An individual tree height increment model for mixed white spruce–aspen stands in Alberta,Canada

Individual tree-height increment models were developed for white spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.) growing in the boreal mixed-species in Alberta. The models were formulated based on a selected base function (the Box–Lucas function), and the method of parameter prediction. Height increment was modeled as a nonlinear function of tree height, tree diameter, diameter increment, stand density, relative competitiveness of the tree in the stand, site productivity, and species composition. Since the data from permanent sample plots used in this study were time-dependent and cross-sectional, diagnostic techniques were applied to identify the models' error structure. Appropriate fits based on the identified error structure were accomplished using the nonlinear least squares procedures with a first-order autoregressive process. The models were also validated on independent testing data sets representing the population on which the models are to be used. Results showed that the average prediction biases were not significantly different from zero at α = 0.05, suggesting that the fitted models appropriately described the data and performed well when predictions were made. Biological implications of the variables that affect height increment in mixed-species stands were discussed.     

Allometric equations from a non-destructive approach for biomass prediction in natural forest and plantation in West Africa

Allometric equations are required for a rapid estimation of commercial timber volume and forest biomass stocks. In order to preserve the forest ecosystem, this study applied a non-destructive sampling approach to measure biophysical properties of living trees. From these measurements, volume and biomass models were developed for 11 dominant tree species in a semi-deciduous natural forest and for Acacia auriculiformis in a plantation located in southern Benin. The observations were combined to develop also generic models applicable to non-dominant tree species. Wood samples of the tree species were collected with an increment borer and analysed in the laboratory to determine species-specific wood densities. The sample size was composed of 243 trees in natural forest and 21 trees in plantation. The measurements were conducted in 30 plots of 50 m × 50 m. The graphical assessment of correlation between model outputs (biomass and volume) and variables (diameter and height) and the statistical analysis confirmed that the logarithmic model with two variables had the best predictions. The assessment also confirmed that the model using diameter only as a variable had good predictions when observations on height were unavailable. The comparative analysis of model predictions showed that the generic model in this study over-estimated biomass by up to 74.80% for certain species and under-estimated biomass by 21.18% for other species. The study shows that there are no statistically significant differences between the wood densities in this research and that published in previous studies.     

Models for predicting tree and stand development on larch plantations in Hallormsstaður,Iceland

The aim was to model the growth of Siberian larch (Larix sibirica Ledeb.) and Russian larch (Larix sukaczewii Dyl., syn. L. sibirica var. sukaczewii) plantations in Hallormsstaeur, Iceland. The field inventory was carried out in eastern Iceland in June 2006. Models were constructed for predicting dominant height, total tree height and 5-year diameter increment. Several linear and non-linear forms of models were tested in preliminary analyses to find the equations that fitted the modelled characteristics best. Due to the spatially hierarchical correlation structure of the data (stands, plots and trees), the assumption of non-correlated error terms did not hold. Therefore, a random parameter modelling approach was adopted using mixed models when the estimates obtained for the random effects were statistically significant. The variance estimates for the random effects can be further used to calibrate the models. The models generated here performed well with independent test data and were consistent with the forest growth theory. They can be used to evaluate site quality and to estimate the growth and yield of larch stands in eastern Iceland in connection with forest planning.     

A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria

Because of the gradual shift from pure even-aged forest management in central Europe, existing yield tables are becoming increasingly unreliable for forest management decisions. Individual tree-based stand growth modeling can make accurate stand growth predictions for the full range of conditions between pure even-aged and mixed-species uneven-aged stands. The central model in such a simulator is basal area increment for individual trees. Spatial information is not needed, and age and site index are intentionally not used to gain generality for all possible stand conditions. A basal area increment model is developed for all the main forest species in Austria: spruce (Picea abies), fir (Abies alba), larch (Larix decidua), Scots pine (Pinus sylvestris), black pine (Pinus nigra), stone pine (Pinus cembra), beech (Fagus silvatica), oak (Quercus robur, Quercus petraea and Quercus cerris), and for all other broadleaf species combined. The Austrian National Forest Inventory provided 5-year basal area increment from 44 761 remeasured trees growing on 5416 forested plots in the 1980s. This large sample is representative of forest conditions and forest management practices throughout Austria and therefore provides an excellent data base for the development of an increment model. The resulting increment model explained from 20 to 63% of the variation for all nine species and from 33 to 63% of the variation if the minor species Pinus cembra is excluded. These results compared quite closely with those of Wykoff for mixed conifer stands in the Northern Rocky Mountains. In the Austrian model, size variables (breast height diameter and crown length) accounted for 14–47% of the variation in basal area increment, depending on tree species. The best competition measure was the basal area of larger trees, which provides a tree-specific measure of competition without requiring spatial information; crown competition factor provided only minor improvement. Competition variables accounted for 9% of the variation on average, and up to 15% for some species. Topographic factors (elevation, slope, aspect) explained up to 3% of the variation, as did soil factors. Remaining site factors; such as vegetation type and growth district accounted for a maximum of 3% of the variation in increment. In total, site factors explained from 2 to 6% of the variation. Even though site factors account for a small percentage of the variation, they are not only significant, but serve to localize a particular prediction. These species-specific interrelationships between basal area increment and the various size, competition, and site varibles correspond quite well with ecological expectations and silvicultural understanding of these species in Austria. Because the sample base is so strong, the resulting growth models can be recommended not only for all of Austria but for surrounding regions with similar growth conditions.     

基于两层次线性混合效应模型的杉木林单木胸径生长量模型

基于两层次线性混合效应模型方法,建立江西省杉木人工林单木胸径生长量模型.研究所用数据来自于长期观测的固定样地数据,数据库包括82个区域、365个样地、5416株树木共计16248条记录.为了解决不同区域及不同样地之间的差异,本文构建的混合模型分别考虑样地层次、区域层次及两层次的随机参数效应.针对数据存在的重复测量及嵌套结构特性,在模拟时选择合适的异方差和自相关模型矩阵来解决此类问题.最后利用独立的抽样验证数据对模拟结果进行验证.结果表明:林分断面积、对象木胸径、林分内大于对象木的断面积之和与对象木胸径的比值以及海拔对单木胸径生长量有显著影响.与林业中常用的传统最小二乘方法相比,采用混合效应模型方法后模型的模拟精度和验证精度均有提高.选择适合的异方差和自相关函数后,模型比只考虑参数的随机效应有更好的适应性,并体现出了混合效应模型的灵活性和准确性.     

米老排人工林生长规律的研究

应用广西大青山2～26年生米老排人工林试验样地数据和树干解析木资料,研究其幼林生长节律及与气候的关系,以及成熟林的生长规律.研究结果表明:(1)米老排幼林生长的季节变化呈双峰曲线,5月和9月生长量最大,月生长量与月均气温相关性显著;(2)早期速生特性明显,胸径、树高连年生长和年均生长高峰均在3～4年生时出现,且高速生长期持续较长;(3)材积生长伴随树高和胸径的快速生长后,于6年生时出现第1次生长高峰,连年生长量达0.023 4 m3;6～15年生材积年生长量最大,15～17年生平均生长量达最高峰,并与连年生长量曲线相交,因此确定此林龄为材积生长的数量成熟龄.     

Sheep grazing in young oak Quercus spp. and ash Fraxinus excelsior plantations: vegetation control, seasonality and tree damage

An experiment was carried out where sheep were grazed in temporary fenced paddocks at a stocking rate of 178 LSU ha⁻¹ in a 5-year old broadleaf plantation of oak (Quercus spp.) and ash (Fraxinus excelsior) (1.5 m spacing) on fertile, former lowland pasture in Northern Ireland. The grazing regime was rotational and intensive, with two grazing periods of 5 days in February and October 2001. Results showed that a significant proportion of the rank herbage height was removed within the first 24 h of livestock introduction. Herbage biomass was reduced by approximately half after 5 days. Sward height in grazed plots remained significantly lower than control plots for over 6 months after cessation of grazing, whilst biomass remained significantly lower for over 4 months after cessation of grazing. No significant tree damage to either oak or ash was measured during the February grazing trial, however significant damage to the lateral branches of both oak and ash was observed in the October grazing trial. Leader damage did not occur on trees greater than 152 cm. Ash was more commonly browsed than oak. Annual height increment of both tree species was unaffected by grazing, but annual stem diameter increment was significantly reduced in both oak and ash in February grazed plots. Oak trees in both February and October grazed plots were found to have a significantly smaller annual increase in canopy diameter than those in control plots. Results are discussed with regard to practical implementation of controlled grazing in young broadleaf forestry plantations on fertile, lowland soils.     

Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model

A diameter increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in the United States using a multilevel linear mixed model. Stochastic variability is broken down among period, locale, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, site index, and competition indices are included in the model as fixed effects in order to explain residual variability. The data set used in this study came from long-term permanent research plots in even-aged, pure stands both planted and of natural origin. The data base consists of six levels-of-growing stock studies supplemented by initial spacing and other permanent-plot thinning studies for a total of 310 plots, 34,263 trees and 153,854 observations. Regression analysis is the preferred technique used in growth and yield modeling in forestry. We choose the mixed effects models instead of the regression analysis approach because it allows for proper treatment of error terms in a repeated measures analysis framework. Regional growth and yield models exist for ponderosa pine. However, data collection and analysis procedures differ. As a result, comparisons of growth responses that may be due to geographic variation of the species are not possible. Our goal is to present a single distance-independent diameter increment model applicable throughout the geographic range of ponderosa pine in the United States and by using only data from long-term permanent plots on sites capable of the productivity estimated by Meyer [Meyer, W.H., 1938. Yield of Even-Aged Stands of Ponderosa Pine. US Department of Agriculture Technical Bulletin 630].     

Estimating and predicting bark thickness for seven conifer species in the Acadian Region of North America using a mixed-effects modeling approach: comparison of model forms and subsampling strategies

In many situations, information on stem diameters inside bark (dib) are more desirable than on diameters outside bark (dob). However, obtaining dib measurements is usually expensive, time-consuming, and prone to significant measurement errors when done on standing trees. Many bark thickness equations have been proposed to estimate the dibs of standing trees. In this study, we compared several commonly used bark thickness equations for seven conifer species in the Acadian Region of North America. Mixed-effects modeling techniques were employed to fit linear and non-linear bark thickness equations. We found the equation proposed by Cao and Pepper (South J Appl Forestry 10:220?C224, 1986; Eq. 5) performed significantly better than other equations for most of our study species. The Cao and Pepper (South J Appl Forestry 10:220?C224, 1986) equation is a function of dob, relative height in the stem, tree height, and the ratio of dib to dob at breast height. The mean absolute bias was found to be reduced up to 74% compared with using a fixed ratio approach employed in the widely used Northeastern variant of the Forest Vegetation Simulator (FVS-NE) growth and yield model. Leave-one-out cross validation was further performed to determine the location of suitable prior measurements in the prediction process for three of the most well-behaved equations. Results show that no unified prior measurement can provide best predictive abilities across all species as the choice of prior dib measurements depends on both species and bark thickness equations.     

Individual tree height increment model for managed even-aged stands of ponderosa pine throughout the western United States using linear mixed effects models

A height increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in western United States. The data set used in this study came from long-term permanent research plots in even-aged, pure stands both planted and of natural origin. The data base consists of six levels-of-growing stock studies supplemented by initial spacing and other permanent-plot thinning studies for a total of 310 plots, 34,263 trees and 122,082 observations. Regression analysis is the most commonly used statistical method in forest modeling. However, research studies with repeated measurements are common in forestry and other biological disciplines. We choose the mixed models instead of the regression analysis approach because it allows for proper treatment of error terms in a repeated measures analysis. The model is well behaved and possessed desirable statistical properties. Our goal is to present a single height increment model applicable throughout the geographic range of ponderosa pine in the United States and by using only data from long-term permanent plots on sites capable of the productivity estimated by Meyer [Meyer, W.H., 1938. Yield of Even-aged Stands of Ponderosa Pine. US Department of Agriculture Technical Bull. 630].     

Response to canopy opening does not act as a filter to Fagus sylvatica and Acer sp. advance regeneration in a mixed temperate forest

? In mixed-species forest stands, large losses in tree species diversity often occur during the regeneration phase. In a former coppice-with-standards, we investigated whether the limiting stage in the recruitment process of advance regeneration is the immediate seedling response to canopy release. Experimental canopy gaps were opened and the survival and growth of advance seedlings (Fagus sylvatica, Acer pseudoplatanus, Acer campestre, Acer platanoides) growing in the gaps or under closed canopy were monitored for three years.

? All species responded positively and rapidly to canopy release. Survival was not affected by gap opening. Diameter increment after gap opening was similar across species, and height increment was greater for Acer platanoides and for Acer pseudoplatanus. Post-release diameter and height growth were mainly determined by pre-release seedling size. Competition from neighbouring seedlings did not affect growth in the three years following canopy opening.

? In the recruitment process of F. sylvatica and Acer sp. advance regeneration, the recovery from canopy release did not appear as a limiting step that would filter against some species. Pre-release size was the main factor accounting for post-release growth and is probably a major determinant of long-term seedling dominance.

     

Total tree,merchantable stem and branch volume models for miombo woodlands of Malawi

The objective of this study was to develop general (multispecies) models for prediction of total tree, merchantable stem and branch volume including options with diameter at breast height (dbh) only, and with both dbh and total tree height (ht), as independent variables. The modelling data set was based on destructively sampled trees and comprised 74 trees from 33 tree species, collected from four forest reserves located in different ecological zones of Malawi. The dbh and ht ranges for the data set were 5.3–111.2?cm and 3.0–25.0?m, respectively. A number of alternative model forms were tested and the final model selection was based on root mean square error (RMSE) values calculated using a leave-one-out cross-validation procedure. The model performances and the evaluations of the finally selected models (R? 2 range 0.72 to 0.92; RMSE range 38% to 71%; mean prediction errors range ?1.4% to 1.3%) suggest that all models can be used over a wide range of geographical and ecological conditions in Malawi with an appropriate accuracy in predictions. The appropriateness of the developed models was also supported by the fact that the mean prediction errors of these models were much lower than the mean prediction errors (range ?23.6% to 48.9%) of some previously developed models tested on our data.     

Annualized diameter and height growth equations for Pacific Northwest plantation-grown Douglas-fir, western hemlock, and red alder

Simulating the influence of intensive management and annual weather fluctuations on tree growth requires a shorter time step than currently employed by most regional growth models. High-quality data sets are available for several plantation species in the Pacific Northwest region of the United States, but the growth periods ranged from 2 to 12 years in length. Measurement periods of varying length complicate efforts to fit growth models because observed growth rates must be interpolated to a common length growth period or those growth periods longer or shorter than the desired model time step must be discarded. A variation of the iterative technique suggested by Cao [Cao, Q.V., 2000. Prediction of annual diameter growth and survival for individual trees from periodic measurements. Forest Sci. 46, 127–131] was applied to estimate annualized diameter and height growth equations for pure plantations of Douglas-fir, western hemlock, and red alder. Using this technique, fits were significantly improved for all three species by embedding a multi-level nonlinear mixed-effects framework (likelihood ratio test: p < 0.0001). The final models were consistent with expected biological behavior of diameter and height growth over tree, stand, and site variables. The random effects showed some correlation with key physiographic variables such as slope and aspect for Douglas-fir and red alder, but these relationships were not observed for western hemlock. Further, the random effects were more correlated with physiographic variables than actual climate or soils information. Long-term simulations (12–16 years) on an independent dataset using these annualized equations showed that the multi-level mixed effects models were more accurate and precise than those fitted without random effects as mean square error (MSE) was reduced by 13 and 21% for diameter and height growth prediction, respectively. The level of prediction error was also smaller than an existing similar growth model with a longer time step (ORGANON v8) as the annualized equations reduced MSE by 17 and 38% for diameter and height growth prediction, respectively. These models will prove to be quite useful for understanding the interaction of weather and silviculture in the Pacific Northwest and refining the precision of future growth model projections.     

A spatially explicit height�Cdiameter model for Scots pine in Estonia

This contribution presents an approach to model individual tree height?Cdiameter relationships for Scots pine (Pinus sylvestris) in multi-size and mixed-species stands in Estonia using the Estonian Permanent Forest Research Plot Network. The dataset includes 22,347 trees. The main focus of the study was to use an approach that is spatially explicit allowing for high accuracy prediction from a minimum set of predictor variables that can be easily derived. Consequently, the height?Cdiameter relationship is modeled as a function of only the stand quadratic mean diameter (dg) and the plot geographical coordinates. A specific generalized additive model gam is employed that allows for the integration of a varying coefficient term and 2-dimensional surface estimators representing a spatial trend and a spatially varying coefficient term. The high flexibility of the model is needed due to the very few predictor variables that subsume a variety of potential influential factors. Subsequently, a linear mixed model is used that quantifies the random variation between plots and between measurement occasions within plots, respectively. Hence, our model is based on the theory of structured additive regression models (Fahrmeir et al. 2007) and separates a structured (correlated) spatial effect from an unstructured (uncorrelated) spatial effect. Additionally, the linear mixed model allows for calibration of the model using height measurements as pre-information. Model bias is small, despite the somewhat irregular distribution of experimental areas within the country. The overall model shows some similarity with earlier applications in Finland. However, there are important differences involving the model form, the predictors and the method of parameter estimation.     

稠李、斑叶稠李生长特性研究

采用临时标准地法,对20块标准地的40株平均木和优势木进行了树干解析,采用IBMPC系列程序集对所得数据进行计算,以分析稠李、斑叶稠李树高、胸径和材积的生长规律。结果表明:稠李、斑叶稠李都属早期速生树种,稠李高生长在12年时已达高峰,胸径生长在32年时已趋最高,材积生长在40年左右时达到最佳。斑叶稠李高生长在18年达到高峰,胸径生长在32年趋于最高,材积生长在45年左右达到最佳水准。     

Prediction of annual tree growth and survival for thinned and unthinned even-aged maritime pine stands in Portugal from data with different time measurement intervals

An annual individual tree survival and growth model was developed for pure even-aged stands of maritime pine in Portugal, using a large data set containing irregularly time-spaced measurements and considering thinning effects. The model is distance-independent and is based on a function for diameter growth, a function for height growth and a survival function. Two approaches are compared for modeling annual tree growth. The first approach directly estimates a future diameter or height using well-known growth functions formulated in difference form. The second approach estimates diameter or height using a function in differential form estimating the increment over a year period. In both approaches, the function parameters were related to tree and stand variables reflecting the competition status of the tree as well as of a thinning response factor. Variable growth and survival rates were assumed in the modeling approaches. An iterative method was used to continuously update tree and stand attributes using a cut-off to convert the survival probability for a living or a dead tree. The individual tree diameter growth model and the survival probability model were fitted simultaneously using seemingly unrelated regression (SUR). Parameters of the height function were obtained separately as the number of observations for height was much lower than the number of observations for diameter, which may affect the statistical inference and the estimation of contemporaneous cross-equation error correlation inherent to the system of equations. PRESS residuals were used to evaluate the predictive performance of the diameter and the height growth functions. Additional statistics based in the log likelihood function and also in the survival probability were computed to evaluate the survival function. The second modeling approach, which integrates components of growth expansion and decline, performed slightly better than the first approach. A variable accounting for the thinning response that was tested proved to be significant for predicting diameter growth, even if the model already included competition-related explanatory variables, namely the basal area of trees larger than the subject tree. However, this thinning response factor was not significant for predicting height growth.     

Response of branch growth and mortality to silvicultural treatments in coastal Douglas-fir plantations: Implications for predicting tree growth

Static models of individual tree crown attributes such as height to crown base and maximum branch diameter profile have been developed for several commercially important species. Dynamic models of individual branch growth and mortality have received less attention, but have generally been developed retrospectively by dissecting felled trees; however, this approach is limited by the lack of historic stand data and the difficulty in determining the exact timing of branch death. This study monitored the development of individual branches on 103 stems located on a variety of silvicultural trials in the Pacific Northwest, USA. The results indicated that branch growth and mortality were significantly influenced by precommercial thinning (PCT), commercial thinning, fertilization, vegetation management, and a foliar disease known as Swiss needle cast [caused by Phaeocryptopus gaeumannii (T. Rohde) Petr.]. Models developed across these datasets accounted for treatment effects through variables such as tree basal area growth and the size of the crown. Insertion of the branch growth and mortality equations into an individual-tree modeling framework, significantly improved short-term predictions of crown recession on an independent series of silvicultural trials, which increased mean accuracy of diameter growth prediction (reduction in mean bias). However, the static height to crown base equation resulted in a lower mean square error for the tree diameter and height growth predictions. Overall, individual branches were found to be highly responsive to changes in stand conditions imposed by silvicultural treatments, and therefore represent an important mechanism explaining tree and stand growth responses.     

Comparing an individual tree growth model for <Emphasis Type="Italic">Pinus halepensis</Emphasis> Mill. in the Spanish region of Murcia with yield tables gained from the same area

To support forest management decisions on converting stands from even-aged to uneven-aged management, tree models are needed that can simulate both options. Therefore, an individual tree model for Pinus halepensis Mill. is compared with the respective yield table. The individual tree model is built from data of two Spanish forest inventories in this province and evaluated with published yield tables, which have been built from permanent observational plots. The individual tree model consists of a basal area increment model and a height increment model, both based on two measurements of about 4,000 trees from single species stands of Aleppo pine. The R2 values of 0.362 and 0.107 for the basal area increment model and the height increment model, respectively, are within the range of other published models of this type. Comparing the model with the yield tables for different site indices, we find that our model matches the yield table well. Only in higher ages where the database for the yield table was poor, our model indicates higher basal area growth rates than the yield table.     

基于随机森林的杉木标准树高曲线

以湖北省赤壁市国有林场40块杉木人工林实测数据为例,运用随机森林方法,以胸径、优势树高、优势胸径为自变量,建立树高预测模型。首先根据随机森林的置换精度重要性筛选出建模的自变量,并确定决策树的数量和竞争节点变量数,得到决定系数R2为0.9450,均方误差MSE为2.6966的随机森林树高预测模型。利用检验数据对随机森林树高预测模型和传统树高预测模型分别进行精度检验。结果表明：随机森林模型的拟合效果与预测效果都优于该传统树高模型,随机森林模型可以作为有效的树高预测技术。 关键词：杉木;标准树高曲线;随机森林     

Simulation of competition for light in even-aged stands of Douglas Fir

Three versions of an explanatory model to simulate competition between trees within forest stands are presented, based on the distribution of photosynthetically active radiation (PAR) over the trees in the stand. From the amount of PAR absorbed, the rates of assimilation and volume increment are calculated for the trees, which are presented in size classes. Volume increments calculated this way for periods of 35–45 years are compared with measurements from permanent field plots to evaluate different versions of the model.In the first elementary version of the model, it is assumed that the foliage of all trees is distributed uniformly over the field area, neglecting any differences in individual tree height. In this case, the growth of each tree is proportional to its share of the total foliage area of the stand and approximately proportional to its size. This model version slightly underestimated the variation in diameters observed in the field plots.The second version of the model takes into account differences in tree height. As a result of the prior assumption that the foliage of all classes is distributed uniformly over the field area, this model version severely overestimated the shading of short trees by tall neighbours, and the variation in diameters was overestimated as compared to the field data.The third version of the model accounts for clustering of needles within individual crowns in addition to height differences between the classes. This approach gave the better fit to the field data for normally stocked and for dense stands.