2 m.     

A stem taper equation compatible to volume equation for <Emphasis Type="Italic">Paraserianthes falcataria </Emphasis>in Pare,East Java,Indonesia: its implications for the plantation management

A stem taper equation compatible to the volume equation was derived from the data of 172 trees sampled in the three plantations of Paraserianthes falcataria in Pare, East Java. The stem taper equation in this study was based on a conventional logarithmic volume equation, with the addition of one free parameter that minimized the standard errors of estimate to the observed diameter of stems at 1.0-m intervals. The derived equation was able to predict the stem taper of P. falcataria reasonably well, while it was not flexible enough to describe delicate changes of the taper in the upper portion of stem. The equation was able to predict bole length and the volume up to the top diameter 20 cm, the diameter size merchantable for sawn timber in Indonesia, with reasonable accuracy. An appropriate rotation age for sawn-timber production was found to be 8–9 years old, at which the mean annual increment of sawn timber would be maximized.     

A non-linear hierarchical mixed model to describe tree height growth

A non-linear hierarchical mixed model approach is used to describe height growth of Norway spruce from longitudinal measurements. The parameter variation in the model was divided into unknown random effects, fixed effects and covariate-dependent effects in order to model tree height growth. The values for fixed effect parameters and the variance–covariance matrix of random effects were estimated. Covariates could only explain up to 10% of parameter variability. Height curves were calibrated by means of BLUPs for the unknown random effects using prior height measurements and evaluated using a separate dataset. The resulting curves had a small error variance and plausible shapes.     

基于非线性混合模型的落叶松树干削度模型

以黑龙江省带岭林业局大青川林场84株人工落叶松解析木数据为例,采用Max和Burkhart分段削度模型作为基础模型,利用SAS软件中的似乎不相关回归过程得到该分段削度模型的4个参数和2个拐点参数同时估计。参数估计显著性检验(P<0.000 1)以及模型检验(F=31 392.30,P<0.000 1)都证明该分段模型能较好地描述落叶松树干干形变化。然后以该分段模型为基础模型,采用非线性混合模型的方法,建立落叶松人工林树干削度混合效应模型。结果表明:当考虑样地效应影响时,b1,b2同时作为混合参数时模型拟合最好;当考虑树木效应影响时,b2,b4同时作为混合参数时模型拟合最好。无论考虑样地效应影响还是考虑树木效应影响,混合模型的拟合精度都比基本模型的拟合精度高,并且考虑树木效应影响要比考虑样地效应影响的精度更高。模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度。     

A model for the relationship between form-factors for stem volume and those for stem surface area in coniferous species

A model that describes the relationship between the form-factors for stem volume and those for stem surface area in coniferous species is proposed. The model is derived assuming that the stem form of a tree can be expressed by Kunze's equation. The model indicated that the form-factor for stem surface area was directly proportional to the square root of the form-factor for stem surface volume, independent of the stem position. The proposed model expressed the relationship of the form-factors for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees well. Therefore, the form-factors for stem surface area could be estimated from those for stem volume. No significant difference in the coefficient was found between Japanese cedar and Japanese cypress trees, indicating that the proportional coefficient would be common between the two species. Many studies have shown that the form-factors for stem volume at 0.7 and 0.5 in relative height were, respectively, almost steady at 0.7 and 1.0, independent of species, district, density control, and growth stage. Substituting these universal values into the proposed model, the form-factors for stem surface area at 0.7 and 0.5 in relative height were estimated to be 0.730 and 0.873, respectively. The estimated values of the form-factors for stem surface area would be universal for coniferous species. The proposed model also showed that the breast height form-factor for stem surface area decreased sharply with the increase in total tree height, when the height was less than 10 m. However, after the tree attained the total height of 10 m, the breast height form-factor gradually decreased with the total tree height approaching its asymptotic value of 0.605. In conclusion, the model proposed here can be used to describe the relationship between form-factors for stem volume and those for stem surface area successfully.     

A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.)

A nonlinear mixed-effects modelling approach was used to model the individual tree height–diameter relationship in pyrenean oak (Quercus pyrenaica Willd.). A set of 24,627 pairs of height–diameter measurements were used to fit the model. These were taken at 950 Spanish National Forest Inventory plots embracing six different biogeoclimatic strata. Eleven biparametric nonlinear height–diameter equations were evaluated to find a local model, which only includes the dimensions of the tree as explanatory variables. After selecting the local model, a regional or generalized model was studied. The following stand variables were tested for inclusion in the model as fixed effects: stand density, quadratic mean diameter, arithmetic mean diameter, dominant diameter, arithmetic mean height, dominant height and basal area. Dominant height and basal area of the stand were found to produce the most satisfactory fits in the stand model. Interregional variability was studied by including strata effects as dummy categorical variables and was analysed using the non-linear extra sum of squares method and the Lakkis–Jones test. Height–diameter models were found to be similar for the six biogeoclimatic strata. Finally, a mixed nonlinear model technique was applied to fit the definitive model. By calibrating the model it is possible to predict random components of definitive model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model.     

A provisional growth model with a size–density relationship for a plantation of <Emphasis Type="Italic">Paraserianthes falcataria</Emphasis> derived from measurements taken over 2 years in Pare,Indonesia

A growth model for a plantation of Paraserianthes falcataria was provisionally derived from measurements of 32 permanent plots taken over a period of 2 years in Pare, Indonesia. This model first predicts height growth with the polymorphic site index equation. Then density-related growth and mortality, that is, diameter and stand density, are calculated to satisfy the mathematical relationship for the reciprocal and self-thinning equations, both of which were based on the maximum size–density line with the slope of −1.759 identified in this study. Cumulative predictions on diameter and stand density, starting with each of three age classes, 3, 4, and 5 years after planting, and continuing for the next 2 years, agreed well with the observations of age-class mean. An exception was for stands that were 7 years old, which were marginal, but closest to the rotation age of 8 years. Contrasting height/diameter relationships among the three age classes were described reasonably well with this model, and the predicted basal growth area was found to agree fairly well with observations. These results suggest that the growth model presented here has good potential for applying size–density control for plantations of P. falcataria. However, measurements for an additional few years might be necessary to derive a model that will more accurately predict diameter size at the rotation age.