Stem Slenderness Research Articles

Modeling the effect of initial planting density on within tree variation of stiffness in loblolly pine

Modulus of elasticity (MOE) is an important mechanical property determining the end-use and value of loblolly pine (Pinus taeda L.) lumber. In this study, a model was developed to predict the within tree variation of MOE, from pith-to-bark and stump-to-tip, using data collected from a 21-year-old unthinned stand where trees were planted under seven initial stand density levels (746–2,243 trees/hectare). The study was laid out in a randomized complete block design, with seven levels of initial planting density, replicated three times. Seven trees were destructively sampled from each plot, and bolts were cut from each tree at heights of 2.4, 7.3, and 12.2 m. Static bending samples (of dimension 2.5 × 2.5 × 40.6 cm) representing pith-to-bark variation were cut from each bolt and MOE measured. A three-parameter logistic function was used to model the pith-to-bark variation in stiffness with distance from pith as an explanatory variable. Based on the final fitted model, it was found that the asymptotic parameter (maximum outerwood MOE = 13.48 GPa) was not influenced by sampling height, initial planting density, and stem slenderness. However, the inflection and scale parameters were significantly influenced by these variables. In summary, we found that initial planting density had a significant influence on the amount of corewood produced with higher initial planting densities producing a lower proportion of corewood as indicated by a linear decrease in inflection point with an increase in planting density.

The relative importance of above- versus belowground competition for tree growth during early succession of a tropical moist forest

Competition between neighboring plants plays a major role in the population dynamics of tree species in the early phases of humid tropical forest succession. We evaluated the relative importance of above- versus below-ground competition during the first years of old-field succession on soil with low fertility in Southern Mexico, using the premise that competition for light is size-asymmetric, unlike competition for nutrients. Plant growth is thus expected to be disproportionally impeded by larger neighbors. We studied how growth and survival of 3.5–5.5 m tall saplings of Cecropia peltata and Trichospermum mexicanum, two pioneer species that dominate the secondary forests in the study region, varied with the abundance and size of neighboring trees in 1–2 year old secondary vegetation. We found that local neighborhood basal area varied 10-fold (3 to 30 cm2 m-2) and explained most of the variation in diameter and height growth of the target saplings. Most growth variables were strongly affected by the neighbors bigger than the focal trees with no significant additive effect of the smaller neighbors, indicating asymmetric competition. Smaller neighbors did have a small but significant additive effect on the diameter growth of Cecropia saplings and stem slenderness of Trichospermum saplings. We conclude that competition for light was more important than belowground competition in this initial phase of moist tropical forest successional, despite the low soil fertility.

Development of a model describing modulus of elasticity across environmental and stand density gradients in plantation-grown Pinus radiata within New Zealand

Modulus of elasticity (E) is an important property in plantation grown softwoods that describes resistance of timber to deformation under load and is a key criterion in machine stress grading. This paper presents an accurate (R2 = 0.96) site-level model of E for radiata pine ( Pinus radiata D. Don) that is applicable across a wide range of tree ages and broad environmental gradients and sensitive to a wide variation in stand density. In the final model, E increased sigmoidally with age and increased linearly with both stem slenderness (height/diameter at 1.4 m) and mean minimum autumn air temperature. For a given age, the model shows stem slenderness to be the main determinant of environmental variation in E, with variation in E ranging approximately 10 GPa across the range in slenderness. Given the simple formulation, this model could be readily used by managers to gain greater understanding of how they can manipulate stands to achieve desired end-use products and maximize crop value. Further research should extend the developed framework so that it can be used to account for intratree, intertree, and clonal variation in E.

An architectural approach to the growth forms of Nothofagus pumilio (Nothofagaceae) along an altitudinal gradient

Variations in the architecture and axis structure of different growth forms of Nothofagus pumilio (Poepp. et Endl.) Krasser (Nothofagaceae) were studied along an altitudinal gradient. We evaluated the primary growth and branching pattern of annual shoots belonging to the main axis categories (trunk, main branches, and secondary (short) branches) of four growth forms developed at different altitudes (1200–1600 m a.s.l.) in northern Patagonia: (i) low shrubs at the high-altitude timberline, (ii) high shrubs at high altitude, (iii) low trees at mid-altitude slopes, and (iv) high trees at low-altitude single-species forests. Shoot structure and branch distribution along shoots were similar for all axis categories and growth forms. Significant differences between axis categories were found regarding the sizes of shoots, which decreased from trunk to secondary/short branches. For each axis category, shoots of similar size differed between growth forms in stem slenderness and internode length. The extent of differentiation between axis categories is key in the structural distinction between growth forms of N. pumilio.

Effects and etiology of sudden aspen decline in southwestern Colorado, USA

Sudden aspen decline (SAD), affecting Populus tremuloides, was first observed in Colorado in 2004. By 2008 it affected at least 220,000 ha, an estimated 17% of the aspen cover type in the state. In southwestern Colorado, we examined site and stand features in paired healthy and damaged plots to assess the effects of SAD on aspen and to identify factors associated with decline. Root mortality increased significantly with recent crown loss. Consequently, density of regeneration did not increase as the overstory deteriorated, and regeneration that originated since 2002 decreased significantly in stands with moderate to severe SAD. However, mortality of regeneration did not increase with that of the overstory. Remeasurement of a subset of plots after 1–2 yrs showed significant increases in severity. Contrary to expectations, overstory age and diameter were not related to SAD severity as measured by recent crown loss or mortality. Severity of SAD was inversely, but weakly, related to basal area, stem slenderness, and site index, and positively related to upper slope positions. This is consistent with moisture stress as an underlying factor. To test the role of climate as an inciting factor for SAD, a landscape-scale climate model was used to compare moisture status of declining and healthy aspen at the height of the warm drought in water year 2002. Polygons identified as damaged aspen in the 2008 aerial survey had greater moisture deficits than healthy aspen in the 2002 water year. SAD has led to loss of aspen cover in some stands, and is occurring in areas where early loss of aspen due to climate change has been predicted. Further warm, dry growing seasons will likely lead to recurrence of SAD.

Influence of initial planting spacing and genotype on microfibril angle, wood density, fibre properties and modulus of elasticity in Pinus radiata D. Don corewood

Pinus radiata D. Don trees from six clones, grown at initial spacings of 2500 stems ha −1 and 833 stems ha −1 were destructively harvested. For these trees wood properties were measured on radial slices sampled at a height of 1.4 m above the ground. Relative to wide spacing, close initial stand spacing significantly reduced microfibril angle (MFA) and ring width and significantly increased dynamic modulus of elasticity (MOE), fibre length, latewood percentage and cell wall thickness. Density and fibre width were not significantly different between spacing treatments. Examination of the influence of genetic population on wood properties indicated that genotype significantly influenced MFA, MOE and ring width. The key wood properties MFA, MOE and fibre length were regressed against tree diameter, height and stem slenderness. All three wood properties were most strongly correlated with stem slenderness. Multiple regression models developed for MFA, MOE and ring width accounted for respectively 62%, 81% and 58% of the variation in these variables. The following changes occurred in sampled properties with increasing ring number: MFA and ring width declined markedly; MOE and fibre length increased markedly; latewood percentage and cell wall thickness increased slightly; and density and fibre width did not show any radial trend.

Modelling the influence of site and weed competition on juvenile modulus of elasticity in Pinus radiata across broad environmental gradients

Data from a nationwide set of Pinus radiata D. Don plots established at a range of conventional stand densities were analysed at age 6 to (i) determine how environment and competition from weeds influence dynamic modulus of elasticity ( E) of the lower stem base, (ii) develop a predictive multiple regression model of E for basal stemwood and (iii) identify significant direct and indirect environmental influences (through stem slenderness) on E using path analysis. Site had a highly significant ( P < 0.001) influence on E, which exhibited a 3-fold range from 1.6 to 5.3 GPa, across 30 sites. When compared to the weed-free controls, weed competition had a significant ( P < 0.0001) and substantial effect on E, increasing values by on average 16% (2.76 GPa vs. 2.38 GPa). The positive linear relationship between stem slenderness (determined as tree height/ground-line tree diameter) and E was by far the strongest relationship ( R 2 = 0.71; P < 0.001) among the 20 variables that were significantly related to E. A multiple regression model that included stem slenderness, mean minimum air temperature in mid-autumn, T min, as positive linear relationships and net nitrogen (N) mineralisation in a negative linear form accounted for 86% of the variance in E. A cross-validation indicated that this model was stable and unbiased, with the validation accounting for 82% of the variance in E. The final path analysis model included T min, net N mineralisation, below canopy solar radiation and stem slenderness as significant ( P < 0.05) direct influences on E. Below canopy radiation, maximum air temperature during mid-summer, soil total phosphorus and carbon:nitrogen ratio were indirectly associated with E through their significant ( P < 0.05) direct relationship with stem slenderness. These results provide considerable insight into how environment regulates E of juvenile P. radiata. Low fertility sites that have warm air temperatures and either a high canopy leaf area index, or high levels of woody weed competition, are most likely to produce trees with high stem slenderness and high E. Conversely, sites that are cool over summer and autumn and high in fertility, with low levels of intra- or inter-specific competition for light are likely to produce trees with low stem slenderness and low E.

Effect of stocking on juvenile wood stiffness for three Eucalyptus species

The effects of stocking on wood stiffness (MoE) for three Eucalyptus species are quantified using a 6-year-old trial established in New South Wales, Australia. An acoustic time-of-flight tool measured the velocity between two probes in the outerwood, from which the stiffness was estimated. Four stocking levels (714, 1,250, 1,667 and 3,333 sph) were examined. Stiffness varied significantly between all species, with E. cloeziana showing the highest stiffness (14.2–15.7 GPa), followed by E. pilularis (12.2–13.5 GPa) and E. dunnii (10.7–12.6 GPa). There was a stiffness increase (around 11%) between 714 and 1,250 stems/ha for all species but thereafter differences between stockings were not always significant. Trees were also assessed for basic density, dbh, total height, crown area, green crown height and stem slenderness (height/dbh). Only stem slenderness had a significant association (0.41 ± 0.17) with stiffness. These findings suggest that, where stiffness is a priority, forest managers could reduce establishment costs with low stockings (around 1,250 stems/ha).

Calibrating jack pine allometric relationships with simultaneous regressions

Allometric equations for estimating foliage biomass, sapwood area, and branch basal area from tree diameters and crown lengths for jack pine ( Pinus banksiana Lamb.) in eastern Canada were calibrated using mixed models. A first model is presented that relates branch foliage biomass to branch diameter and relative position within the crown. These results show that a branch’s foliage biomass is inversely proportional to its depth within the crown. At the tree level, foliage biomass was found to be proportional to crown length and to vary with stem age and slenderness. Pipe model parameters (sapwood area and branch basal area to foliage biomass) were also calculated. The sapwood area to foliage biomass parameter is proportional to stand density, whereas branch basal area to foliage biomass is constant. The tree-level allometeric models were calibrated using a mixed-effects seemingly unrelated regression to account for between-model correlations.

Effect of thinning on the development of compression wood in stems of Corsican pine

This study considered the effects of thinning on the development of compression wood in stems of 35-year-old stand of Corsican pine (Pinus nigra L.). Part of the stand had been thinned at 5-yearly intervals and part left unthinned. Twenty trees each from the thinned and unthinned stands were randomly selected and felled. Measurements were made on tree height, stem diameter, stem slenderness and canopy depth. Wood samples were removed from the central part of the main log and cross-sectional measurements made on ring width, basic density and compression wood content. Cross-sectional area of compression wood was found to be three time higher in stems from the unthinned trees in comparison with those from the thinned trees. No significant differences in mean radial ring width or basic density were found between treatments. Correlations indicated that, with increasing in stem diameter, compression wood content increased in the unthinned trees, while a decline in compression was observed in the thinned trees. Tree height was also positively correlated with compression wood content in unthinned trees, while no equivalent relationship was observed in thinned trees. Observations from this study, while not conclusive, suggest that phototropic stimulus may be producing stem inclinations in the unthinned stand as trees compete for space in the canopy, whereas crown competition has been largely eliminated in the thinned stand; and that this is responsible for compression wood levels recorded in this study.

Modelling the influence of environment and stand characteristics on basic density and modulus of elasticity for young Pinus radiata and Cupressus lusitanica

Data taken from 261 4-year-old trees growing within a nationwide set of site quality plots where Pinus radiata D. Don and Cupressus lusitanica Mill. were established at high stand densities (40,000 stems ha −1) were analysed to (i) determine how site, species and fertilisation influence the wood properties basic density and green dynamic modulus of elasticity (MOE) for the stem at the tree base, and (ii) develop predictive models of basic density and MOE for both species. A further objective was to examine the utility of the “experimentation in miniature” (EIM) approach used here, to identify key determinants of wood properties across an environmental gradient. Site mean variation for both wood properties was highly significant with treatment-averaged values ranging from 27% (365 to 465 kg m −3) for density to twofold for MOE (2.4–5.9 GPa). Basic density of C. lusitanica significantly exceeded that of P. radiata by 12% (457 versus 407 kg m −3), while MOE of P. radiata significantly exceeded that of C. lusitanica by 33% (4.4 versus 3.3 GPa). Neither fertilisation nor the interaction of fertilisation and species had a significant effect on either basic density or MOE. Although key determinants of basic density were very different between species, they exhibited considerable similarity for MOE. In the final multiple regression model of basic density for C. lusitanica ground-line diameter accounted for 88% of the variance, while for P. radiata 90% of the variance in basic density was explained by total soil phosphorus (P), average leaf area index (LAI), total annual radiation, and average minimum air temperature during winter. The final multiple regression model of MOE for C. lusitanica accounted for 90% of the variance using stem slenderness, average air temperature during winter, and average LAI, while stem slenderness and total soil P accounted for 96% of the variance in P. radiata MOE. Key determinants of P. radiata basic density previously identified across an environmental gradient at conventional stockings were consistent with our results. Results from our study also demonstrate that previously unmeasured variables, within these conventionally stocked stands, such as total soil P and LAI may also have an important influence on P. radiata basic density. Although preliminary and limited to a single wood property in P. radiata this comparison suggests that EIM has some utility for identifying key determinants of wood quality across environmental gradients.

Modelling the influence of stand structural, edaphic and climatic influences on juvenile Pinus radiata fibre length

The objectives of this study were to determine the influence of site, fertilisation and age on fibre length and develop predictive models of fibre length from a comprehensive set of climatic, edaphic and stand variables. Data were collected from a nationwide set of 22 site quality plots where Pinus radiata D. Don was established at high stand densities (40 000 stems ha −1) and grown over a period of 4 years. The main environmental drivers of fibre length were identified by assessing the strength of bivariate correlations and use of multiple regression. Path analysis was used as an extension to multiple regression to separate cause from effect and quantify the direct influence of variables significantly related to fibre length. Fibre length exhibited significant variation between sites. When averaged across fertiliser treatments, site variation for fibre length in rings 1–4 ranged from 1.08 to 1.76 mm. Fertilisation did not significantly affect fibre length. Fibre length significantly increased with age from an average of 1.10 mm in rings 1–2 to 1.62 mm in rings 3–4. The interaction between age and fertilisation was insignificant. In total 16 variables were significantly related to fibre length. For rings 1–4, fibre length exhibited the strongest significant relationships with stem slenderness ( r = 0.69), mean minimum air temperature ( r = 0.67), green crown height ( r = 0.66), tree height ( r = 0.64) and average air temperature ( r = 0.62). The best multiple regression models for both age classes and the whole stem included mean minimum air temperature and stem slenderness in a linear formulation. Path analysis indicated that the direct positive contribution of both these variables to fibre length was of a similar magnitude (path coefficients of 0.52 versus 0.49). Significant determinants of P. radiata fibre length in our study were similar to those identified in trees grown at conventional stockings across a similar environmental gradient in New Zealand. Although these studies did not examine how stem slenderness influences fibre length, they found average air temperature to be the strongest environmental determinant of fibre length, and that soil fertility, as indexed by Olsen phosphorus and total nitrogen and pH had little influence on fibre length. Further research is needed in conventionally stocked stands to confirm the link found here between stem slenderness and fibre length.

Carica papaya (Caricaceae): a case study into the effects of domestication on plant vegetative growth and reproduction

Few studies have quantitatively evaluated the gender specific effects of cultivation on plant growth and reproduction. The availability of cultivated and wild populations of different genders of Carica papaya L. (Caricaceae) on Guam provided an opportunity to study these effects quantitatively. We compared the gender specific allometry of height vs. basal stem diameter (H vs. D), stem slenderness ratio (H/D), and the height at first flowering (H(fl)) of carpellate and staminate plants growing under natural conditions (N = 150 each) with those of carpellate and hermaphroditic plants (N = 250 each) from two cultivars (Sunrise and Tainung 2). These comparisons indicated that (1) wild carpellate and staminate plants are significantly taller than either gender of the two cultivars with equivalent D; (2) the scaling exponent governing the H vs. D relationship of both genders of wild plants is significantly higher than that of either cultivated gender; (3) cultivar type does not affect the H vs. D exponent, but gender expression does; (4) gender expression (but not cultivar-type) also affects H(fl) (cultivation substantially reduces carpellate plant H(fl)); and (5) the onset of sexual maturity is associated with a dramatic reversal in H/D ontogeny. Cultivation therefore has "condensed" patterns of vegetative growth in a gender specific manner, whereas gender expression alters both vegetative and reproductive growth significantly more so than does cultivar-type.

Influence of tree morphology, genetics, and initial stand density on outerwood modulus of elasticity of 17-year-old Pinus radiata

The influence of initial stand density, genotype, propagation method and physiologically aged cuttings on outerwood dynamic modulus of elasticity ( E) of 17-year-old Pinus radiata was examined at a Nelder spacing experiment in Canterbury, New Zealand. Outerwood dynamic modulus of elasticity was determined using the stress wave method on 385 trees in one Nelder plot. The experiment incorporated three genetic breeding series (850, 870 and 268 series), two propagation methods from the 268 series (seedlings and cuttings) and two different physiologically aged cuttings (cuttings taken from 1-year-old and 3-year-old parents) grown at 10 different initial stand densities ranging from 209 to 2551 stems ha −1. Dynamic modulus of elasticity was significantly influenced by initial stand density ( P < 0.0001) and genotype ( P < 0.0001), but not their interaction. Dynamic modulus of elasticity increased by 39%, from 5.4 to 7.5 GPa, between 209 and 2551 stems ha −1, with the majority of this increase (33%) occurring between 209 and 835 stems ha −1. The 3-year-old cuttings exhibited the highest E of 7.7 GPa, which significantly exceeded E for the 1-year-old cuttings, and seedlings from the 870, 268, and 850 breeding series by 15, 17, 22, and 26%, respectively. Stem slenderness (height/diameter) exhibited the strongest relationship with E ( r 2 = 0.49), displaying a significant ( P < 0.0001) positive linear correlation. Dynamic modulus of elasticity also exhibited a significant ( P < 0.0001) positive linear relationship with green crown height ( r 2 = 0.46) and a significant ( P < 0.0001) negative linear relationship with diameter at breast height ( r 2 = 0.44). The final path analysis model included stem slenderness and green crown height as significant positive direct influences on E explaining 53% of the variance in the dataset. Tree diameter and height were indirectly associated with E through their significant direct relationship with stem slenderness and green crown height. This study demonstrates the strong influence of initial stand density on E and suggests that the use of physiologically aged cuttings of greater maturation status improves E. Results also strongly suggest that the effects of diameter and height on E are mediated through stem slenderness and green crown height.

Effective height development of four co-occurring species in the gap-phase regeneration of Douglas fir monocultures under nature-oriented conversion

Natural regeneration in gaps in Douglas fir forest stands in the Netherlands mainly consists of Betula pendula (Roth.), Pinus sylvestris (L.), Larix kaempferi (Carr.), and Pseudotsuga menziesii (Mirb. Franco). Even though these species are well known, the autogenic development of these species in an unmanaged plant community falls outside of traditional silvicultural experience. We therefore present an explorative study, aimed to map out differences between these species under conditions of co-occurrence, and develop hypotheses on the further development of these sapling communities. We focused on differences in height, and particularly the architectural contribution to height. We analyzed interspecific differences in the height–mass and height–DBH relationship, biomass partitioning, and slenderness for a total of 177 saplings up to 13.7 cm DBH and 11.8 m high. Average annual height and diameter growth rates of an additional 48 saplings are presented for comparison with the static architectural data. Betula had a high stem biomass, high stem slenderness, and low leaf mass. The reverse was true for Pseudotsuga. Larix behaved as an intermediate species. Pinus however deviated from the classical pioneer–climax dichotomy in having a low slenderness and low height per unit biomass while being a highly light-demanding species. The static height-mass relationship shows a similar species ranking when compared to average annual height growth rates, but not when compared to diameter growth rates. This underlines the importance of a species’ architecture for its height development and suggesting a predictable stratification between species. Based on the results regarding species’ stratification in heights and a priori information on light demand, it is hypothesized that in the studied gap-phase regeneration Betula, Larix and Pseudotsuga will partition the available light. Pinus however will be overtopped and given its need for high-light environments, is expected to be competitively excluded.

Modelling Environmental Variation in Young's Modulus for Pinus radiata and Implications for Determination of Critical Buckling Height

Although density-specific stiffness, E/rho, (where E is Young's modulus and rho is wood density) is often assumed constant by the elastic similarity model, and in determination of critical buckling height (H(crit)), few studies have tested this assumption within species. Here this assumption is tested for Pinus radiata growing across an environmental gradient, and theory is combined with data to develop a model of Young's modulus. Analyses use an extensive series of environmental plots covering the range of climatic and edaphic conditions over which P. radiata is grown in New Zealand. Reduced major axis regression was used to determine scaling exponents between log-log plots of H(crit) vs. groundline diameter (D), and E/rho vs. D. Path analysis was used to identify significant direct and indirect (through stem slenderness) edaphic and climatic influences on E. Density-specific stiffness exhibited 3-fold variation. As E/rho scaled positively with D, the exponent of 0.95 between H(crit) and D exceeded the assumed value of 0.67 under constant E/rho. The final path analysis model included mean air temperature in early autumn (T(aut)) and slenderness as significant (P < 0.05) positive direct influences on E. Tree leaf area index and T(aut) were indirectly associated with E through their significant (P < 0.05) positive direct relationship with stem slenderness. Young's modulus was most sensitive to T(aut), followed by stem slenderness then leaf area index, and the final model explained 76 % of the variance in E. The findings suggest that within species E/rho variation may influence H(crit) and the scaling exponent between D and H(crit) so important in assumptions regarding allometric relationships. The model presented may provide a useful means of determining variation in E, E/rho and H(crit) across environmental gradients.

Modelling the influence of stand structural, edaphic and climatic influences on juvenile Pinus radiata dynamic modulus of elasticity

Data from a nationwide set of Pinus radiata site quality plots established at high stand densities and grown over a period of 4 years were analysed to (i) determine how site and fertiliser influence dynamic modulus of elasticity ( E) of the stem at the tree base, and (ii) develop a predictive model of E for basal stemwood. Site had a highly significant ( P < 0.001) influence on E, which exhibited an almost three-fold range from 2.3 to 6.3 GPa, across the 21 site quality plots. When compared to the unfertilised controls, fertilisation had a relatively minor and insignificant effect on E, reducing values by on average 6%. This demonstrated the insensitivity of E to Bray phosphorus (P), Olsen P, inorganic P, and exchangeable potassium which were elevated in the soil by on average two- to three-fold by application of fertiliser. In total, 13 variables were found to be significantly related to E. Minimum temperature during early autumn (March) and tree slenderness (determined as tree height/ground-line tree diameter), also known as taper, exhibited the strongest correlations with E, accounting for 61 and 60% of the variance in this property, respectively. A multiple regression model with these two variables predicted 75% of the variance in E. Residuals from this model exhibited little apparent bias with predicted values, or independent variables. Results indicate that E may be relatively simple to predict across environments as stem slenderness can be readily obtained from either regional growth models or stand inventory, while temperature data can be obtained from regional or national climate surfaces. The relationship found between E and stem slenderness is consistent with the Euler buckling formula which suggests in a competitive situation increases in stem slenderness will induce increases in E to reduce the risk of stem buckling. The significant influence of temperature during early autumn on E may be mediated through regulation of latewood development. Given that latewood with high E is forming during early autumn, sites with higher temperatures and increased growth rates over this month are likely to develop a greater percentage of high E latewood, and as a consequence a higher overall stem E.

Tree characteristics related to stem breakage of Picea glehnii and Abies sachalinensis

Stem breakage is a major cause of tree death in coniferous cool temperate forests that are subjected to typhoons and heavy snowfall. Changes in stability with tree growth, in terms of loading processes on the crown and overturning bending moments on the stem, may produce a good mechanistic understanding of tree stability. To examine how diameter growth and crown expansion of two conifer species (Picea glehnii and Abies sachalinensis) influenced patterns of stem breakage in a crowded Picea–Abies mixed forest in northern Japan, the relationships between mode of tree death (standing, uprooting, and stem breakage) and crown size were analyzed along the growth trajectory. Over a 6-year study period (1995–2001), the two conifer species showed contrasting modal changes in patterns of tree death with increasing diameter. No P. glehnii of small diameter (<8 cm) were killed by stem breakage, while almost all large-diameter (>32 cm) P. glehnii that died during the study were killed by stem breakage. Mortality owing to stem breakage was high in A. sachalinensis of small diameter (<16 cm), but decreased in trees of large-diameter (>16 cm). For both species, the probability of stem breakage at a given diameter was positively associated with crown silhouette, crown projection area, and the lowest branch height, but was not associated with the stem slenderness ratio. Estimated bending moments using mechanical equations also confirmed the relationships between tree stability and crown dimensions. For these two monopodial conifer species, crown shape emerged as the most important predictor of modal changes in tree death under conditions of frequent loading.

Allometric model of the Reineke equation for Japanese cypress (Chamaecyparis obtusa) and red pine (Pinus densiflora) stands

An allometric model that explains the mechanism of the difference in the slope of the Reineke equation (A) among species was proposed based on the allometric relationships of mean tree height (H) to quadratic mean diameter D (H ∝ Dθ) and stand density N (H ∝ Nδ), i.e., A = θ/δ. The proposed model was fitted to Japanese cypress (Chamaecyparis obtusa Endl.) and red pine (Pinus densiflora) stands. The allometric exponents θ and δ were, respectively, 0.8995 and −0.5000 for cypress and 0.8612 and −0.6619 for pine. The difference between cypress and pine was significant for δ but not for θ. Inserting the exponents into the model resulted in predicted slopes of −1.7991 for cypress and −1.3011 for pine. The difference in the slope of the Reineke equation between the two species was produced by characteristics related to the tree crown, rather than characteristics related to stem slenderness. The proposed model enables us to estimate the slope of the Reineke equation from commonly measured stand attributes, such as mean tree height and quadratic mean diameter. Therefore, the proposed model is expected to be practical and convenient for estimating the slope of the Reineke equation and for explaining the mechanism of its variation among species. The model should be also accepted as a generalized model of the stand density versus quadratic mean diameter relationship, whereas the original Reineke equation should be seen as a specific case of this model.

Relationships of stem surface area to other stem dimensions for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees

I investigated the relationships between stem surface area outside bark and other stem dimensions for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees. The stem dimensions used here were the basal area and the product of diameter at breast height (dbh) and total tree height. The regression equation of the stem surface area s against basal area g was s = 184.216 g for the cedar trees and s = 156.878 g for the cypress trees. The slope of the equation was significantly different between the two species. For the same dbh, the cedar trees tended to have a higher total tree height than the cypress trees. The cedar trees also had a larger surface area of relative stem form than the cypress trees. These results indicated that the difference in the slope was produced by the differences in both the stem slenderness and tapering between the two species. On the other hand, the regression equation between the stem surface area and the product of dbh and total tree height dh was s = 1.937 dh for the cedar trees and s = 1.921 dh for the cypress trees, whereas no significant difference in the slope was found. The obtained slopes for the cedar and cypress trees seemed to be in accord with that for other coniferous species reported in earlier studies, suggesting that the variation in the slope among coniferous species would be small. The estimation from the basal area would provide a simpler means for estimating the stem surface area and would be useful in obtaining an approximation of the surface area. By contrast, the estimation from the product of dbh and total tree height would provide a more accurate and precise estimate as well as a wider applicable range, i.e., a parameter for physiological growth models. In conclusion, it could not be judged which regression equation examined in the present study was superior to the other, and thus it was important to select an appropriate equation depending both on the purpose and on the time and labor available.