Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta,Canada

Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within- and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance–covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating tree-specific predictions of diameter inside bark, whole tree volume, and sectioned log volume.     

Selection of mixed-effects parameters in a variable–exponent taper equation for birch trees in northwestern Spain

Context

Taper equations predict the variation in diameter along the stem, therefore characterizing stem form. Several recent studies have tested mixed models for developing taper equations. Mixed-effects modeling allow the interindividual variation to be explained by considering both fixed-effects parameters (common to the population) and random-effects parameters (specific to each individual).

Aims

The objective of this study is to develop a mixed-effect variable exponent taper equation for birch trees in northwestern Spain by determining which fixed-effects parameters should be expanded with random-effects parameters.

Methods

All possible combinations of linear expansions with random effects in one and in two of the fixed-effects model parameters were tested. Upper stem diameter measurements were used to estimate random-effects parameters by the use of an approximate Bayesian estimator, which calibrated stem profile curves for individual trees.

Results

Parameter estimates for more than half of the mixed models investigated were nonsignificant. A first order autoregressive error structure was used to completely remove the autocorrelation between residuals, as mixed-effects modeling were not sufficient for this purpose.

Conclusion

The mixed model with the best fitting statistics did not provide the best calibration statistics for all upper stem diameter measurements. From a practical point of view, model calibration should be considered an essential criterion in mixed model selection.     

Effects of environmental changes on the vitality of forest stands

Using the physiological single tree growth model BALANCE, vitality of forest stands was simulated in dependence of the site-related factors, climate and stand structure. At six level II plots in southern Germany with the main tree species beech (Fagus sylvatica L.), oak (Quercus robur L.), spruce (Picea abies [L.] Karst.), and pine (Pinus sylvestris L.), simulated results were compared to measured values (soil water content, bud burst and leaf colouring, diameter at breast height, tree height and crown density) in order to validate the model. Sensitivity tests were done to examine the influence and the interactions of the environmental parameters. The validation results show that BALANCE is capable of realistically simulating the growth and vitality of forest stands for central European regions for medium term time spans (several years). The validation of the water balance module produces mean absolute errors based on field capacity between 2.7 and 6.9% in dependence of sites and forest stands. Senescence of foliage as well as crown density is reproduced with a correlation coefficient of 0.70 compared to measurements. Differences between measured and simulated diameter values were smaller than 1% for spruce and smaller than 6.5% for beech after 7 years of simulation, and smaller than 1% for oak after 8 years of simulation. On the other hand, the simulations for pine trees conform less with the measurements (difference: 22.6% after 8 years). The sensitivity of the model on environmental changes and on combinations of these parameters could be demonstrated. The responses of the forest stands were quite different.     

Regional mixed-effects height–diameter models for loblolly pine (<Emphasis Type="Italic">Pinus taeda</Emphasis> L.) plantations

A height–diameter mixed-effects model was developed for loblolly pine (Pinus taeda L.) plantations in the southeastern US. Data were obtained from a region-wide thinning study established by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. The height–diameter model was based on an allometric function, which was linearized to include both fixed- and random-effects parameters. A test of regional-specific fixed-effects parameters indicated that separate equations were needed to estimate total tree heights in the Piedmont and Coastal Plain physiographic regions. The effect of sample size on the ability to estimate random-effects parameters in a new plot was analyzed. For both regions, an increase in the number of sample trees decreased the bias when the equation was applied to independent data. This investigation showed that the use of a calibrated response using one sample tree per plot makes the inclusion of additional predictor variables (e.g., stand density) unnecessary. A numerical example demonstrates the methodology used to predict random effects parameters, and thus, to estimate plot specific height–diameter relationships.     

基于非线性混合模型的东北兴安落叶松树高和直径生长模拟

以黑龙江省带岭林业局大青川林场80株人工兴安落叶松解析木数据为例,采用Richards生长模型作为基础模型,利用S-PLUS软件中的NLME过程,分别拟合非线性树高和直径生长模型。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精度进行比较分析。结果表明:当对树高-年龄关系进行拟合时,b1、b3同时作为混合参数时模型拟合最好;当对直径-年龄关系进行拟合时,b1、b3同时作为混合参数时模型拟合最好。把相关性结构包括一阶自回归结构AR(1)、一阶移动平均结构MA(1)及一阶自回归与移动平均结构[ARMA(1,1)]加入到树高和直径最优混合模型中,一阶自回归结构AR(1)显著提高了树高混合模型的拟合精度,一阶移动平均结构MA(1)显著提高了直径混合模型的拟合精度。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。因此,混合模型在应用上不但能反映树高和直径的平均预测趋势,还能用方差协方差结构和误差相关性结构校正随机参数来反映个体之间的差异。     

Biomass equations for seven different tree species growing in coppice-with-standards forests in Central Germany

With an increasing demand of sustainable raw materials for bioenergy use, coppicing as management approach to increase the biomass production of forests is becoming of greater importance. This study describes the parameterization of biomass equations for six tree species traditionally used in coppices forests, namely sycamore maple (Acer pseudoplatanus L.), field maple (Acer campestre L.), European ash (Fraxinus excelsior L.), European hornbeam (Carpinus betulus L.), downy birch (Betula pubescens Ehrh.), and common hazel (Corylus avellana L.) growing in coppice-with-standard systems in Lower Saxony, Germany. The parameterization was based on measurements of over 950 trees sampled from two forest sites. The sampled trees were felled and separated into three biomass compartments (stem, coarse branches, and fine brushwood) and weighed on site. The dry weight of sub samples from each compartment was measured. Equations were derived for total aboveground biomass, stem biomass, and crown biomass using regression analyses. We either used diameter at breast height as single independent explanatory variable or in combination with tree height. Biomass production of stump sprouts and generatively grown stems was compared for ash and sycamore maple. In the same age classes, it was found that ash stump sprouts had a slightly higher production than seed-grown stems. For sycamore maple, no difference was detected.     

Biomass,stem basic density and expansion factor functions for five exotic conifers grown in Denmark

Adequate allometric equations are needed for estimating carbon pools of fast growing tree species in relation to international reporting of CO₂ emissions and for assessing their possible contribution to increasing forest biomass resources. We developed models for predicting biomass, stem basic density and expansion factors of stem to above-ground biomass for five fast growing conifers. Data included destructive measurements of 236 trees from 14 sites, covering a wide range of growth conditions. To ensure model efficiency, models for predicting stem, crown and total above-ground biomass for the five species were estimated simultaneously using a linear, mixed effects model that allowed contemporaneous correlations between the different tree components. Models differed among species and included dbh and tree height. The models explained more than 98% of the variation in above-ground biomass and reflected differences in the allometry between tree species. Stem density differed among species but generally declined with increasing site index and dbh. The overall model for predicting stem basic density included dbh, H₁₀₀ and site index and explained 66% of the total variation. Expansion factors decreased from 1.8–2.0 in small trees (dbh < 10 cm) to 1.1–1.2 for large trees (dbh > 25 cm), but differed among species. The overall model explained 86% of the variation and included quadratic mean diameter and dbh.     

Development and validation of a stem volume equation for Cupressus lusitanica in Gergeda Forest,Ethiopia

Stem volume equations were fitted for Cupressus lusitanica in Gergeda Forest, Ethiopia using six different established equation forms. A total of 260 trees were measured for their diameter at breast height (D), total height (H?)and stem volume using destructive sampling methods. The data set was randomly divided into equal size for equation development and equation validation. Five fit statistics comprising of the fit index, root mean square error, bias (ē?), absolute mean deviation and coefficient of variation were used to evaluate the performance of each equation. Among the different equations, the Schumacher and Hall function of the form V = b₁D^b2H^b3 (model 5), which estimates volume (V?) using diameter at breast height and total height as predicting variables, performed best and was then fitted to the combined data set for prediction of volume over-bark of C. lusitanica in Gergeda Forest. Overall, volume equations with two independent variables (D and H?) performed better than those with only one variable (D). The equations developed in this study can provide forest managers with accurate estimations of stem volumes for C. lusitanica in Gergeda Forest.     

A simple stem taper model with mixed effects for boreal black spruce

We simplified Kozak’s taper model by setting the inflection point at 1.3 m (dbh) without losing accuracy and precision. The simplification was required to facilitate the estimation of the covariance parameters when using a mixed-effects method. This method was necessary to take into account the correlation among multiple diameter measurements on an individual stem. The simple stem taper model was fitted to an extended data set collected across the province of Quebec, Canada. Comparison of the predicted stem taper and the derived stem volume with those obtained using existing models showed a comparable predictive power for the simple model. Including a prediction of the tree random effects based on supplementary diameter measurements of the bole improves the predictive ability of the model around the extra diameter observation. This model offers welcome simplicity as a means of predicting tree taper at coarse resolution for planning tree harvesting.     

A comparison between three different methods of measuring knot parameters in picea abies

Both foresters and sawmillers are interested in the knot structure of trees; in particular, position and number of knots, knot diameter, knot length and dead knot border. For research purposes, it is possible today to carry out non‐destructive measurements using computer tomography (CT) and image analysis. The aim of this study was to measure knot parameters on Norway spruce (Picea abies (L.) Karst.) using a non‐destructive method developed for Scots pine (Pinus sylvestris L.), and to compare the results of this method with the results of two different destructive methods. In order to do this, two Norway spruce stems were scanned by CT. Then five logs from one stem were cut into flitches 20 mm thick and the defects on the sawn surfaces were scanned manually. The other stem was cut just above every whorl and then each knot was split through its centre and the knot parameters were measured manually. The study showed that the CT method compares well with the destructive methods. It is a reasonably fast, non‐destructive method which measures position and diameter of knots and detects larger knots with acceptable accuracy. The study also showed that a large number of smaller knots were not found by the CT method and that the CT method measured knot length and dead knot border with low accuracy. This means that the CT method has to be adjusted to Norway spruce in order to improve its ability to measure knot length and dead knot border and to detect smaller knots.     

Modelling day-to-day stem diameter variation and annual growth of balsam fir (Abies balsamea (L.) Mill.) from daily climate

In the present context of global climate changes and the continuous development of forest management strategies based on the concept of sustainable use, it is important to develop a better understanding of the climatic factors controlling the growth of boreal forests. In this study, we report the results of a five-year field research within which day-to-day balsam fir (Abies balsamea (L.) Mill.) stem diameter variation was measured with dendrometers and examined in relation with various daily climatic variables. A model built with data from three growing seasons that included solar radiation, relative humidity, temperature and precipitation explained 84% of the variance in day-to-day stem diameter variation from June to September. The model has approximately the same predictive capability when validated with independent daily data from two other growing seasons. The model captured both the cumulative increment associated with the irreversible growth and the high frequency variation of day-to-day fluctuations associated to changes in the stem water content. In general, rainy days during which relative humidity was high and solar radiation was low favored stem diameter expansion (growth and swelling) while stem diameter decreased during periods of low relative humidity and high solar radiation. Similar models were obtained when the June-September period was divided into two parts (June-July and August-September) to better represent the period during which most of the cumulative annual stem increment is observed (June-July). Inter-annual variation in stem growth computed from the modeled day-to-day variation in stem diameter was significantly correlated to the inter-annual variation in annual growth determined from tree core measurements over a 10 year period (p = 0.023). The model was notably able to capture a particularly poor growing year (2006) presumably due to a short-term heat stress period. Results suggest that the inclusion of daily data in growth-climate models may contribute to improve predictions of the potential tree growth response to climate by identifying particular climatic events that may escape to a classical dendroclimatic approach.     

Development and validation of stem volume models for Pinus kesiya in Benguet province,Philippines

Stem volume equations (overbark) were developed, using established volume equation forms, and validated using a subset of the data collected for Pinus kesiya in Benguet province, Philippines. A total of 481 trees from Pinus kesiya stands in Benguet were measured through non-destructive sampling. The data set was randomly split into two subsets for initial model development (80% of the data set) and validation (20% of the data set). The performance of the different models was evaluated using evaluation statistics: fit index (FI), root mean square error (RMSE), bias (ē), absolute mean difference (AMD) and coefficient of variation (CV%). The best model forms were selected for final model development using the combined data set (100%). Overall, volume models with two independent variables (DBH and total height) performed better than models with only one (DBH). In the validation of the models, it was observed that AMD of the models converged in the DBH classes with higher sample size. Furthermore, one of the best models in this study, Model 2, also performed better when compared to the general single volume equation developed for the non-dipterocarp species in regions 1, 2, 3 and the Cordillera Administrative Region (CAR) of the Philippines. The models developed in this study may assist forest managers acquire improved stem volume predictions of Pinus kesiya in the forests of Benguet, Philippines.     

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 evaluation of the conical approximation as a generic model for estimating stem volume, biomass and nutrient content in young Eucalyptus plantations

Accurately and non-destructively quantifying the volume, mass or nutrient content of tree components is fundamental for assessing the impact of site, treatment, and climate on biomass, carbon sequestration, and nutrient uptake of a growing plantation. Typically, this has involved the application of allometric equations utilising diameter and height, but for accurate results, these equations are often specific to species, site, and silvicultural treatment. In this study, we assessed the value of incorporating a third piece of information: the height of diameter measurement. We derived a more general volume equation, based on the conical approximation, using a diameter projected to the base of the tree. Common equations were developed which allowed an accurate estimate of stem volume, dry weight and nutrient content across two key plantation grown eucalypt species, Eucalyptus grandis W. Hill ex Maiden and Eucalyptus globulus (Labill.). The conical model was developed with plantation-grown E. grandis trees ranging from 0.28 to 15.85 m in height (1.05 g to 80.3 kg stem wood dry weight), and E. globulus trees ranging from 0.10 to 34.4 m in height (stem wood dry weight from 0.48 g to 652 kg), grown under a range of contrasting cultural treatments, including spacing (E. grandis), site (E. globulus) and fertilization (nitrogen and phosphorus) for both species. With log transformed data the conical function (V_con) was closely related to stem sectional volume over bark and stem weight (R² = 0.996 and 0.990, respectively) for both E. grandis and E. globulus, and the same regressions can be applied to both species. Back transformed data compared with the original data yielded modelling efficiencies of 0.99 and 0.97, respectively. Relationships between V_con and bark dry weight differed for the two species, reflecting differing bark characteristics. Young trees with juvenile foliage had a different form of relationship to older trees with intermediate or adult foliage, the change of slope corresponding to heights about 1.5 m for E. grandis and age 1 year for E. globulus. The V_con model proved to be robust, and unlike conventional models, does not need additional parameters for estimating biomass under different cultural treatments. More than 99% of the statistical variance of the logarithm of biomass was accounted for in the model. V_con captures most of the change in stem taper associated with cultural treatments and some of the change in stem form that occurs after the crown base has lifted appreciably. Fertilization increased N and P concentrations in stem wood and bark, and regressions to estimate N and P contents (the products of biomass and concentration) were dependent on treatment. For instance, there was a large growth response to N fertilization in E. globulus corresponding with a change (P < 0.05) in the intercept of the regression to estimate N content.     

Volume growth and wood density of plus tree progenies of Pinus contorta in two Swedish field trials

Seventy‐four half‐sib families of lodgepole pine (Pinus contorta ssp. latifolia Engelm.) plus trees were measured for vigour, height growth, stem diameter, wood density and ring width in two Swedish field trials at age 9. Height growth, wood density and ring width differed between families within provenances with variance components of 3–8 %. Coefficients of variation were highest for height growth and lowest for ring width. Heritabilities were similar for height growth and wood density but lower for ring width. These genetic parameters seemed to be equal for all provenances. Indirect selection for high dry stem biomass was more effective using height growth than wood density, and a correlated response in wood density of 2.1 % of mean by selecting the 15 highest parent trees was indicated. Juvenile wood density looks uncertain as a selection criterion for mature wood density.     

基于树高和树冠因子的立木材积模型研究

[目的]由于激光雷达技术已经能准确测定立木树高及相关树冠因子,应用该技术建立基于树高和树冠因子的立木材积模型,为激光技术在森林蓄积估计中提供技术支撑.[方法]利用云杉、冷杉、栎树、桦树4个树种组的3 010株实测样木数据,分析了立木材积与胸径、树高、树冠因子之间的相关关系;并通过对数回归方法构建了基于树高和树冠因子的立木材积模型,用确定系数R²和平均预估误差MPE等6项指标对模型进行评价.[结果]表明,立木材积与单一因子之间的相关,以胸径最为紧密,其次是树高,再次是冠长和冠幅.基于树高和树冠因子的立木材积模型中,以树高和冠幅作为解释变量的二元模型效果较好,再增加冠长因子的三元模型改进不大.云杉、冷杉、栎树、桦树4个树种组基于树高冠幅的立木材积模型,其R²分别为0.81、0.80、0.76和0.77,MPE分别为4.7%、5.3%、5.4%和5.3%,模型预估精度均能达到95%左右.[结论]本文对材积与林木因子之间相关关系的定量分析,建立了云杉、冷杉、栎树、桦树4个树种的立木材积模型,模型预估精度高.为激光雷达技术定量估测森林参数提供了依据.     

25年生大花序桉种源生长与形质性状的遗传变异及选择

[目的]研究广西国有东门林场25年生大花序桉种源生长与形质性状的遗传变异,筛选优良种源及单株,为大花序桉良种繁育及中大径材培育提供优质遗传材料。[方法]采用方差分析、构建性状选择指数方程综合分析等方法,对11个大花序桉种源进行生长与形质性状遗传变异分析及选择。[结果]表明:大花序桉胸径(DBH)、树高(H)、单株材积(V)、树干通直度(ST)和树干圆满度(SF)在种源间呈极显著差异;上述5个主要性状的种源遗传力(H2)为0.634 0.895,单株遗传力(h2)为0.136 0.342;以DBH、H、V、ST和SF 5个性状指标构建大花序桉种源/单株选择指数方程,按标准选择出4个优良种源和13株优良单株,优良种源平均材积遗传增益达11.2%,优良单株平均材积遗传增益达29.7%,选择效果尚好。[结论]大花序桉5个主要性状遗传变异在种源水平受中度至较强遗传控制,在单株水平受弱度遗传控制。优良种源D47、S14127、B47和S12195生长材性兼优,可用作培育优质中大径材。     

Modelling dimensional growth of three street tree species in the urban forest of the City of Tshwane,South Africa

Tree height, crown height, crown diameter and stem diameter were measured for 282 trees of the indigenous species Combretum erythrophyllum, Searsia lancea and S. pendulina. Growth relationships were modelled using age as explanatory variable for stem diameter and subsequently stem diameter as explanatory variable for tree height, crown height and crown diameter. Coefficients are presented for predicting tree dimensions using a logarithmic function. There were strong correlations for stem diameter and age (r ² ≥ 0.75), and crown diameter and stem diameter (r ² ≥ 0.74) for all three of the species investigated. Correlations were weaker for tree height and stem diameter (r ² ≥ 0.63), and crown height and stem diameter (r ² ≥ 0.60) for S. pendulina but stronger for both C. erythrophyllum (r ² ≥ 0.83) and S. lancea (r ² ≥ 0.70) in both instances. The results can be used in forecasting the physical dimensions of these species as a function of time. The results could also be used in the process of modelling energy use reduction, air pollution uptake, rainfall interception, carbon sequestration and microclimate modification of urban forests such as those found in the City of Tshwane.     

Modelling diapause termination and phenology of the Japanese beetle,Popillia japonica

We deve?loped a mechanistic, stage-structured model simulating the phenology of Popillia japonica. The model simulates the influence of soil temperature on the larval diapause termination and on the development rate function of post-overwintering larvae and pupae. Model parameters are estimated based on literature evidence for pupae development and on a parameterisation process that allows estimating parameters for larval diapause termination and for the development rate function (and the related uncertainty) of post-overwintering larvae. Data used for model parameterisation and validation refer to time-series adult trap catches collected during the P. japonica monitoring programme performed by the Phytosanitary Service of Lombardy Region within the infested area in Lombardy (Italy) from 2015 to 2019. A total of 12 randomly selected locations are used to estimate biologically realistic model parameters (parameterisation dataset). We applied a Jackknife nonparametric resampling procedure on the parameterisation dataset to quantify uncertainty associated with parameters’ estimates. Parameterised model is then validated on time-series adult trap catches data referring to a different set of 12 randomly selected locations (validation dataset) surveyed in Lombardy. The model successfully predicted the beginning of adult emergence and the overall curve of adult emergence in the validation dataset. The model presented can support the definition of the best timing for the implementation of monitoring and control activities for the local and the area-wide management of P. japonica.

     

Trends in allometric models and aboveground biomass of family Rhizophoraceae mangroves in the Coral Triangle ecoregion,Southeast Sulawesi,Indonesia

This study aims to establish allometric models and estimate aboveground biomass (AGB) of mangroves Rhizophoraceae in the Southeast Sulawesi, Indonesia. Allometric models of the AGB of mangroves Rhizophora apiculata, R. mucronata, and Ceriops tagal were established using independent variables consisting stem diameter at 30 cm from the ground (D₃₀), diameter at breast height (DBH), D₃₀²H and DBH²H. The AGB of mangroves was estimated by applying allometric model and tree census. The results showed that the best fitting allometric models of AGB for R. apiculata is based on variable DBH, while DBH²H is the best variable for R. mucronata trees. Conversely, the D₃₀ is the best variable for estimating AGB of C. tagal trees. Thus, there is some variation of independent variables on allometric models for the estimation of AGB for Rhizophoraceae mangroves. The AGB (ton ha^?1) of R. apiculata, R. mucronata, and C. tagal was estimated respective 651.60, 232.11 and 154.56 in the protected area, and respective 137.59, 189.35 and 39.06 ton ha^?1 in the unprotected area. Higher AGB of mangroves growing in the protected area indicated the suitable condition and undisturbed by human activities. The conservation of mangroves is necessary for the sustainability of mangroves and coastal ecosystems in the Coral Triangle ecoregion.