<?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">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">10.21266/2079-4304.2026.259.159-174</article-id><article-id custom-type="elpub" pub-id-type="custom">isplta-781</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>Анализ и оценка результатов прогноза динамики лесного фонда Ленинградской области по модели EFISCEN</article-title><trans-title-group xml:lang="en"><trans-title>Analysis and evaluation of the results of forecasting the dynamics of the Leningrad region forest fund using the EFISCEN model</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8795-2888</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Алексеев</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Alekseev</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>АЛЕКСЕЕВ Александр Сергеевич – заведующий кафедрой лесной таксации, лесоустройства и геоинформационных систем, профессор, доктор географических наук</p><p>194021, Институтский пер., д. 5, Санкт-Петербург</p></bio><bio xml:lang="en"><p>ALEKSEEV Aleksandr S. – DSc (Geographical), Professor, Head of the Department of Forest Inventory, Management and GIS</p><p>194021. Institute per. 5. St. Petersburg</p></bio><email xlink:type="simple">a_s_alekseev@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0003-3243-3425</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шариф</surname><given-names>Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Shareef</surname><given-names>D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ШАРИФ Дима – аспирант кафедры лесной таксации, лесоустройства и геоинформационных систем</p><p>194021, Институтский пер., д. 5, Санкт-Петербург</p></bio><bio xml:lang="en"><p>SHAREEF Deema – PhD student, Department of Forest Inventory, Management and GIS</p><p>194021. Institute per. 5. St. Petersburg</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Санкт-Петербургский государственный лесотехнический университет имени С.М. Кирова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>St.Petersburg State Forest Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>24</day><month>08</month><year>2026</year></pub-date><volume>1</volume><issue>259</issue><fpage>159</fpage><lpage>174</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Алексеев А.С., Шариф Д., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Алексеев А.С., Шариф Д.</copyright-holder><copyright-holder xml:lang="en">Alekseev A.S., Shareef D.</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/781">https://izvestiya-lta.spbftu.ru/jour/article/view/781</self-uri><abstract><p>В статье проведен анализ и получены количественные оценки результатов прогнозирования динамики лесного фонда Ленинградской области по модели EFISCEN. Приведен краткий обзор основных имитационных и других математических моделей, применяемых для прогнозирования динамики лесного фонда. Для моделирования на период с 1990 по 2020 гг. с помощью модели EFISCEN были использованы следующие пять сценариев: идеальное управление лесами, обычная практика ведения лесного хозяйства, сценарий, направленный на достижение максимально возможного устойчивого уровня лесопользования, сценарий, предполагающий восстановление лесохозяйственного производства и заготовки древесины конца 1980-х гг. в течение первых 20 лет, и сценарий восстановления, но с учетом дополнительных требований охраны природы. Результаты прогнозирования по модели сравнивались по следующим трем показателям: средний запас древостоев, средний прирост древостоев, объем заготовки древесины. Сравнение проводилось с фактическими значениями указанных показателей по данным Государственного лесного реестра о состоянии лесов Ленинградской области в 2021 г. в абсолютных и относительных величинах. Для сравнения качества прогнозирования по 5 сценариям и определения наиболее точного из них для каждого из сценариев рассчитывался индекс расхождения прогнозных результатов моделирования и фактических данных. Наиболее точным оказался прогноз по сценарию №2 – «Обычная практика ведения лесного хозяйства». Этот результат позволяет предположить, что наиболее надежным методом прогнозирования на срок 30 лет может быть простая экстраполяция. Прогнозы, которые дают сценарии №1 – «Идеальное управление лесами» – и №3 – «Максимально возможный устойчивый уровень лесопользования», позволяют оценить потенциал лесного хозяйства Ленинградской области. Метод имитационного моделирования, в том числе и модель EFISCEN, несмотря на все его недостатки, остается полезным инструментом для научного изучения динамики лесного сектора в условиях изменяющейся окружающей среды.</p></abstract><trans-abstract xml:lang="en"><p>The article analyzes and quantifies the results of forecasting the dynamics of the Leningrad Region forest fund using the EFISCEN model. A brief overview of the main simulation and other mathematical models used to predict the dynamics of the forest fund is given. The following five scenarios were used for modeling for the period from 1990 to 2020 using the EFISCEN model: ideal forest management, common forest management practices, a scenario aimed at achieving the highest possible sustainable level of forest management, a scenario involving the restoration of forestry production and timber harvesting in the late 1980s during the first 20 years and restoration scenario, but taking into account additional requirements of nature protection. The model's forecasting results were compared according to the following three indicators: the average growing stock of tree stands, the average wood stock increment of stands, and the volume of timber harvesting. The comparison was carried out with the actual values of these indicators according to the data of the State Forest Register on the state of forests of the Leningrad Region in 2021 in absolute and relative terms. To compare the quality of forecasting for 5 scenarios and determine the most accurate one, an index of discrepancy between the predicted modeling results and actual data was calculated for each scenario. The forecast turned out to be the most accurate according to scenario No. 2 – “Common forestry practice”. This result suggests that the most reliable forecasting method for a period of 30 years may be a simple extrapolation. The forecasts given by scenarios No. 1 – “Ideal forest management” and No. 3 – “The maximum possible sustainable level of forest management” – allow us to assess the potential of forestry in the Leningrad region. The simulation method, including the EFISCEN model, despite all its disadvantages, remains a useful tool for the scientific study of the dynamics of the forest sector in a changing environment</p></trans-abstract><kwd-group xml:lang="ru"><kwd>лесной фонд</kwd><kwd>запас древостоев</kwd><kwd>прирост древостоев</kwd><kwd>лесопользование</kwd><kwd>имитационное моделирование</kwd><kwd>модель EFISCEN</kwd><kwd>сценарий</kwd><kwd>прогноз</kwd></kwd-group><kwd-group xml:lang="en"><kwd>forest fund</kwd><kwd>wood stock of stands</kwd><kwd>increment of wood stock</kwd><kwd>forest management</kwd><kwd>simulation modeling</kwd><kwd>EFISCEN model</kwd><kwd>scenario</kwd><kwd>forecast</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">Алексеев А.С. Влияние на динамику лесного фонда смены пород и характера ведения лесного хозяйства в ряде областей Северо-запада РФ // Известия Санкт-Петербургской лесотехнической академии. 2009. Вып. 186. С. 4-15.</mixed-citation><mixed-citation xml:lang="en">Alekseev A.S. Influence on the dynamics of the forest fund the change of species and the style of forest management in a number of regions of the North-West of the Russian Federation. Izvestia Sankt-Peterburgskoj Lesotehniceskoj Akademii, 2009, iss. 186, pp. 4-15. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Зубкова Е.В., Жукова Л.А, Фролов П.В, Шанин В.Н. Работы А.С. Комарова по клеточно-автоматному моделированию популяционно-онтогенетических процессов у растений // Компьютерные исследования и моделирование. 2016. Т. 8, №2. С. 285−295. DOI: 10.20537/2076-7633-2016-8-2-285-295.</mixed-citation><mixed-citation xml:lang="en">Chertov O.G., Komarov A.S., Karev G.P. Modern Approaches in Forest Ecosystem Modelling. European Forest Institute Research Reports, 1999a, vol. 8, 116 p. DOI: 10.1163/9789004612570.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Карев Г.П. Структурные модели естественной динамики лесного покрова // ДАН. 1994. Т. 337, № 2. С. 354-356.</mixed-citation><mixed-citation xml:lang="en">Chertov O.G., Komarov A.S., Tsiplianovsky A.V. A combined simulation model of Scots pine, Norway spruce and Silver birch ecosystems in European boreal zone. Forest Ecology and Management, 1999b, no. 116, pp. 189-206. DOI: 10.1016/S0378- 1127(98)00456-3.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Карев Г.П. Структурные модели лесных экосистем // Сибирский лесной журнал. 1999. №4. С. 381-396.</mixed-citation><mixed-citation xml:lang="en">Chumachenko S.I. Basic model of the dynamics of a multi-species forest cenosis of different ages. Sci. works of MSUL, 1993, iss. 248, pp. 147-180. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Леса России и изменение климата. Европейский институт леса, 2020. 140 c.</mixed-citation><mixed-citation xml:lang="en">Chumachenko S.I., Syssouev V.V., Palenova M.M., Bredikhin M.A., Korotkov V.N. Imitation modeling of heterogeneous uneven-aged stands spatial dynamics taking into account silvicultural treatment. IUFRO Conf. Copenhagen, 1996, pp. 484–492.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Медоуз Д.Л., Медоуз Д.Х., Рандерс Й., Беренс У. Пределы роста. М.: Изд-во МГУ, 1991. 208 с.</mixed-citation><mixed-citation xml:lang="en">Chumachenko S.I., Korotkov V.N., Palenova M.M., Politov D.V. Simulation modelling of long-term stand dynamics at different scenarios of forest management for conifer – broad-leaved forests. Ecol. Modeling, 2003, vol. 170, pp. 345–361. DOI: 10.1016/S0304-3800(03)00238-2.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Медоуз Д.Х., Медоуз Д.Л., Рандерс Й. Пределы роста. 30 лет спустя М.: Академкнига, 2007. 342 с.</mixed-citation><mixed-citation xml:lang="en">Chumachenko S.I., Palenova M.M., Korotkov V.N. Forecast of the dynamics of taxation indicators of forest plantations under different scenarios of forestry. Eastern European forests: history in the Holocene and modernity. Moscow, 2004, pp. 492-507. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Моделирование динамики органического вещества в лесных экосистемах. М.: Наука, 2007. 380 с.</mixed-citation><mixed-citation xml:lang="en">Chumachenko S.I., Palenova M.M., Pochinkov S.V., Kukharkina E.V. Simulation modeling of FORRUS-S plantation dynamics is a tool for choosing forestry strategy and planning. Lesnoy Vestnik, 2007, no. 5, pp. 143-152. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Модель EFISCEN // Официальный сайт Европейского института леса. URl: https://efi.int/knowledge/models/efiscen (дата обращения: 28.04.2025).</mixed-citation><mixed-citation xml:lang="en">Computer applications in Sustainable Forest management. Springer, 2006. 278 p.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Форрестер Дж. Основы кибернетики предприятия (Индустриальная динамика). М.: Прогресс, 1971. 340 с.</mixed-citation><mixed-citation xml:lang="en">De Lara M., Doyen L. Sustainable management of natural resources. Mathematical models and methods. Springer, 2008. 266 p. DOI: 10.1007/978-3-540-79074-7.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Форрестер Дж. Динамика развития города. М.: Прогресс, 1974. 286 с.</mixed-citation><mixed-citation xml:lang="en">EFISCEN model. The official website of the European Forest Institute. URL: https://efi.int/knowledge/models/efiscen (accessed April 28, 2025). Forests of Russia and climate change. European Forest Institute, 2020. 140 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Форрестер Дж. Мировая динамика. М.: АСТ, 2003. 384 с.</mixed-citation><mixed-citation xml:lang="en">Forrester J. Dynamics of urban development. Moscow: Progress, 1974. 286 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Чумаченко С.И. Базовая модель динамики многовидового разновозрастного лесного ценоза // Науч. тр. МГУЛ. 1993. Вып. 248. С. 147–180.</mixed-citation><mixed-citation xml:lang="en">Forrester J. Fundamentals of enterprise Cybernetics (Industrial dynamics). Moscow: Progress, 1971. 340 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Чумаченко С.И., Паленова М.М., Коротков В.Н. Прогноз динамики таксационных показателей лесных насаждений при разных сценариях ведения лесного хозяйства // Восточноевропейские леса: история в голоцене и современность. М., 2004. С. 492–507.</mixed-citation><mixed-citation xml:lang="en">Forrester J. World dynamics. Moscow: AST, 2003. 384 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Чумаченко С.И., Починков С.В., Кухаркина Е.В. Имитационное моделирование динамики насаждений FORRUS-S – инструмент выбора стратегии и планирования лесного хозяйства // Лесной вестник. 2007. №5. С. 143-152.</mixed-citation><mixed-citation xml:lang="en">Karev G.P. Structural models of natural dynamics of forest cover. Reports to Russian Academy of Science, 1994, vol. 337, no. 2, pp. 354-356. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Chertov O.G., Komarov A.S., Karev G.P. Modern Approaches in Forest Ecosystem Modelling // European Forest Institute Research Reports. 1999a. Vol. 8. 116 p. DOI: 10.1163/9789004612570.</mixed-citation><mixed-citation xml:lang="en">Karev G.P. Structural models of forest ecosystems. Siberian Forest Journal, 1999, no. 4, pp. 381-396. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Chertov O.G., Komarov A.S., Tsiplianovsky A.V. A combined simulation model of Scots pine, Norway spruce and Silver birch ecosystems in European boreal zone // Forest Ecology and Management. 1999b. №116. P. 189-206. DOI: 10.1016/S0378-1127(98)00456-3.</mixed-citation><mixed-citation xml:lang="en">Komarov A., Chertov O., Zudin S., Nadporozhskaya M., Mikhailov A., Bykhovets S., Zudina E., Zoubkova E. EFIMOD 2 – a model of growth and elements cycling in boreal forest ecosystems. Ecological Modelling, 2003, №170 (2-3), pp. 373-392. DOI: 10.1016/S0304-3800(03)00240-0.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Chumachenko S.I., Syssouev V.V., Palenova M.M., Bredikhin M.A., Korotkov V.N. Imitation modeling of heterogeneous uneven-aged stands spatial dynamics taking into account silvicultural treatment // IUFRO Conf. Copenhagen, 1996. P. 484–492.</mixed-citation><mixed-citation xml:lang="en">Leslie P.H. On the use of matrices in certain population mathematics. Biometrika, 1945, vol. 33, iss. 3, pp. 183–212. DOI: 10.1093/biomet/33.3.183.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Chumachenko S.I., Korotkov V.N., Palenova M.M., Politov D.V. Simulation modelling of long-term stand dynamics at different scenarios of forest management for conifer – broad-leaved forests // Ecol. Modeling. 2003. Vol. 170. P. 345–361. DOI: 10.1016/S0304-3800(03)00238-2.</mixed-citation><mixed-citation xml:lang="en">Liang J., Picard N. Matrix Model of Forest Dynamics: An Overview and Outlook. Forest Science, 2013, vol. 59, iss. 3, pp. 359-378. DOI: 10.5849/forsci.11-123.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Computer applications in Sustainable Forest management. Springer, 2006. 278 p.</mixed-citation><mixed-citation xml:lang="en">Logofet D.O. Convexity in projection matrices: Projection to a calibration problem. Ecol. Model., 2008, vol. 216, iss. 2, pp. 217–228. DOI: 10.1016/j.ecolmodel.2008.03.004.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">De Lara M., Doyen L. Sustainable management of natural resources. Mathematical models and methods. Springer, 2008. 266 p. DOI: 10.1007/978-3-540-79074-7.</mixed-citation><mixed-citation xml:lang="en">Logofet D.O., Lesnaya E.V. The mathematics of Markov models: What Markov chains can really predict in forest successions. Ecol. Model., 2000, vol. 126, iss. 2–3, pp. 285–298. DOI: 10.1016/S0304-3800(00)00269-6.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Komarov A., Chertov O., Zudin S., Nadporozhskaya M., Mikhailov A., Bykhovets S., Zudina E., Zoubkova E. EFIMOD 2 – a model of growth and elements cycling in boreal forest ecosystems // Ecological Modelling. 2003. №170 (2-3). P. 373-392. DOI: 10.1016/S0304-3800(03)00240-0.</mixed-citation><mixed-citation xml:lang="en">Meadows D.L., Meadows D.H., Randers J., Berens W. The Limits of growth. Moscow: Publishing House of Moscow State University, 1991. 208 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Leslie P.H. On the use of matrices in certain population mathematics // Biometrika. 1945. Vol. 33, iss. 3. P. 183–212. DOI: 10.1093/biomet/33.3.183.</mixed-citation><mixed-citation xml:lang="en">Meadows D.H., Meadows D.L., Randers J. Limits of growth. 30 years later. Moscow: Akademkniga, 2007. 342 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Liang J., Picard N. Matrix Model of Forest Dynamics: An Overview and Outlook // Forest Science. 2013. Vol. 59, iss. 3. P. 359-378. DOI: 10.5849/forsci.11-123.</mixed-citation><mixed-citation xml:lang="en">Modeling the dynamics of organic matter in forest ecosystems. Moscow: Nauka, 2007. 380 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Logofet D.O. Convexity in projection matrices: Projection to a calibration problem // Ecol. Model. 2008. Vol. 216, iss. 2. P. 217–228. DOI: 10.1016/j.ecolmodel.2008.03.004.</mixed-citation><mixed-citation xml:lang="en">Nabuurs G.-I., Lioubimov A.V. Future development of the Leningrad region forests under nature-oriented forest management. Forest Ecology and Management, 2000, no. 130, pp. 235-251. DOI: 10.1016/S0378-1127(99)00179-6.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Logofet D.O., Lesnaya E.V. The mathematics of Markov models: What Markov chains can really predict in forest successions // Ecol. Model. 2000. Vol. 126, iss. 2–3. P. 285–298. DOI: 10.1016/S0304-3800(00)00269-6.</mixed-citation><mixed-citation xml:lang="en">Pretzsch H. Forest Dynamics, Growth and Yield. From Measurement to Model. Berlin-Heidelberg: Springer-Verlag, 2009. 655 p. DOI: 10.1007/978-3-540-88307-4.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Nabuurs G.-I., Lioubimov A.V. Future development of the Leningrad region forests under nature-oriented forest management // Forest Ecology and Management. 2000. No. 130. P. 235-251. DOI: 10.1016/S0378-1127(99)00179-6.</mixed-citation><mixed-citation xml:lang="en">Pretzsch H., Biber P., Dursky J. The single tree based stand simulator SILVA. Construction, application and evaluation. Forest Ecology and Management, 2002, vol. 162, pp. 3–21. DOI: 10.1016/S0378-1127(02)00047-6.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Pretzsch H. Forest Dynamics, Growth and Yield. From Measurement to Model. Berlin-Heidelberg: Springer-Verlag, 2009. 655 p. DOI: 10.1007/978-3-540-88307-4.</mixed-citation><mixed-citation xml:lang="en">Sallnas O. A matrix growth model of the Swedish forest. Studia For. Suec., 1990, no. 183, 23 p.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Pretzsch H., Biber P., Dursky J. The single tree based stand simulator SILVA. Construction, application and evaluation // Forest Ecology and Management. 2002. Vol. 162. P. 3–21. DOI: 10.1016/S0378-1127(02)00047-6.</mixed-citation><mixed-citation xml:lang="en">Usher M.B. A matrix model for forest management. Biometrics, 1969, no. 25 (2), pp. 309 –315. DOI: 10.2307/2528791.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Sallnas O. A matrix growth model of the Swedish forest // Studia For. Suec. 1990. No. 183. 23 p.</mixed-citation><mixed-citation xml:lang="en">Usher M.B. Markovian approaches to ecological succession. Journal of Animal Ecology, 1979, no. 48 (2), pp. 413– 426. DOI: 10.2307/4170.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Usher M.B. A matrix model for forest management // Biometrics. 1969. №25 (2). P. 309 –315. DOI: 10.2307/2528791.</mixed-citation><mixed-citation xml:lang="en">Usher M.B. Modelling ecological succession with particular reference to Markovian models. Vegetatio, 1981, no. 46-47, pp. 11–18. DOI: 10.1007/BF00118380.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Usher M.B. Markovian approaches to ecological succession // Journal of Animal Ecology. 1979. №48 (2). P. 413– 426. DOI: 10.2307/4170.</mixed-citation><mixed-citation xml:lang="en">Zubkova E.V., Zhukova L.A., Frolov P.V., Shanin V.N. A. S. Komarov's work on cellular automaton modeling of population-ontogenetic processes in plants. Computer research and modeling, 2016, vol. 8, no. 2, pp. 285-295. DOI: 10.20537/2076-7633-2016-8-2-285-295. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Usher M.B. Modelling ecological succession with particular reference to Markovian models // Vegetatio. 1981. №46-47. P. 11–18. DOI: 10.1007/BF00118380.</mixed-citation><mixed-citation xml:lang="en">Usher M.B. Modelling ecological succession with particular reference to Markovian models // Vegetatio. 1981. №46-47. P. 11–18. DOI: 10.1007/BF00118380.</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>
