Predicting crown width for Larix gmelinii based on linear quantiles groups

Crown width is a critical variable in reflecting the individual tree growth status and in developing forest growth and yield models. With the crown width base model as reference, we developed the crown width quantile regression models for different quantiles (0.50, 0.90, 0.93, 0.95, 0.96, 0.99) based on the data of 2763 Korean pines in 66 permanent plots from the 10-55 years old plantations in Dabiangou forest farm, mountainous areas of eastern Liaoning Province. We used the reparameterization method by introducing the single tree competition index (Rd) and used the dummy variable method by introducing stand density and forest layer variables. We then selected optimal quantile of maximum crown width in the stand by comparing our model developed routine to the traditional methods. The final crown width linear mixed effect quantile regression model was developed based on the optimal quantile at the plot level. The influence of each variable on crown width was analyzed to reflect the difference of crown width among individual trees in the stand. The models with different stand densities and forest layers had significant difference based on F statistical test: the Ra2 of the model increased by 0.0104, the root mean square error decreased by 0.0115 and the mean square error reduction was 7.4%, after the variables of forest layer, forest density, and competition being incorporated into the basic model. The developed quantile regression model performed better than that of the ordinary least square method in simulating the maximum crown width of a single tree in the forest stand. The selected best quantile of the quantile regression model for the upper forest layer and lower forest layer was 0.96 and 0.93, respectively. The linear quantile regression model with the mixed effect was superior to the traditional quantile regression model in Akaike, Bayesion and HQ information criterion and other evaluation para-meters, the standard error for the parameters of estimates was significantly reduced, and the introduced mixed effect well explained differences among different plots. For the upper forest layer and lower forest layer, the maximum crown width decreased with increasing stand density, increased with increasing relative diameters. The influence of stand density on the crown width of the lower forest layer was greater than that of the upper forest layer. The crown width would increase first and then decrease with the increases of DBH when the stand density was large enough. The mixed effect of the quantile regression model developed here could significantly improve the fitting stability of the model. The sustainable development of Korean pine plantation in the mountainous area of eastern Liaoning Pro-vince should be realized by adjusting stand density and moderate tending and thinning in the future.

Crown width (CW) is an important indicator for assessing tree health, vitality, and stability, as well as being used to predict forestry models and evaluate forest dynamics. However, acquiring CW data is laborious and time-consuming, making it crucial to establish a convenient and accurate CW prediction model for forest management. In this study, we developed three models capable of conducting calibration: generalized models (GM), quantile regression models (QR), and mixed-effects models (MIXED). The aim was to effectively improve the prediction accuracy of CW using data from Dahurian larch (Larix gmelinii Rupr.) in Northeastern China. Different sampling designs were applied, including selecting the thickest, thinnest, intermediate, and random trees, with 1 to 10 sample trees for each design. The results showed that all models achieved accurate CW predictions. MIXED displayed the most superior fitting statistics than GM and QR. In model validation, with the increase in the number of sample trees, the model prediction accuracy gradually improved and the model differences gradually reduced. MIXED produced the smallest RMSE, MAE, and MAPE across all sampling designs. The intermediate tree sampling design with the best validation statistics for the given sample size was selected as the final sampling design. Under intermediate tree sampling design, MIXED required a minimum of five sample trees, while GM and QR required at least five and six sample trees for calibration, respectively. Generally, we suggested selecting MIXED as the final CW prediction model and using the intermediate tree sampling design of five trees per plot. This study could provide ideas and support for forest managers to accurately and efficiently predict CW.

RUSSIAN JOURNAL OF FOREST SCIENCE, 2021, No. 5, P. 494–508 VARIABILITY OF VEGETATIVE ORGAN CHARACTERISTICS OF DAHURIAN LARCH IN ZABAYKALSKY REGION V. P. Makarov, O. F. Malykh, T. V. Zhelibo Institute of Natural Resources, Ecology and Cryology, Siberian Branch of the RAS Nedorezova st. 16a, Chita, 672014, Russia E-mail: vm2853@mail.ru Received 22 October 2020 The article summarizes for the first time the results of a study of the morphological organs variability in 38 populations of Dahurian larch ( Larix gmelinii (Rupr.) Rupr.) in various natural conditions of the Zabaykalsky Region. There are also presented the characteristics of the trunk, crown, needles and seed production intensity. The correlation was found among the different features, as well as between the features and environmental conditions. The stands were distinguished, possessing important selection traits and properties that may prove economically useful. It was found that the variability of the trunk straightness in a number of larch populations reaches a very high level. The value of the trait is statistically reliably related to the steepness and exposure of the slope, the hydrotope type, as well as the altitude and geographic coordinates of the habitat. The variability of the crown width in relation to the height of the trunk is can vary highly, from very low to high levels. A correlation was also found between the trait and geographic longitude and hydrotope type. The crown width also varies considerably, which is reliably correlated with geographical coordinates and altitude, as well as with the ecological conditions of the habitat – the steepness and exposure of the slope, and the type of hydrotope. The average values of the branching angle in populations are in the range of 60–90 °. Trees with obtuse branching angles are rare. The trait significantly correlates with the geographic and ecological parameters of the habitat. It was found that the number of needles in the bundle correlates with the geographical coordinates and altitude, as well as the ecological conditions of the habitat. The length of the needles is correlated with the geographical latitude, however the correlation of the trait with the ecological conditions of the habitat has not been established. The seed production intensity has a close correlation with the geographical latitude, altitude, and hydrotope type. Individual variability of the trait occurs on an increased level. The article also presents the results of the correlation analysis of the morphological traits of the Dahurian larch. Keywords: Dahurian larch, morphological diversity, traits correlation, environment DOI: 10.31857/S0024114821050119 REFERENCES Abaimov A.P., Adrianova I.Yu., Artyukova E.V., Barchenkov A.P., Vasyutkina E.A., Gukov G.V., Zhuravlev Yu.N., Zyryanova O.A., Isaev A.P., Katyshev A.I., Karpyuk T.V., Kvitko O.V., Knyazeva S.G., Kozyrenko M.M., Konstantinov Yu.M., Larionova A.Ya., Milyutin L.I., Milyutina I.L., Mikhaleva L.G., Muratova E.N., Oreshkova N.V., Pimenov A.V., Reunova G.D., Sedel'nikova T.S., Sizykh O.A., Sudachkova N.E., Chikidov I.I., Bioraznoobrazie listvennits Aziatskoi Rossii (Larches biodiversity of Asian Russia), Novosibirsk: GEO, 2010, 160 p. Abaimov A.P., Koropachinskii I.Y., Listvennitsy Gmelina i Kayandera ( Larix gmelinii and Larix cajanderi ), Novosibirsk: Nauka, 1984, 121 p. Barchenkov A.P., Izmenchivost' listvennitsy v Severnom Zabaikal'e (Stanovoe nagor'e) (Variability of larch in Northern Transbaikalia (Stanovoe plateau)), Vestnik Tomskogo gosudarstvennogo universiteta. Biologiya , 2008, No. 3(4), pp. 7–15. Barchenkov A.P., Milyutin L.I., Morfologicheskaya izmenchivost' listvennitsy v Srednei Sibiri (Morphological variability of larch in Central Siberia), Khvoinye boreal'noi zony , 2007, Vol. 24, No. 4–5, pp. 367–372. Debrinyuk Yu.M., Formovoe raznoobrazie listvennitsy evropeiskoi ( Larix decidua Mill.) kak introdutsenta v Prikarpat'e (Form diversity of European larch ( Larix decidua Mill.) As an introduced species in the Carpathian region), Plodovodstvo, semenovodstvo, introduktsiya drevesnykh rastenii , 2011, No. 14, pp. 38–41. Dylis N.V., Listvennitsa (Larch), Moscow: Lesn. prom-ost', 1981, 96 p. Dylis N.V., Sibirskaya listvennitsa. Materialy k sistematike, geografii i istorii (Siberian larch. Materials for taxonomy, geography and history), Moscow: izd-vo MOIP, 1947, 137 p. Hu X.-S., Ennos R.A., Population structure and genetic relationships of taxa in the Larix Gmelinii complex in China, Forest Geneyics , 2001, Vol. 8, No. 3, pp. 225–232. Iroshnikov A.I., Listvennitsy Rossii. Bioraznoobrazie i selektsiya (Larches of Russia. Biodiversity and selection), Moscow: VNIILM, 2004, 182 p. Jia QingBin, Zhang Hanguo, Zhang Lei, Zhang Haixiao, Variation analysis of hybrid Larch families and superior families selection, Journal of Northeast Forestry University , 2016, Vol. 4, pp. 1–7. Kruklis M.V., Milyutin L.I., Listvennitsa Chekanovskogo (Larix Czekanovskii), Moscow: Nauka, 1977, 210 p. Makarov V.P., Bobrinev V.P., Milyutin L.I., Geograficheskie kul'tury listvennitsy v Vostochnom Zabaikal'e (Provenance trial plantations of larch in Eastern Transbaikalia), Ulan-Ude: Izd-vo Buryatskogo NTs SO RAN, 2002, 187 p. Makarov V.P., Izmenchivost' morfologicheskikh vidov i klimatipov listvennitsy v geograficheskikh kul'turakh (Vostochnoe Zabaikal'e) (Variability of larch morphological species and climatypes in provenances (Eastern Transbaikal region)), Lesovedenie , 2005, No. 4, pp. 67–75. Mamaev S.A., Formy vnutrividovoi izmenchivosti drevesnykh rastenii (The forms of intraspecies variation of woody plants), Moscow: Nauka, 1972, 284 p Milyutin L.I., Bioraznoobrazie listvennits Rossii (Biodiversity of Russian larch), Khvoinye boreal'noi zony , 2003, Vol. 21, No. 1, pp. 6–9. Oreshkova N.V., Populyatsionno-geneticheskie parametry listvennitsy Gmelina v Vostochnom Zabaikal'e (Chitinskaya oblast') (Population-genetic parameters of Gmelin larch in Eastern Zabaikalje (Chita region)), Vestnik Tomskogo gosudarstvennogo universiteta , 2009, No. 28, pp. 193–198. Panarin I.I., Tipy listvennichnykh lesov Chitinskoi oblasti (Types of larch forests of the Chita region), Moscow: Nauka, 1965, 103 p. Pogrebnyak P.S., Osnovy lesnoi tipologii (Basics of forest typology), Kiev: Izd-vo AN USSR, 1955, 456 p. Rysin L.P., Listvennichnye lesa Rossii (Larch forests of Russia), Moscow: Tovarishchestvo nauchnykh izdanii KMK, 2010, 343 p. Tyrchenkova I.V., Fenotipicheskie priznaki ustoichivosti sosny obyknovennoi k rekreatsionnomu vozdeistviyu (Phenotypic evidence of resistance of Scotch pine to recreation impact), Lesotekhnicheskii zhurnal , 2017, No. 2, pp. 115–121. Yang Chuanping, Liu Guifeng, Xu Jiachun, Cai Baoming, Xia Dean, Yang Shuwen, Zhang Peigao, Geographic variation pattern of Larix olgensis , Journal of Forestry Research , 1997, Vol. 8, pp. 3–9. Yang Chuanping, Zhang Wei, Yu Bingjun, Qin Sihua, Study on geographic variation of Dahurian larch in China, Journal of Northeast Forestry University , 1991, Vol. 2, pp. 34–41. Yu Bingjun., A study on the geographic variation and selection of the best provenance of Larix olgensis, Journal of Northeast Forestry University , 1994, Vol. 5, pp. 1–9. Zhang Xin-bo, Feng Jing-hua, Ren Jian-ru, Morphological variance and natural types' division of plus trees of Larix principis-rupprechtii Mayr., Journal of Northeast Forestry University , 2001, Vol. 12, pp. 123–127. Zhu Dao Guang, Xu Xue Hong, Yang Li Bin, Fan Yang, Li Jin Bo, Cui Fu Xing, Ye Wan Hu, Ni Hong Wei, Characteristics of leaves, stems and roots of dominant trees in Larix gmelinii forest in the cold temperate zone, Scienta sinica Vitae , 2020, Vol. 50, No .4, pp. 398–405.

Larix gmelinii is the fourth most important tree species in China and a typical zonal climax species in the cold temperate region, with high ecological and resource value. However, intensive logging, high-density afforestation, and insufficient scientific management have led to overly dense, homogeneous, and unstable plantations, severely limiting productivity. To clarify the mechanisms by which structural dynamics regulate productivity, we established a space-for-time sequence (T1–T3, T2-D, CK) under a consistent early-tending background. Using the “1 + 4” nearest-neighbor framework and six spatial structural parameters, we developed tree and forest spatial structure indices (TSSI and FSSI) and integrated nine structural–functional indicators for multivariate analysis. The results showed that TSSI and FSSI effectively characterized multi-level stability and supported stability classification. Along the stand-age gradient, structural stability and spatial use efficiency improved significantly, with FSSI and biomass per hectare (BPH) increasing by 91% and 18% from T1 to T3, though a “structural improvement–functional lag” occurred at T2. Moderate thinning markedly optimized stand configuration, reducing low-stability individuals from 86.45% in T1 to 42.65% in T2-D, while DBH, crown width, FSSI, and BPH (229.87 t·hm−2) increased to near natural-forest levels. At the tree scale, DBH, tree height, crown width, and TSSI were positive drivers, whereas a high height–diameter ratio (HDR) constrained growth. At the stand scale, canopy density, species richness, and mean DBH promoted FSSI and BPH, while mean HDR and stand density imposed major constraints. A critical management window was identified when DBH < 25 cm, HDR > 10, and TSSI < 0.25 (approximately 10–30 years post-planting). We propose a stepwise, moderate, and targeted thinning strategy with necessary underplanting to reduce density and slenderness, increase diameter and canopy structure, and enhance diversity, thereby accelerating the synergy between stability and productivity. This framework provides a practical pathway for the scientific management and high-quality development of L. gmelinii plantations.

The impacts of climate, competition, and their interactions on crown width for three major species in Chinese boreal forests

Crown architecture has long been evaluated for its impact on taper modeling. However, most of the research has focused on a limited number of crown dimensions. This study examined the effect of adding several crown dimensions in improving the diameter and volume estimates of Dahurian larch, Korean spruce, and Manchurian fir in northeast China. The crown dimensions included crown length, crown ratio, crown width, height to live crown base, diameter at the crown base, and crown shape. A well-known taper model of Clark et al. (1991) was fitted to the data of 276 trees from natural stands. To adjust the inherent autocorrelation in the data, we added a third-order continuous-time error structure in the model fit. Model fitting was carried out with the NLMIXED procedure (Non-linear Mixed Procedure), followed by the MODEL procedure of SAS using the generalized nonlinear least-squares method. Fit statistics and graphical assessments were used to evaluate the original and modified models. Above 98% of the total variance of d was explained by the models for all species. The addition of crown variables showed slight improvements for root mean square error (RMSE) values in the analyzed species. The RMSE plots indicated that the models with crown variables slightly improved the diameter and volume predictions for the species but only for the upper stem (>50%–90%). The study demonstrated that crown dimensions influence the stem taper, but the original model of Clark et al. (1991) reasonably realized that effect.

Key messageThe non-linear seemingly unrelated regression mixed-effects model (NSURMEM) and generalized additive model (GAM) were applied for the first time in crown width (CW) additive models of larch (Larix gmelinii Rupr.), birch (Betula platyphylla Suk.), and poplar (Populus davidiana Dode). The crown radii in four directions (CR) exhibited different growth trends and responded differently to tree size and competition variables. In the absence of calibration, GAM was more accurate than NSURMEM for CR and CW predictions.ContextCrown radii in four directions (CR) and crown width (CW) are fundamental indicators used to describe tree crowns. The complexity of the CR growth in four directions of different tree species in natural forests is often ignored. There is logical additivity among CR and CW that is also often overlooked. Furthermore, the existing methods applied to CW additive models have some drawbacks.AimsWe aim to: (i) evaluate the utility of two new methods in developing CW additive models for larch (Larix gmelinii Rupr.), birch (Betula platyphylla Suk.), and poplar (Populus davidiana Dode) in natural secondary forests of Northeastern China; and (ii) explore the growth patterns of CR in four directions to gain important ecological insights.MethodsThe non-linear seemingly unrelated regression mixed-effects model (NSURMEM) and generalized additive model (GAM) were used to develop CW additive models and to explore crown growth patterns. The predictive ability of the additive models was evaluated using leave-one-plot-out cross-validation (LOOCV).ResultsAt a fair level without calibration, GAM provided slightly better results than NSURMEM. The response of the four CR to tree size and competition variables is different and may be non-uniform due to complex stand conditions and tree growth strategies.ConclusionThe newly provided methods applied to additive models are available for external datasets. GAM is recommended in the absence of calibration. This study has important implications for the understanding of natural forest dynamics and decision-making for critical stand management.

A total of 138 Dahurian larch (Larix gmelinii Rupr.) trees and 108 white birch (Betula platyphylla Suk.) trees were harvested in the eastern Daxing’an Mountains, northeast China. We developed four additive systems of biomass equations as follows: the first additive model system (MS-1) used the best combination of tree variables as the predictors; the second additive model system (MS-2) included tree diameter at breast height (D) as the sole predictor; the third additive model system (MS-3) included both D and tree height (H) as the predictors; and the fourth additive model system (MS-4) included D, H, and crown attributes (crown width (CW) and crown length (CL)) as the predictors. The model coefficients were simultaneously estimated using seemingly unrelated regression (SUR). The heteroscedasticity in model residuals was addressed by applying a unique weight function to each equation. The results indicated that: (1) the stem biomass accounted for the largest proportion of the total tree biomass, while the foliage biomass had the smallest proportion for the two species; (2) the four additive systems of biomass equations exhibited good model fitting and prediction performance, of which the model Ra2 > 0.81, the mean prediction error (MPE) was close to 0, and the mean absolute error (MAE) was relatively small (<9 kg); (3) MS-1 and MS-4 significantly improved the model fitting and performance; the ranking of the four additive systems followed the order of MS-1 > MS-4 > MS-3 > MS-2. Overall, the four additive systems can be applied to estimate individual tree biomass of both species in the Chinese National Forest Inventory.