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Aim: To test the extent to which the vertical structure of tropical forests is determined by environment, forest structure or biogeographical history. Location: Pan-tropical. Methods: Using height and diameter data from 20,497 trees in 112 non-contiguous plots, asymptotic maximum height (H AM ) and height—diameter relationships were computed with nonlinear mixed effects (NLME) models to: (1) test for environmental and structural causes of differences among plots, and (2) test if there were continental differences once environment and structure were accounted for; persistence of differences may imply the importance of biogeography for vertical forest structure. NLME analyses for floristic subsets of data (only/excluding Fabaceae and only/excluding Dipterocarpaceae individuals) were used to examine whether family-level patterns revealed biogeographical explanations of cross-continental differences. Results: H AM and allometry were significantly different amongst continents. H AM was greatest in Asian forests (58.3 ± 7.5 m, 95% CI), followed by forests in Africa (45.1 ± 2.6 m), America (35.8 ± 6.0 m) and Australia (35.0 ± 7.4 m), and height—diameter relationships varied similarly; for a given diameter, stems were tallest in Asia, followed by Africa, America and Australia. Precipitation seasonality, basal area, stem density, solar radiation and wood density each explained some variation in allometry and H AM yet continental differences persisted even after these were accounted for. Analyses using floristic subsets showed that significant continental differences in H AM and allometry persisted in all cases. Main conclusions: Tree allometry and maximum height are altered by environmental conditions, forest structure and wood density. Yet, even after accounting for these, tropical forest architecture varies significantly from continent to continent. The greater stature of tropical forests in Asia is not directly determined by the dominance of the family Dipterocarpaceae, as on average non-dipterocarps are equally tall. We hypothesise that dominant large-statured families create conditions in which only tall species can compete, thus perpetuating a forest dominated by tall individuals from diverse families.

High-value timber species such as monarch birch (Betula maximowicziana Regel), castor aralia (Kalopanax septemlobus (Thunb.) Koidz), and Japanese oak (Quercus crispula Blume) play important ecological and economic roles in forest management in the cool temperate mixed forests in northern Japan. The accurate measurement of their tree height is necessary for both practical management and scientific reasons such as estimation of biomass and site index. In this study, we investigated the similarity of individual tree heights derived from conventional field survey, digital aerial photographs derived from unmanned aerial vehicle (UAV-DAP) data and light detection and ranging (LiDAR) data. We aimed to assess the applicability of UAV-DAP in obtaining individual tree height information for large-sized high-value broadleaf species. The spatial position, tree height, and diameter at breast height (DBH) were measured in the field for 178 trees of high-value broadleaf species. In addition, we manually derived individual tree height information from UAV-DAP and LiDAR data with the aid of spatial position data and high resolution orthophotographs. Tree heights from three different sources were cross-compared statistically through paired sample t-test, correlation coefficient, and height-diameter model. We found that UAV-DAP derived tree heights were highly correlated with LiDAR tree height and field measured tree height. The performance of individual tree height measurement using traditional field survey is likely to be influenced by individual species. Overall mean height difference between LiDAR and UAV-DAP derived tree height indicates that UAV-DAP could underestimate individual tree height for target high-value timber species. The height-diameter models revealed that tree height derived from LiDAR and UAV-DAP could be better explained by DBH with lower prediction errors than field measured tree height. We confirmed the applicability of UAV-DAP data for obtaining the individual tree height of large-size high-value broadleaf species with comparable accuracy to LiDAR and field survey. The result of this study will be useful for the species-specific forest management of economically high-value timber species.

Summary In perennial woody plants, the coordinated increase of stem height and diameter during juvenile growth improves competitiveness (i.e. access to light); however, the factors underlying variation in stem growth remain unknown in trees. Here, we used linkage‐linkage disequilibrium (linkage‐LD) mapping to decipher the genetic architecture underlying three growth traits during juvenile stem growth. We used two Populus populations: a linkage mapping population comprising a full‐sib family of 1,200 progeny and an association mapping panel comprising 435 unrelated individuals from nearly the entire natural range of Populus tomentosa. We mapped 311 quantitative trait loci (QTL) for three growth traits at 12 timepoints to 42 regions in 17 linkage groups. Of these, 28 regions encompassing 233 QTL were annotated as 27 segmental homology regions (SHRs). Using SNPs identified by whole‐genome re‐sequencing of the 435‐member association mapping panel, we identified significant SNPs (P ≤ 9.4 × 10−7) within 27 SHRs that affect stem growth at nine timepoints with diverse additive and dominance patterns, and these SNPs exhibited complex allelic epistasis over the juvenile growth period. Nineteen genes linked to potential causative alleles that have time‐specific or pleiotropic effects, and mostly overlapped with significant signatures of selection within SHRs between climatic regions represented by the association mapping panel. Five genes with potential time‐specific effects showed species‐specific temporal expression profiles during the juvenile stages of stem growth in five representative Populus species. Our observations revealed the importance of considering temporal genetic basis of complex traits, which will facilitate the molecular design of tree ideotypes.

Systematic tests of longitudinal compression, bending, longitudinal shear, and longitudinal tensile strength of bamboo were conducted to study the variation of mechanical properties and the height-diameter ratio of bamboo. The predictive relations of mechanical properties and height-diameter ratio were fitted by linear regression analysis. The results showed that the mechanical properties of longitudinal compression, bending, longitudinal shear, and longitudinal tensile strength of bamboo increased with the increase of the height-diameter ratio. In this paper, the method of deducing the relationship between mechanical properties and height-diameter ratio of bamboo through the linear fitting relationship between mechanical properties and height-diameter ratio was shown to have high applicability and accuracy for bamboo. This paper has a certain reference value for the evaluation of mechanical properties of bamboo and has a certain practical value for reducing the testing cost.

Relationship of total height and diameter at breast height (hereafter diameter) of the trees is generally nonlinear, and therefore has complex characteristics, which can be accurately described by the height-diameter model developed using the back propagation (BP) neural network approach. The multiple hidden layered-BP neural network has several hidden layers and neurons, and is therefore considered more appropriate modeling approach compared to the single hidden layered-BP neural network approach. However, the former approach is not widely applied for tree height prediction due to absence of the effective optimization method, but it can be done using the BP neural network modeling approach. The poplar (Populus spp. L.) plantation data acquired from Guangdong province of China were used for evaluating the BP neural network modeling approach and compared its results with those obtained from the traditional regression modeling and mixed-effects modeling approaches. We determined the best BP neural network structure with two hidden layers and five neurons in each layer, and logistic sigmoid transfer functions. Relative to the Mitscherlich height-diameter model that had the highest fitting precision among the six traditional height-diameter models evaluated, coefficient of determination (R2) of the neural network height-diameter model increased by 10.3%, root mean squares error (RMSE) and mean absolute error (MAE) decreased by 12% and 13.5%, respectively. The BP neural network height-diameter model also appeared more accurate than the mixed-effects height-diameter model. Our study proposes the method of determining the optimal numbers of hidden layers, neurons of each layer, and transfer functions in the BP neural network structure. This method can be useful for other modeling studies of similar or different types, such as tree crown modeling, height, and diameter increments modeling, and so on.

Systematic tests of longitudinal compression, bending, longitudinal shear, and longitudinal tensile strength of bamboo were conducted to study the variation of mechanical properties and the height-diameter ratio of bamboo. The predictive relations of mechanical properties and height-diameter ratio were fitted by linear regression analysis. The results showed that the mechanical properties of longitudinal compression, bending, longitudinal shear, and longitudinal tensile strength of bamboo increased with the increase of the height-diameter ratio. In this paper, the method of deducing the relationship between mechanical properties and height-diameter ratio of bamboo through the linear fitting relationship between mechanical properties and height-diameter ratio was shown to have high applicability and accuracy for bamboo. This paper has a certain reference value for the evaluation of mechanical properties of bamboo and has a certain practical value for reducing the testing cost.

Key messageCrown, height and stem allometry vary with stand density and species composition, the plasticity in response to inter- and intra-specific competitions being related to species shade tolerances.Determining the way in which variability in tree allometry is modulated by intra- and inter-specific competitions in different species and stand compositions is of particular interest for forest modelling and practice. In this study, we explore this variability by developing models for tree crown diameter, total height and diameter at a height of 4 m, which include intra- and inter-specific competition terms. More than 19,000 Scots pine, silver fir, sessile oak and European beech trees from 4711 sample plots belonging to the Spanish National Forest Inventory were included in the study, covering both monospecific and two species mixed stands in Northern Spain. Trees growing under conditions of high competition displayed narrower crowns, greater heights and less taper for a given tree diameter, the plasticity in crown and height in response to intra-specific competition being related to species shade tolerance. The inter-specific competition effect on crown diameter and height was related to the difference in shade tolerance between the two species of the mixture, while stem taper did not exhibit this pattern. These results suggest that trees in mixed stands indeed show a modified allometry, which might be related to complementary resource acquisition strategies. The large variability observed in tree allometry indicates the need to consider both intra- and inter-specific competitions in allometric models.

Key messageHeight–diameter models were developed specifically for Pinus nigra Arn., an important commercially species extending in the Mediterranean and central Europe region. The accuracy of the proposed models is expected to substantially improve the tree volume and total biomass estimations.Three types of nonlinear height–diameter models, simple, generalized mixed effects and fixed, were evaluated against independent data from even-aged black pine (Pinus nigra Arn.) natural stands located in Olympus National Park in Greece in an effort to accurately predict total tree height (h). A total of 3442 pairs of height–diameter data were collected from 66 randomly selected non-permanent plots. Using the diameter at breast height (d) as independent variable, a number of simple nonlinear mixed-effects models were fitted to select the most appropriate for further analysis. Continuously, basic stand parameters were added as predictors, so as to develop a generalized (h–d) model with increased applicability prospects. At that stage, a mixed-effects modeling approach was applied to improve height predictability based on the reduction of the Root Mean Squared Error (RMSE). The analysis showed that the inclusion of dominant height and dominant diameter as predictors improved the accuracy of the Chapman–Richards model. Moreover, the random components within the nonlinear (h–d) model explained a great part of the height variation, which was not possible to explain previously. The mixed-effects modeling approach provides an adequate framework for predicting the black pine tree height accurately, which could save intensive fieldwork.

An individual-tree height-diameter model was developed for stone pine (Pinus pinea L.) in Spain. Five biparametric nonlinear equations were fitted and evaluated based on a data set consisting of 8614 trees from 455 plots located in the four most important regions where the species occurs in Spain. Because of the problem of high correlation among observations taken from the same sampling unit, a mixed-model approach, including random coefficients, is proposed. Several stand variables, such as density, dominant height, or diametric distribution percentiles, were included in the model as covariates to explain among plot variability. To determine interregional variability among the regions studied, regional effects were included in the model using fixed dummy variables. Two models, one for inland regions and one for coastal regions, were found to be sufficient to explain regional variability in the height-diameter relationship for the species in Spain. Mixed models allow predictive role in two ways: a typical response, including only fixed effects, and a calibrated response, where random effects are predicted and included in the model from the prior measurement of the height in a subsample of trees. Different alternatives were tested to determine optimum subsample size. Measurement of the height of the 20% largest trees in the plot has been shown to be a useful approach.

In underground projects such as mining and tunneling, the presence of coal rock columns plays a certain supporting role, and the instability of coal rock columns is often related to their size and shape of presence. Therefore, in order to investigate the compressive damage characteristics and damage evolution law of rocks of different sizes, uniaxial compression tests were conducted on sandstones with different height−diameter ratios to explore the mechanical properties and damage characteristics of sandstones with different height−diameter ratios, analyze the connection between acoustic emission ringing count rate, accumulated energy, peak frequency, and b-value changes and height–diameter ratio, and analyze the evolution law of sandstones during damage based on damage variables, and draw the following conclusions. As the height-to-diameter ratio increases, the less affected by the end effect, the rock strength shows a nonlinear decreasing trend, and the decreasing trend becomes slow. The acoustic emission ringing count rate evolved from intermittent to continuous occurrence, showing multiple peaks as the test proceeded. The accumulated energy rises sharply before rupturing after several steps from stable development. As the height-to-diameter ratio increases, the acoustic emission signal before rupture rises more intensively, and the damage is more concentrated. The overall level of the b-value shows an increasing trend, the proportion of acoustic emission high-frequency signal gradually increases, and the development of tiny cracks inside the rock more intensively. Therefore, the sudden change of acoustic emission signal can be used as a precursor of rock damage. The rock damage curve has smaller values in the stable damage phase. With the increase in the height-to-diameter ratio, the non-stable damage stage damage showed a trend of decreasing and then increasing and reached the minimum at L/D = 2.0.