<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">hbz</journal-id><journal-title-group><journal-title xml:lang="ru">Хвойные бореальной зоны</journal-title><trans-title-group xml:lang="en"><trans-title>Conifers of the boreal area</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1993-0135</issn><publisher><publisher-name>СибГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.53374/1993-0135-2024-1-36-42</article-id><article-id custom-type="elpub" pub-id-type="custom">hbz-199</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>БИОЛОГИЯ И ЭКОЛОГИЯ, ЛЕСНОЕ ХОЗЯЙСТВО</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>BIOLOGY AND ECOLOGY, FORESTRY</subject></subj-group></article-categories><title-group><article-title>Отношение диаметра кроны к диаметру ствола: всеобщие модели лесообразующих видов Евразии</article-title><trans-title-group xml:lang="en"><trans-title>The ratio of crown diameter to stem diameter: generic models of forest-forming species of Eurasia</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4587-8952</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Усольцев</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Usoltsev</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>620100, Екатеринбург, Сибирский тракт, 37</p><p>620144, Екатеринбург, ул. 8 марта, 202а</p></bio><bio xml:lang="en"><p>37, Sibirskiy Trakt, Yekaterinburg, 620100</p><p>202а, 8 Marta Str., Yekaterinburg, 620144</p></bio><email xlink:type="simple">Usoltsev50@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Плюха</surname><given-names>Н. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Plyukha</surname><given-names>N. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>620100, Екатеринбург, Сибирский тракт, 37</p></bio><bio xml:lang="en"><p>37, Sibirskiy Trakt, Yekaterinburg, 620100</p></bio><email xlink:type="simple">nikcskript@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4747-5017</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Цепордей</surname><given-names>И. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Tsepordey</surname><given-names>I. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>620144, Екатеринбург, ул. 8 марта, 202а</p></bio><bio xml:lang="en"><p>202а, 8 Marta Str., Yekaterinburg, 620144</p></bio><email xlink:type="simple">ivan.tsepordey@yandex.ru</email><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Уральский государственный лесотехнический университет; Ботанический сад Уральского отделения РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural State Forest Engineering University; Botanical Garden, Ural Branch of RAS</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Уральский государственный лесотехнический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural State Forest Engineering University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Ботанический сад Уральского отделения РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Botanical Garden, Ural Branch of RAS</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>08</day><month>02</month><year>2025</year></pub-date><volume>42</volume><issue>1</issue><fpage>36</fpage><lpage>42</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Усольцев В.А., Плюха Н.И., Цепордей И.С., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Усольцев В.А., Плюха Н.И., Цепордей И.С.</copyright-holder><copyright-holder xml:lang="en">Usoltsev V.A., Plyukha N.I., Tsepordey I.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://hbz.elpub.ru/jour/article/view/199">https://hbz.elpub.ru/jour/article/view/199</self-uri><abstract><p>Кроны деревьев подвергались гораздо меньшему количественному изучению, чем их стволы, в первую очередь из-за их более низкой потребительной стоимости. Однако размер кроны, тесно связанный с фотосинтетической способностью дерева, является важным параметром при изучении роста деревьев. В сомкнутых и загущенных древостоях измерение диаметра кроны менее точно и гораздо более трудозатратно по сравнению с другими показателями. Поэтому наличие аллометрических моделей для оценки диаметра крон снижает затраты при получении новых исходных данных. В литературных источниках отношение диаметра кроны к диаметру ствола на высоте груди (относительный диаметр кроны) использовалось для прогнозирования размера площади роста дерева и разработки режимов прореживания, для прогнозирования густоты древостоя при заданном среднем диаметре ствола и для оценки диаметра ствола по диаметру кроны, измеренному с помощью методов дистанционного зондирования. Цель нашего исследования – для основных лесообразующих видов и родов Евразии рассчитать всеобщие аллометрические зависимости относительного диаметра кроны от диаметра ствола дерева. По фактическим данным измерений 5497 модельных деревьев 23 лесообразующих видов и родов (подродов) Евразии впервые составлены всеобщие аллометрические модели связи относительного диаметра кроны с диаметром ствола на высоте груди. Согласно выполненному ранжированию, виды и роды по величине относительного диаметра кроны распределяются в следующей последовательности в порядке убывания: Juglans, Phellodendron, Maackia, Acer, Ulmus, Chosenia, Salix, Quercus, Carpinus, Tilia, Fraxinus, Robinia, Populus, Larix, Fagus, Betula, Haploxylon, Chamaecyparis, Abies, Picea, Alnus, Pinus, Cryptomeria. Модели на уровне родов могут быть применены для тех видов в пределах рода, данные по которым пока отсутствуют. </p></abstract><trans-abstract xml:lang="en"><p>The crowns of trees were subjected to much less quantitative study than their stems, primarily because of their lower use value. However, the size of the crown, closely related to the photosynthetic ability of the tree, is an important parameter in the study of tree growth. In closed and thickened stands, measuring the diameter of the crown is less accurate and much more labor-consuming compared to other indicators. Therefore, the availability of allometric models for estimating the diameter of crowns reduces costs when obtaining new initial data. In literature, the ratio of crown diameter to stem diameter at breast height (relative crown diameter) was used to predict the size of the tree growth area and to develop thinning regimes, to predict the stand density at a given average stem diameter and to estimate the stem diameter by crown diameter measured using remote sensing methods. The purpose of our study is to calculate the generic allometric dependences of the relative diameter of the crown on the diameter of the tree stem for the main forest-forming species and genera of Eurasia. According to the actual measurement data of 5,497 model trees of 23 forest-forming species and genera (subgenera) of Eurasia, allometric models of the relationship between the relative diameter of the crown and the stem diameter at breast height were compiled for the first time. According to the ranking performed, species and genera are distributed according to the relative diameter of the crown in the following descending order: Juglans, Phellodendron, Maackia, Acer, Ulmus, Chosenia, Salix, Quercus, Carpinus, Tilia, Fraxinus, Robinia, Populus, Larix, Fagus, Betula, Haploxylon, Chamaecyparis, Abies, Picea, Alnus, Pinus, Cryptomeria. Models at the level of genera can be applied to those species for which data are not yet available within the genus. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>относительный диаметр кроны</kwd><kwd>аллометрические модели</kwd><kwd>ранжирование видов и родов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>relative crown diameter</kwd><kwd>allometric models</kwd><kwd>ranking of species and genera</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена согласно государственному заданию Ботанического сада УрО РАН.</funding-statement><funding-statement xml:lang="en">The publication was prepared based on the results of the research carried out within the framework of the state task of the Botanical Garden, Ural Branch of RAS.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Усольцев В. А. Фитомасса модельных деревьев для дистанционной и наземной таксации лесов Евразии. Электронная база данных. 3-е дополненное издание. Екатеринбург: Ботанический сад УрО РАН, Уральский государственный лесотехнический университет, 2023. 1 электрон. опт. диск (CD-ROM). URL: https://elar.usfeu.ru/handle/123456789/12451.</mixed-citation><mixed-citation xml:lang="en">Usoltsev V. A. Single-tree biomass data for remote sensing and ground measuring of Eurasian forests: digital version. The third edition, enlarged. Yekaterinburg: Botanical Garden of Ural Branch of RAS, 2023. URL: https://elar.usfeu.ru/handle/123456789/12451.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Усольцев В. А., Цепордей И. С. Морфология кроны лесообразующих родов Евразии: аллометрия и ранжирование // Хвойные бореальной зоны. 2023. Т. 41(6). С. 504–514. DOI: 10.53374/1993-0135-2023-6504-514.</mixed-citation><mixed-citation xml:lang="en">Usoltsev V. A., Tsepordey I. S. Crown morphology of forest-forming genera of Eurasia: allometry and ranking // Conifers of the Boreal Area. 2023. Vol. XLI. No. 6. P. 504–514. DOI: 10.53374/1993-0135-2023-6-504-514.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Усольцев В. А., Цепордей И. С., Часовских В. П. Модели для оценки биомассы деревьев лесообразующих видов по диаметру кроны в связи с использованием дронов // Хвойные бореальной зоны. 2023. Т. 41(4). С. 300–305. DOI: 10.53374/1993-0135-2023-4300-305.</mixed-citation><mixed-citation xml:lang="en">Usoltsev V. A., Tsepordey I. S., Chasovskikh V. P. Models for estimating biomass of forest-forming species by crown diameter as related to drone involving // Conifers of the Boreal Area. 2023. Vol. 41(4). P. 300- 305. DOI: 10.53374/1993-0135-2023-4-300-305.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Baskerville G. L. Use of logarithmic regression in the estimation of plant biomass // Canadian Journal of Forest Research. 1972. Vol. 2. P. 49–53.</mixed-citation><mixed-citation xml:lang="en">Baskerville G. L. Use of logarithmic regression in the estimation of plant biomass // Canadian Journal of Forest Research. 1972. Vol. 2. P. 49–53.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Binkley D., Campoe O. C., Gspaltl M. et al. Light absorption and use efficiency in forests: why patterns differ for trees and stands // Forest Ecology and Management. 2013. Vol. 288. P. 5–13.</mixed-citation><mixed-citation xml:lang="en">Binkley D., Campoe O. C., Gspaltl M. et al. Light absorption and use efficiency in forests: why patterns differ for trees and stands // Forest Ecology and Management. 2013. Vol. 288. P. 5–13.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Briegleb P. A. An approach to density measurement in Douglas fir // Journal of Forestry. 1952. Vol. 50. P. 529–536.</mixed-citation><mixed-citation xml:lang="en">Briegleb P. A. An approach to density measurement in Douglas fir // Journal of Forestry. 1952. Vol. 50. P. 529–536.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Buchacher R., Ledermann T. Interregional crown width models for individual trees growing in pure and mixed stands in Austria // Forests. 2020. Vol. 11. Article 114. DOI: 10.3390/f11010114.</mixed-citation><mixed-citation xml:lang="en">Buchacher R., Ledermann T. Interregional crown width models for individual trees growing in pure and mixed stands in Austria // Forests. 2020. Vol. 11. Article 114. DOI: 10.3390/f11010114.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Choi J., Lorimer C. G., Vanderwerker J. et al. A crown model for simulating long-term stand and gap dynamics in northern hardwood forests // Forest Ecology and Management. 2001. Vol. 152 (1). P. 235–258.</mixed-citation><mixed-citation xml:lang="en">Choi J., Lorimer C. G., Vanderwerker J. et al. A crown model for simulating long-term stand and gap dynamics in northern hardwood forests // Forest Ecology and Management. 2001. Vol. 152 (1). P. 235–258.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Dawkins H. C. Crown diameters: their relation to bole diameter in tropical forest trees // Commonwealth Forestry Review. 1963. Vol. 42. P. 318–333.</mixed-citation><mixed-citation xml:lang="en">Dawkins H. C. Crown diameters: their relation to bole diameter in tropical forest trees // Commonwealth Forestry Review. 1963. Vol. 42. P. 318–333.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Fu L., Sharma R. P., Hao K. et al. A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China // Forest Ecology and Management. 2017. Vol. 389. P. 364-373. DOI: 10.1016/j.foreco.2016.12.034.</mixed-citation><mixed-citation xml:lang="en">Fu L., Sharma R. P., Hao K. et al. A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China // Forest Ecology and Management. 2017. Vol. 389. P. 364–373. DOI: 10.1016/j.foreco.2016.12.034.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Gering L. R., May D. M. The relationship of diameter at breast height and crown diameter for four species groups in Hardin County, Tennessee // Southern Journal of Applied Forestry. 1995. Vol. 19. P. 177–181.</mixed-citation><mixed-citation xml:lang="en">Gering L. R., May D. M. The relationship of diameter at breast height and crown diameter for four species groups in Hardin County, Tennessee // Southern Journal of Applied Forestry. 1995. Vol. 19. P. 177–181.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Gominski D., Kariryaa A., Brandt M. et al. Benchmarking individual tree mapping with sub-meter imagery // ISPRS Journal of Photogrammetry and Remote Sensing. 2023 (in press). DOI: 10.48550/arXiv.2311.07981.</mixed-citation><mixed-citation xml:lang="en">Gominski D., Kariryaa A., Brandt M. et al. Benchmarking individual tree mapping with sub-meter imagery // ISPRS Journal of Photogrammetry and Remote Sensing. 2023 (in press). DOI: 10.48550/arXiv.2311.07981.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Hein S., Spiecker H. Crown and tree allometry of open-grown ash (Fraxinus excelsior L.) and sycamore (Acer pseudoplatanus L.) // Agroforestry Systems. 2008. Vol. 73. P. 205–218.</mixed-citation><mixed-citation xml:lang="en">Hein S., Spiecker H. Crown and tree allometry of open-grown ash (Fraxinus excelsior L.) and sycamore (Acer pseudoplatanus L.) // Agroforestry Systems. 2008. Vol. 73. P. 205–218.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Hemery G. E., Savill P. S., Pryor S. N. Applications of the crown diameter–stem diameter relationship for different species of broadleaved trees // Forest Ecology and Management. 2005. Vol. 215. P. 285–294. DOI:10.1016/j.foreco.2005.05.016.</mixed-citation><mixed-citation xml:lang="en">Hemery G. E., Savill P. S., Pryor S. N. Applications of the crown diameter–stem diameter relationship for different species of broadleaved trees // Forest Ecology and Management. 2005. Vol. 215. P. 285–294. DOI:10.1016/j.foreco.2005.05.016.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Hou R., Chai Z. Predicting crown width using nonlinear mixed-effects models accounting for competition in multi-species secondary forests // Peer Journal. 2022. Vol. 10. Article e13105. http://doi.org/10.7717/peerj.13105.</mixed-citation><mixed-citation xml:lang="en">Hou R., Chai Z. Predicting crown width using nonlinear mixed-effects models accounting for competition in multi-species secondary forests // Peer Journal. 2022. Vol. 10. Article e13105. http://doi.org/10.7717/peerj.13105.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Ishii H. T., Tanabe S. I., Hiura T. Exploring the relationships among canopy structure, stand productivity, and biodiversity of temperate forest ecosystems // Forest Science. 2004. Vol. 50 (3). P. 342–355.</mixed-citation><mixed-citation xml:lang="en">Ishii H. T., Tanabe S. I., Hiura T. Exploring the relationships among canopy structure, stand productivity, and biodiversity of temperate forest ecosystems // Forest Science. 2004. Vol. 50(3). P. 342–355.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Luo Y., Wang X., Ouyang Z. et al. A review of biomass equations for China's tree species // Earth System Science Data. 2020. Vol. 12 (1). P. 21–40. DOI: 10.5194/essd-12-21-2020.</mixed-citation><mixed-citation xml:lang="en">Luo Y., Wang X., Ouyang Z. et al. A review of biomass equations for China's tree species // Earth System Science Data. 2020. Vol. 12(1). P. 21–40. DOI: 10.5194/essd-12-21-2020.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Nowak D. J., Dwyer J. F. Understanding the benefits and costs of urban forest ecosystems // Urban and community forestry in the Northeast, 2nd ed. J. E. Kuser (ed.). Springer, 2007. P. 25–46.</mixed-citation><mixed-citation xml:lang="en">Nowak D. J., Dwyer J. F. Understanding the benefits and costs of urban forest ecosystems // Urban and community forestry in the Northeast, 2nd ed. J. E. Kuser (ed.). Springer, 2007. P. 25–46.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Philip M. S. Measuring trees and forests, 2nd ed. CAB International: Wallingford, 1994. 310 p.</mixed-citation><mixed-citation xml:lang="en">Philip M. S. Measuring trees and forests, 2nd ed. CAB International: Wallingford, 1994. 310 p.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Pretzsch H., Biber P., Uhl E. et al. Crown size and growing space requirement of common tree species in urban centres, parks, and forests // Urban Forestry &amp; Urban Greening. 2015. Vol. 14 (3). P. 466–479. dx.doi. org/10.1016/j.ufug.2015.04.006.</mixed-citation><mixed-citation xml:lang="en">Pretzsch H., Biber P., Uhl E. et al. Crown size and growing space requirement of common tree species in urban centres, parks, and forests // Urban Forestry &amp; Urban Greening. 2015. Vol. 14(3). P. 466–479. DOI: 10.1016/j.ufug.2015.04.006.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Putz F. E., Parker G. G., Archibald R. M. Mechanical abrasion and inter crown spacing // The American Midland Naturalist. 1984. Vol. 112 (1). P. 24–28.</mixed-citation><mixed-citation xml:lang="en">Putz F. E., Parker G. G., Archibald R. M. Mechanical abrasion and inter crown spacing // The American Midland Naturalist. 1984. Vol. 112(1). P. 24–28.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Qiu S., Gao P., Pan L. et al. Developing nonlinear additive tree crown width models based on decomposed competition index and tree variables // Journal of Forestry Research. 2023. Vol. 34. P. 1407–1422. DOI: 10.1007/s11676-022-01576-0</mixed-citation><mixed-citation xml:lang="en">Qiu S., Gao P., Pan L. et al. Developing nonlinear additive tree crown width models based on decomposed competition index and tree variables // Journal of Forestry Research. 2023. Vol. 34. P. 1407–1422. DOI: 10.1007/s11676-022-01576-0.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Raptis D., Kazana V., Kazaklis A. et al. A crown width-diameter model for natural even-aged black pine forest management // Forests. 2018. Vol. 9(10). Article 610. https://doi.org/10.3390/f9100610.</mixed-citation><mixed-citation xml:lang="en">Raptis D., Kazana V., Kazaklis A. et al. A crown width-diameter model for natural even-aged black pine forest management // Forests. 2018. Vol. 9(10). Article 610. https://doi.org/10.3390/f9100610.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Schmidt M., Hanewinkel M., Kändler G., et al. An inventory-based approach for modeling single-tree storm damage – an experiences with the winter storm of 1999 in southwestern Germany // Canadian Journal of Forest Research. 2010. Vol. 40(8). P. 1636–1652.</mixed-citation><mixed-citation xml:lang="en">Schmidt M., Hanewinkel M., Kändler G., et al. An inventory-based approach for modeling single-tree storm damage – an experiences with the winter storm of 1999 in southwestern Germany // Canadian Journal of Forest Research. 2010. Vol. 40(8). P. 1636–1652.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Seebach Ch. Der modifizierte Buchen-HochwaldBetrieb // Kritische Blätter für Forstund Jagdwis senschaft. 1845. Vol. 21. P. 147–185.</mixed-citation><mixed-citation xml:lang="en">Seebach Ch. Der modifizierte Buchen-Hochwald- Betrieb // Kritische Blätter für Forst- und Jagdwissenschaft. 1845. Vol. 21. P. 147–185.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Sharma R. P., Bilek L., Vacek Z. et al. Modelling crown width-diameter relationship for Scots pine in the central Europe // Trees-Structure and Function. 2017. Vol. 31. P. 1875–1889. DOI: 10.1007/s00468-017-1593-8.</mixed-citation><mixed-citation xml:lang="en">Sharma R. P., Bilek L., Vacek Z. et al. Modelling crown width-diameter relationship for Scots pine in the central Europe // Trees-Structure and Function. 2017. Vol. 31. P. 1875–1889. DOI: 10.1007/s00468-017-1593-8.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Thill A. Qualites des grumes de quelques essences feuillues, et de l’epicea commun // Bulletin de la Société royale forestière de Belgique. 1980. Vol. 87. P. 1–7.</mixed-citation><mixed-citation xml:lang="en">Thill A. Qualites des grumes de quelques essences feuillues, et de l’epicea commun // Bulletin de la Société royale forestière de Belgique. 1980. Vol. 87. P. 1–7.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Troxel B., Piana M., Ashton M. S. et al. Relationships between bole and crown size for young urban trees in the northeastern USA // Urban Forestry &amp; Urban Greening. 2013. Vol. 12 (2). P. 144–153. DOI: 10.1016/j.ufug.2013.02.006.</mixed-citation><mixed-citation xml:lang="en">Troxel B., Piana M., Ashton M. S. et al. Relationships between bole and crown size for young urban trees in the northeastern USA // Urban Forestry &amp; Urban Greening. 2013. Vol. 12(2). P. 144–153. DOI: 10.1016/j.ufug.2013.02.006.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Wang B., Bu Y., Tao G. et al. Quantifying the effect of crown vertical position on individual tree competition: total overlap index and its application in sustainable forest management // Sustainability. 2020. Vol. 12. Article 7498. DOI: 10.3390/su12187498.</mixed-citation><mixed-citation xml:lang="en">Wang B., Bu Y., Tao G. et al. Quantifying the effect of crown vertical position on individual tree competition: total overlap index and its application in sustainable forest management // Sustainability. 2020. Vol. 12. Article 7498. DOI: 10.3390/su12187498.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Wang H., Wan P., Wang Q. et al. Prevalence of inter-tree competition and its role in shaping the community structure of a natural Mongolian Scots pine (Pinus sylvestris var. mongolica) forest // Forests. 2017. Vol. 8. Article 84. DOI: 10.3390/f8030084.</mixed-citation><mixed-citation xml:lang="en">Wang H., Wan P., Wang Q. et al. Prevalence of inter-tree competition and its role in shaping the community structure of a natural Mongolian Scots pine (Pinus sylvestris var. mongolica) forest // Forests. 2017. Vol. 8. Article 84. DOI: 10.3390/f8030084.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Wang J., Jiang L., Xin S. et al. Two new methods applied to crown width additive models: a case study for three tree species in Northeastern China // Annals of Forest Science. 2023. Vol. 80. Article 11. https://doi.org/10.1186/s13595-022-01165-5.</mixed-citation><mixed-citation xml:lang="en">Wang J., Jiang L., Xin S. et al. Two new methods applied to crown width additive models: a case study for three tree species in Northeastern China // Annals of Forest Science. 2023. Vol. 80. Article 11. https://doi.org/10.1186/s13595-022-01165-5.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">West G. B., Brown J. H., Enquist B. J. A general model for the structure and allometry of plant vascular system // Nature. 1999. Vol. 400. P. 664–667. DOI: 10.1038/23251.</mixed-citation><mixed-citation xml:lang="en">West G. B., Brown J. H., Enquist B. J. A general model for the structure and allometry of plant vascular system // Nature. 1999. Vol. 400. P. 664–667. DOI: 10.1038/23251.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Whitfield J. All creatures great and small // Nature. 2001. Vol. 413. P. 342–344. DOI: 10.1038/35096683.</mixed-citation><mixed-citation xml:lang="en">Whitfield J. All creatures great and small // Nature. 2001. Vol. 413. P. 342–344. DOI: 10.1038/35096683.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Yang Y., Huang S. Allometric modelling of crown width for white spruce by fixed-and mixed-effects models // Forestry Chronicle. 2017. Vol. 93. P. 138–147. DOI: 10.5558/tfc2017-020.</mixed-citation><mixed-citation xml:lang="en">Yang Y., Huang S. Allometric modelling of crown width for white spruce by fixed-and mixed-effects models // Forestry Chronicle. 2017. Vol. 93. P. 138–147. DOI: 10.5558/tfc2017-020.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Zasada M., Stereńczak K., Brach M. Relationship between dbh and crown characteristics derived by airborne laser scanner // Sylwan. 2011. Vol. 155 (11). P. 725−735.</mixed-citation><mixed-citation xml:lang="en">Zasada M., Stereńczak K., Brach M. Relationship between dbh and crown characteristics derived by airborne laser scanner // Sylwan. 2011. Vol. 155(11). P. 725–735.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
