Modeling diameter distributions of Gmelina arborea plantation in Omo Forest Reserve,Nigeria with Johnson’s SB

Diameter distribution modeling is an essential tool for obtaining reliable information on the structure, growth, and yield of forests. However, this tool has not been duly utilized in many forest plantations, especially in Nigeria. Thus, this article presents the effectiveness of using the Johnson S_B function for modeling diameter distributions of a Gmelina arborea plantation in Omo Forest Reserve, Nigeria. Fifty plots of 0.04 ha were randomly selected across three age series. All trees with DBH ≥ 5.0 cm in the selected plots were measured. Three fitting methods for the S_B distribution were compared: conditional maximum likelihood (CML), moments (MOM), and Knoebel and Burkhart (KB) methods. The parameter recovery model (PRM) was used to recover the parameters of the distribution. The assessment was based on Kolmogorov-Smirnov (K-S), mean square error (MSE), mean absolute error (MAE), and bias. The results showed that the underlying diameter distribution of the Gmelina arborea followed the Johnson’s S_B distribution fitted with MOM. The number of rejections by the K-S test was zero for MOM and CML. The mean K-S value for MOM was statistically different from CML and KB methods. The results obtained after recovering the parameters of the S_B distribution were comparable with the real distributions of the Gmelina arborea stand.     

Comparison of beta,Johnson’s SB,Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain)

The purpose of this study was to compare the beta, Johnson SB, Weibull and truncated Weibull functions in describing the diameter distributions of forest stands in Catalonia. The data consisted of permanent sample plots from the Spanish National Forest Inventory in Catalonia. The empirical data represent left-truncated distributions, as the smallest diameter measured in the field was 7.5 cm. A total of 1,242 plots were used to fit the functions and analyze their performance. The distribution functions were fitted to the diameter distributions of the number of stems (DD_N) and stand basal area (DD_G). The performance of the candidate functions was compared by means of their bias and RMSE for different diameter sums measuring the difference between the empirical and fitted distributions. The leftmost part (from 0 to 7.5 cm) of the non-truncated functions was ignored in this analysis. Sensitivity analyses were conducted to check whether the results depended on the number of trees measured in the stand, or the main species of the stand. The truncated Weibull function for the diameter distribution of stand basal area appeared to be in all cases the most accurate and consistent function. Generally, functions describing the distribution of stand basal area performed better than functions that described the distribution of the number of trees. Of the basal area distributions, beta and Johnson’s SB were the second best and nearly equally good with each other. The order of precision of the tested functions was: truncated Weibull for DD_G, truncated Weibull for DD_N, Johnson’s SB for DD_G, beta for DD_G, beta for DD_N and Weibull for DD_G, Weibull for DD_N, and Johnson’s SB for DD_N.     

Comparing normal,lognormal and Weibull distributions for fitting diameter data from Akashmoni plantations in the north-eastern region of Bangladesh

Statistical probability density functions are widely used to model tree diameter distributions and to describe stand structure. The objective of this study was to compare the performance of normal, logarithmic-normal and three-parameter Weibull distributions for fitting diameter data from Akashmoni (Acacia auriculiformis A. Cunn. ex Benth.) plantations grown in the north-eastern region of Bangladesh. Data from 96 plots, established in 24 plantations in north-eastern Bangladesh and ranging in age from 1 to 6 years, were used for this study. The parameters of the Weibull distribution were calculated using maximum likelihood estimation (MLE) and moment estimation (ME) methods. The goodness of fit of normal, lognormal, Weibull MLE and Weibull ME were tested using one-sample Kolmogorov-Smirnov (KS) tests. The KS test results showed that both lognormal and Weibull distributions were equally effective for describing the diameter distributions of these Akashmoni plantations grown in the north-eastern region of Bangladesh.     

Characterising the diameter distribution of Sal plantations by comparing normal,lognormal and Weibull distributions at Tilagarh Eco-park,Bangladesh

For many years foresters have been using statistical probability density functions to describe and characterise stand structure. Predicting the current and future yields of a stand is essential for successful stand and timber management. Implicit prediction of current yield is accomplished by using diameter distribution methods. All diameter distribution yield systems predict the number of trees per unit area by diameter class. In this study, the normal, lognormal and the three-parameter Weibull probability density function were compared to characterise the diameter distributions of Sal (Shorea robusta) plantations grown at Tilagarh Eco-park, Bangladesh. Data from 70 plots, established in three plantations, were used for this study. The Weibull parameters were estimated by the maximum likelihood and moments estimator methods. A one-sample Kolmogorov–Smirnov test was used for the goodness of fit for all models. The Kolmogorov–Smirnov test results showed that both lognormal and Weibull distributions were suitable to characterise the diameter distributions of Sal plantations in the study area and may be applicable for other Sal forests in Bangladesh.     

Stand-level diameter distribution yield model for black spruce plantations

The objectives of this study were to develop and demonstrate a stand-level diameter distribution yield model and associated algorithm for black spruce (Picea mariana (Mill.) B.S.P) plantations. Employing a parameter prediction approach within the context of a stand density management diagram (SDMD), model development consisted of four sequential steps: (1) obtaining maximum likelihood estimates for the location, scale and shape parameters of the Weibull probability density function (PDF) for 296 empirical diameter frequency distributions; (2) developing and evaluating parameter prediction equations in which the parameter estimates of the Weibull PDF were expressed as functions of stand-level variables employing stepwise regression and seemingly unrelated regression techniques; (3) explicitly incorporating the parameter prediction equations into the SDMD modelling framework; and (4) developing an associated PC-based algorithm and demonstrating its utility in density management decision-making. The results indicated that the parameter prediction equations described 74.4, 87.1 and 66.8% of the variation in location, scale and shape parameter estimates, respectively. Incorporating the parameter prediction equations into the structure of the SDMD enabled the prediction of the temporal dynamics of the diameter frequency distribution by density management regime, site quality and region. An algorithmic version of the model is provided as a decision-support aid in which forest managers are able to simultaneously contrast multiple density management regimes in terms productivity, product value and optimal site occupancy.     

Tree improvement effects on tree size distributions for Picea glauca and Picea mariana in New Brunswick,Canada

Abstract

Height and diameter distributions between improved and unimproved (checklot) seedlots for white spruce [Picea glauca (Moench) Voss] and black spruce [Picea mariana (Mill.) BSP] were compared using the two-parameter Weibull function. Individual tree height at age 5–15 years and diameter at breast height at age 15 years that were collected from two series of large-plot realized gain tests were used for this purpose. For both species, improved seedlots did not significantly (α=0.05) change the shape parameter of the distributions relative to their checklots, suggesting that an overall shape value will be adequate to predict tree size distributions of various improved seedlots. The most important finding was that seedlot influenced the scale parameter (related to the range of the distribution) significantly, but from a practical viewpoint, only those scale values of the higher rated seedlots (i.e. seedlots collected from a rogued seed orchard or superior families) were significantly higher (α=0.05) than those of the respective unimproved seedlot. The changes in scale value of the alternative improved seedlots relative to the checklot (Δ_Scale) were comparable in magnitude to the respective realized genetic gains, suggesting that tree improvement effects on the scale value can be adjusted by realized genetic gains. The results also suggest that site and age significantly affected the scale value; in general, Δ_Scale became larger at earlier ages or on better sites. The findings reported here will be used in the development of yield functions for genetically improved white and black spruce in New Brunswick.     

基于线性混合模型的落叶松枝条基径模型

以黑龙江省五营林业局丽林林场30株人工落叶松2 190个枝条基径数据为例,利用逐步回归技术建立了落叶松枝条基径模型:BD=b1+b2DINC+b3DINC2+b4DBH.DINC2。然后,利用S-PLUS软件中的LME过程,拟合线性枝基径模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的拟合效果进行比较分析。结果表明:当拟合枝条基径模型时,b1、b2、b3同时作为混合参数时模型拟合最好。为了矫正混合模型构建过程中产生的异方差现象,把幂函数和指数函数加入到枝条基径混合模型中。指数函数显著提高了枝条基径混合模型的拟合效果,并且消除了异方差现象。模型模拟表明:对于大小相同树木,枝条基径随着着枝深度(DINC)的增加而增大,对于大小不同的树木,枝条基径随着胸径(DBH)的增加而增大。林木的胸径变量很好地反映了不同大小树木的枝条基径的变化。在不知道详细林分信息的前提下,可以利用树木变量合理地预测兴安落叶松人工林的枝条基径的变化规律。     

Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function

Diameter distributions of juvenile loblolly pine (Pinus taeda L.) were characterized utilizing a two-parameter Weibull distribution to aid in forecasting and simulation of young stands. Juvenile diameter distributions were studied to gain insight into the effects of various stand-level factors. Results show that diameter distributions in juvenile loblolly pine stands can be successfully characterized with the two-parameter Weibull function. Repeated measures analysis detected significant planting density, age, and age by planting density interaction effects for the scale and shape parameter estimates from the two-parameter Weibull distribution. Using parameter recovery techniques, estimated diameter distributions were derived from easily attainable stand-level characteristics (i.e. basal area per hectare, planting density, age, and quadratic mean diameter). A thorough understanding of juvenile diameter distributions should prove especially useful for operational planning of stands on short rotations that require estimates of productivity at early ages.     

A flexible modeling of irregular diameter structure for the volume estimation of forest stands

Simple distribution models (SDMs) have deficiencies in portraying irregular forest diameter structure. This paper introduces mixture distribution models (MDMs) to improve the estimation accuracy of stand volume of Siberian larch (Larix sibirica Ledeb.) forests. Stand volume was estimated by combining the suitable diameter mixture model and diameter–height model. Appropriate mixture models are derived by integrating multiple SDMs of Burr III and XII, Johnson S_B, Weibull or lognormal probability density functions (pdf) that satisfied the criteria of goodness of fit tests. Results showed that the average bias of volume estimation for all of the study plots using SDM and MDM approaches are underestimated by 6.93 and 2.42 m³, respectively. Each of the estimates is equivalent to an estimation error of 25.59 ± 18.18 and 7.08 ± 2.97 %. This suggests that the MDM approach is a more flexible and suitable modeling technique for forest volume estimation, in particular for forests that have been frequently disturbed by natural events.     

Goodness-of-fit analysis for lumber data

Summary Four different probability distributions were studied to evaluate their relative goodness-of-fit in describing the modulus of rupture (MOR) and modulus of elasticity (MOE) of populations of dimension lumber. The distributions under consideration were the normal, lognormal, Weibull and Johnson's S_B. The populations of lumber consisted of 96 data sets of various species groups, mechanical properties, sizes, structural grades and growth regions. The goodness-of-fit criteria selected in this study were the log likelihood, Kimball and Kolmogorov-Smirnov (K-S) tests. The K-S statistic was also calculated at the value of the random variable associated with the lower five percent exclusion limit of the empirical cumulative distribution. This value indicated the degree of goodness-of-fit at the lower tail of the distribution. The results indicated that the S_B distribution generally provided the best fit to the data. The maximum likelihood test overwhelmingly recommended the S_B distribution. The Kimball and Kolmogorov-Smirnov tests gave milder endorsements of the S_B distribution. No distribution proved to be superior to the others in modeling the lower five percent exclusion limit of the populations.The author would like to thank the Engineering Data Management (EDM) Inc. of Fort Collins, Colorado, for the use of their parameter evaluation software, STAtistical Data MANager     

Determination of mean diameter by basal area in stands of picea abies and pinus sylvestris in southeastern Norway by means of aerial photographs

Mean diameter by basal area (d_g) is an important stand variable for long‐term economic forecasts of forest holdings. In order to use stand‐by‐stand surveys based on aerial photo interpretation as the data basis for forecasts, d_g has to be determined. The objective was to develop and test a regression function for d_g in mature stands of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) applicable in southeastern Norway. A study of 700 plots was used to estimate a function for d_g . An additive model was found to be most suitable. The independent variables were potential yield capacity, Lorey's mean tree height, crown closure determined by ocular estimation by means of aerial photographs, and the product of potential yield capacity and crown closure. The R² value was 0.604 and the coefficient of variation was 10.8%. The regression fitted most parts of the calibration data quite well, but it may overestimate the mean diameter in pure spruce stands by 1–2%, and underestimate the diameter in pure pine stands by 3%. For mixed coniferous stands the regression seems satisfactory. Testing by means of an independent data set showed systematic errors of 3–23%. The systematic errors were due partly to calibration problems in connection with the ocular crown closure estimation.     

Predicting average growth and size distributions of Douglas-fir saplings competing with sprout clumps of tanoak or Pacific madrone

The average growth and size distributions of Douglas-fir (Pseudotsuga menziesii) saplings in three plantations were studied for 7 years (1983–1989) after thinning of associated sprout clumps of tanoak (Lithocarpus densiflorus) or Pacific madrone (Arbutus menziesii); in some cases understory vegetation (shrubs and herbs) was experimentally suppressed. Biologically based nonlinear equations explained 66, 90, and 53% of the variation in the average annual increment of Douglas-fir height, diameter-squared, and cover, respectively. Equations for annual increment of cover of hardwood and understory vegetation explained only 10 to 12% of the variation, because these parameters exhibited a high degree of variability. Model simulations demonstrated that, for the same initial levels of cover, tanoak had faster rates of cover growth than madrone and also caused greater limitations in growth of Douglas-fir. Suppression of understory vegetation increased growth of Douglas-fir only when hardwood cover was absent. Weibull functions adequately described size distributions for Douglas-fir in 92% of the individual-tree data sets. Regression functions of hardwood cover and average Douglas-fir size explained 51, 93, and 24% of the variation in the Weibull A, B, and C parameters, respectively. Model simulations with predicted Weibull parameters demonstrated that hardwood competition caused a positive skewing in size distributions for height and stem diameter of Douglas-fir.     

Goodness-of-fit analysis on wood properties data from six Brazilian tropical hardwoods

As part of a larger effort to develop design stresses for six hardwood species indigenous to tropical Brazil, a study was conducted to evaluate the relative goodness-of-fit of four distributions (normal, lognormal, Weibull, and S_B) that are used in wood related applications to the characterization of the modulus of elasticity (MOE) and modulus of rupture (MOR) data obtained from tests on lumber and clear wood specimens. Three criteria [maximum likelihood, Kimball, and Kolmogorov-Smirnov (K-S)] were used to evaluate the distributions over their entire domain. The K-S test was also employed at the lower tail of the distributions to evaluate goodness-of-fit at this crucial location for design stress development. The results showed that with respect to both MOR and MOE, the S_B distribution was as good or better than the other distributions. This was especially noticeable with the MOR data, since this data is often more skewed than MOE and the S_B is particularly well suited to describe positively and negatively skewed data. The lognormal and the Weibull were both found to be useful under certain circumstances; the normal distribution, due to its lack of ability to characterize anything but symmetrical distributions, was found to be of virtually no value in this application. Significant distinctions were found between the structure of MOR and MOE data sets obtained from the tropical and temperate zone species. For reasons believed to be related to gross and anatomical structure, more skewness was found in the two temperate zone species studied than in the six tropical species. As such, the S_B distribution, with its greater ability to quantify skewed data, performed overwhelmingly better than the other distributions. In describing the six tropical species, the advantage of the S_B distribution was less pronounced. Received 16 November 1998     

Modeling diameter distribution of Austrian black pine (<Emphasis Type="Italic">Pinus nigra</Emphasis> Arn.) plantations: a comparison of the Weibull frequency distribution function and percentile-based projection methods

The main purpose of the present investigation is to examine and compare three methods for diameter distribution modeling in terms of their fitness to predict from stand level variables the diameter distributions of even-aged Austrian black pine (Pinus nigra Arn.) plantations in Bulgaria. The percentile-based projection method involving empirical probability density function based on 12 percentiles was the first method tested. A new modified approach based on the first method was proposed as the second alternative. The third method was the 2-parameter Weibull functional model in which parameters were recovered from the first and the second raw moments and the second central moment of the empirical distributions. The Kolmogorov–Smirnov test was applied to compare the experimental distributions with the predicted ones, and estimation of the error indices was employed to evaluate the total absolute deviation of the predicted numbers from the actual ones by diameter class. The two-parameter Weibull function proved superior to the examined alternative percentile-based projection methods and the newly proposed percentile method, without a driver percentile showed improved precision compared to the classical percentile method (with a driver percentile). The parameters of the Weibull frequency distribution function can be easily recovered from the stand quadratic mean diameter. Consequently, this diameter distribution model could be incorporated as a sub-model for stand horizontal structure characterization within the Stand Density Management Diagram modeling framework.     

Modelling the diameter distribution of Pinus sylvestris, Pinus nigra and Pinus halepensis forest stands in Catalonia using the truncated Weibull function

Parameter prediction models for the diameter distribution ofPinus sylvestris L., Pinus nigra Arn. and Pinus halepensis Mill.in Catalonia were developed using the truncated Weibull functionas the theoretical distribution. The parameter models allowone to use individual-tree models in the simulation of standdevelopment when only stand-level data are collected in forestinventories. Parameter models for the diameter distributionof stand basal area were developed. The data consisted of permanentsample plots from the Spanish National Forest Inventory in Catalonia.A total of 1780 empirical distributions of P. sylvestris, 1204distributions of P. nigra and 1535 distributions of P. halepensiswere used as modelling data. The empirical data represent left-truncateddistributions, as the smallest diameter measured in the fieldwas 7.5 cm. Two different approaches, namely, regression (two-stepmethod) and optimization approach (one-step method), were usedto find the coefficients of the parameter models. In the two-stepmodelling method, the Weibull parameters were first estimatedseparately for every empirical distribution by maximizing thelog-likelihood function of the Weibull density function. Inthe second-step, regression analysis was used to find the relationshipbetween Weibull parameters and stand basal area, number of treesper hectare and elevation of the site. The one-step method usedoptimization to find such coefficients for the parameter models,which minimized the mean of the squared differences betweenempirical and predicted cumulative tree frequencies in the wholemodelling data. The one-step optimization method performed betterthan the two-step regression method for all tree species. Theparameter prediction models developed in this study enable theprediction of the diameter distribution of P. sylvestris, P.nigra and P. halepensis in Catalonia from limited stand information.     

Predicting and calibrating diameter distributions of Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe

Diameter distribution models for even-aged Eucalyptus grandis plantations in Zimbabwe were developed using the two-parameter Weibull function. The analysis was based on data from Correlated Curve Trend (CCT) experiments replicated on four different sites. Parameters of the Weibull distribution were predicted using stand characteristics as regressors. Two sets of parameter models were estimated: a set with and one without stand basal area as a predictor. Stand variables such as dominant height, age, site index and number of stems were used in both sets. The models were further calibrated to result in a given number of stems and stand basal area simultaneously. The usability of constructed models was tested both in prediction of yield in a stand inventory situation and in simulation of growth in connection with different growth models. The results indicated that models not including stand basal area produce considerably less precise stand volume estimates compared to models including also stand basal area. Calibration improved the accuracy of diameter distribution models. In growth simulation diameter distribution models can be connected both to single tree growth models and to stand projection models. The usability of calibration in growth simulation depends on the accuracy of the prediction of stand characteristics.     

Allometric model of the height–diameter curve for even-aged pure stands of Japanese cedar (<Emphasis Type="Italic">Cryptomeria japonica</Emphasis>)

We derived an allometric model of the height–diameter curve for even-aged pure stands, which was a modification of the earlier model proposed by Inoue (2000a). An individual-dependent allometric equation was used as the height–diameter curve. Using the discriminant analysis method, all trees composed of a stand were stratified into upper and lower trees. It was assumed that both relationships between mean tree height H _m and upper tree height H _u and between mean DBH D _m and mean DBH of upper trees D _u could be described by the time-dependent allometric power equations. The height–diameter curve showed an average relationship between tree height and DBH of a given stand at a given time, and hence it could be assumed that the height–diameter curve contained two points (D _m , H _m ) and (D _u , H _u ). With these assumptions, we derived an allometirc model of height–diameter curve, which allowed the coefficients of the curve to be estimated from mean tree height and mean DBH. The proposed model was fitted to Japanese cedar (Cryptomeria japonica D. Don) data. The error ratio of the allometric model ranged from 2.254% to 13.412% (mean = 6.785%), which was significantly smaller than that of the earlier model. When the error of mean tree height was ±1.0 m or less, the effect of the error of mean tree height on the error ratio was comparatively small. This suggested that the error of ±1.0 m in mean tree height could be accepted in the estimation of height–diameter curve using the allometric model. These features enable us to combine the allometric model with Hirata’s vertical angle-count sampling or growth models. In conclusion, the allometric model would be one of the most practical and convenient approaches for estimating the height–diameter relationship of even-aged pure stands.     

Integrated individual tree biomass simultaneous equations for two larch species in northeastern and northern China

Forest biomass estimation at large scale has become an important topic in the background of facing global climate change, and it is fundamental to develop individual tree biomass equations suitable for large-scale estimation. Based on the measured data of biomass components and stem volume from 100 sample trees of two larch species (Larix gmelinii and L. principis-rupprechtii) in northeastern and northern China, an integrated equation system including individual tree biomass equations, stem volume equation and height–diameter regression model were constructed using the dummy variable model and error-in-variable simultaneous equations. In the system, all the parameters of equations were estimated simultaneously, so that the aboveground biomass equation was compatible to stem volume equation and biomass conversion factor (B_CF) function; the belowground biomass equation was compatible to root-to-shoot ratio (R_SR) function; and stem wood, stem bark, branch and foliage biomass equations were additive to aboveground biomass equation. In addition, the system also ensured the compatibility between one- and two-variable models. The results showed that: (1) whether aboveground biomass equations or belowground biomass equations and stem volume equations, the estimates for larch in northeastern China were greater than those in northern China; (2) B_CF of a larch tree decreased with the growing diameter while R_SR increased with the growing diameter; (3) the proportion of stem wood biomass to aboveground biomass increased with the growing diameter while those of stem bark, branch, and foliage biomass decreased.     

An approach to modeling the joint distribution of tree diameter and height data

Advantages of the application of bivariate distribution models to forest management cannot be overemphasized. However, there are quite a number of flexible statistical distributions not yet evaluated in their bivariate domains. Therefore, in this article, we evaluated the bivariate forms of some probability distribution models used in quantitative forestry. Six bivariate distributions were assessed: Burr XII (Burr XII-2), Dagum (Dagum-2), Kumaraswamy (Kum-2), the new Logit-Logistic-Dagum (LLD-2) distribution, Logit-Logistic (LL-2), and the much used Johnson’s S_BB. All models were constructed using the Plackett’s method except for the S_BB distribution. Appropriate constraints were imposed on the boundary parameters of the bivariate distributions using fractions derived from the Gumbel distribution. Models were fitted with maximum likelihood to the joint distribution of diameter and height data of Eucalyptus camaldulensis Dehn from 90 sample plots. Model assessment was based on negative log-likelihood (-ΛΛ), Corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC). The result showed that the Johnson’s S_BB had the overall best performance. Their ranking order was: S_BB > LLD-2 > Burr XII-2 > Dagum-2 > LL-2 > Kum-2. These models can be used to simulate timber harvesting regime.     

Species differences in total and vertical distribution of branch- and tree-level leaf area for the five primary conifer species in Maine, USA

Vertical distribution of leaf area largely governs both tree structure and function. Models of this important tree attribute have been constructed for several commercially important conifers. However, a limited number of studies have compared alternative modeling techniques and inherent species differences. This study used several existing datasets for the five primary conifer species in Maine, namely balsam fir [Abies balsamea (L.) Mill.], northern white-cedar [Thuja occidentalis (L.)], eastern hemlock [Tsuga canadensis (L.) Carr.], eastern white pine [Pinus strobus (L.)], and red spruce [Picea rubens (Sarg.)] to examine species variation in total and vertical distribution of projected leaf area at the individual branch- and tree-levels. In addition, multiple methods for modeling the vertical distribution of leaf area were examined across the species. For a given branch diameter and location within the crown, eastern hemlock branches held the greatest amount of leaf area, followed by balsam fir, northern white-cedar, white pine, and red spruce. At the tree-level, eastern white pine held the greatest amount of leaf area followed by eastern hemlock, balsam fir, red spruce, and northern white-cedar for a given tree size. Across species, the two-parameter, right-truncated Weibull distribution performed the best for predicting vertical distribution of leaf area when compared to the four-parameter beta and Johnson's S_B distributions (reduction of root mean square error of 1.7–21.1%). Northern white-cedar had a relative distribution of leaf area distinctly different than other species in this study with a mode shifted towards the upper crown. In contrast to red spruce and white pine, the mode of the relative distribution of leaf area for balsam fir and eastern hemlock occurred lower in the crown. Results of this study suggest that differences in total and vertical distribution of leaf area exist between species, but significant amounts of their variation are largely accounted for by bole and crown size.