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<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">isplta</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Санкт-Петербургской лесотехнической академии</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestia Sankt-Peterburgskoj lesotehniceskoj akademii</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2079-4304</issn><issn pub-type="epub">2658-5871</issn><publisher><publisher-name>СПбГЛТУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21266/2079-4304.2021.237.59-74</article-id><article-id custom-type="elpub" pub-id-type="custom">isplta-245</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>ЛЕСНОЕ ХОЗЯЙСТВО</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FORESTRY</subject></subj-group></article-categories><title-group><article-title>Модель смешанных эффектов зависимости высот от диаметров деревьев в сосновых древостоях</article-title><trans-title-group xml:lang="en"><trans-title>Model of mixed effects of height dependence on tree diameters in pine stands</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дубенок</surname><given-names>Н. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Dubenok</surname><given-names>N. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ДУБЕНОК Николай Николаевич – заведующий кафедрой сельскохозяйственных мелиораций, лесоводства и землеустройства, академик РАН, доктор сельскохозяйственных наук, профессор</p><p>127550, Тимирязевская ул., д. 49, г. Москва</p></bio><bio xml:lang="en"><p>DUBENOK Nikolay N. – DSс (Agriculture), professor, academician of RAS, head of the department of Agricultural Reclamation</p><p>127550. Timiryazevskaya str. 49. Moscow</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кузьмичев</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kuzmichev</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>КУЗЬМИЧЕВ Валерий Васильевич – заведующий лабораторией кафедры сельскохозяйственных мелиораций, лесоводства и землеустройства, доктор биологических наук, профессор</p><p>127550, Тимирязевская ул., д. 49, г. Москва</p></bio><bio xml:lang="en"><p>KUZMICHEV Valery V. – DSс (Biology), professor, head of laboratory of the department of Agricultural Reclamation</p><p>127550. Timiryazevskaya str. 49. Moscow</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8939-942X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лебедев</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Lebedev</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ЛЕБЕДЕВ Александр Вячеславович – доцент кафедры сельскохозяйственных мелиораций, лесоводства и землеустройства, кандидат сельскохозяйственных наук</p><p>127550, Тимирязевская ул., д. 49, г. Москва</p></bio><bio xml:lang="en"><p>LEBEDEV Aleksandr V. – PhD (Agriculture), lecturer of the department of Agricultural Reclamation</p><p>127550. Timiryazevskaya str. 49. Moscow</p></bio><email xlink:type="simple">avl1993@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Российский государственный аграрный университет – МСХА имени К.А. Тимирязева</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Forestry and Land Management at Russian State Agrarian University – Moscow Timiryazev Agricultural Academy</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>08</day><month>03</month><year>2024</year></pub-date><volume>0</volume><issue>237</issue><fpage>59</fpage><lpage>74</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Дубенок Н.Н., Кузьмичев В.В., Лебедев А.В., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Дубенок Н.Н., Кузьмичев В.В., Лебедев А.В.</copyright-holder><copyright-holder xml:lang="en">Dubenok N.N., Kuzmichev V.V., Lebedev A.V.</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://izvestiya-lta.spbftu.ru/jour/article/view/245">https://izvestiya-lta.spbftu.ru/jour/article/view/245</self-uri><abstract><p>Основными исходными данными для определения запаса служат результаты обмеров диаметров и высот деревьев. Но обмеры диаметров деревьев на высоте груди выполнить намного проще, чем обмеры высот, поэтому ограничиваются замерами высот 15–25 деревьев. Цель исследования – по материалам измерения модельных деревьев в сосновых древостоях выбрать наиболее адекватную простую модель, которая передает зависимость между высотой деревьев и диаметром на высоте груди. Объектом исследования послужили сосновые древостои искусственного происхождения на постоянных пробных площадях в Лесной опытной даче Российского государственного агарного университета – МСХА имени К.А. Тимирязева. В работе используются данные обмеров деревьев на 17 постоянных пробных площадях с 1934 по 2005 гг. Возраст древостоев на момент проведения измерений от 50 до 125 лет. По итогам проведения 77 перечетов массив данных составил 1157 наблюдений. И модель фиксированных эффектов, и модель смешанных эффектов адекватно описали зависимость между высотами и диаметрами деревьев в культурах сосны. Но, как и ожидалось, первая модель имеет худшие значения метрик качества по сравнению со второй. Модель со смешанными эффектами более точно предсказывает значения высот по сравнению с моделью фиксированных эффектов. Недостающие значения высот большого количества деревьев на участке можно вычислить более точно с помощью модели смешанных эффектов, а не применения модели фиксированных эффектов или использования только фиксированной части (средний отклик) модели смешанных эффектов. Применение разработанной модели должно ограничиваться только в тех условиях, к которым относятся экспериментальные материалы.</p></abstract><trans-abstract xml:lang="en"><p>The main data for the stock of research results is the diameter of measurements and heights of trees. But measurements of the diameter at breast height are much easier to perform than measurements of heights, therefore, they are limited to measuring the heights of 15–25 trees. The aim of the study is to select the most adequate simple model based on the measurements of model trees in pine antiquities, which conveys the relationship between the height of trees and the diameter at breast height. The object of the study was pine stands of artificial origin on permanent test plots in the Forest Experimental Station Russian State Agararian University – Moscow Timiriazev Agricultural Academy. The work uses data from tree measurements on 17 permanent sample plots from 1934 to 2005. The age of the stands at the time of measurements was from 50 to 125 years. As a result of 77 enumerations, the data array amounted to 1157 observations. Both the fixed effects model and the mixed effects model adequately describe the relationship between heights and diameters of trees in pine stumps. But, as expected, the first model has worse quality metrics than the second. The mixed effects model more accurately predicts heights from the fixed effects model. The missing heights of a large number of trees on a site can be calculated accurately using mixed effects models, rather than using fixed effects models or using only a fixed portion (mean response) of the mixed effects model. The application of the developed model should be limited only in those conditions to which the experimental materials are applied.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>высота</kwd><kwd>диаметр на высоте груди</kwd><kwd>сосновый древостой</kwd><kwd>модель смешанных эффектов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>height</kwd><kwd>diameter at breast height</kwd><kwd>pine forest stand</kwd><kwd>mixed effect model</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Атрощенко О.А. Моделирование роста леса и лесохозяйственных процессов. Минск: БГТУ, 2004. 249 с.</mixed-citation><mixed-citation xml:lang="en">O.A. 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