[1] Li Y, Wang W, Zeng W S, et al. Development of crown ratio and height to crown base models for Masson pine in Southern China[J]. Forests, 2020, 11(11): 1216-1216. doi: 10.3390/f11111216
[2] 卢 军, 李凤日, 张会儒, 等. 帽儿山天然次生林主要树种冠长率模型[J]. 林业科学, 2011, 47(6):70-76. doi: 10.11707/j.1001-7488.20110611
[3] Cortini F, MacIsaac D, Comeau P. White spruce growth and wood properties over multiple time periods in relation to current tree and stand attributes[J]. Forests, 2016, 7(3): 49-66. doi: 10.3390/f7030049
[4] Kuprevicius A, Auty D, Achim A, et al. Quantifying the influence of live crown ratio on the mechanical properties of clear wood[J]. Forestry, 2013(3): 361-369.
[5] 郭孝玉. 长白落叶松人工林树冠结构及生长模型研究[D]. 北京: 北京林业大学, 2013.
[6] Soares P, Tome M. A tree crown ratio prediction equation for eucalypt plantations[J]. Annals of Forest Science, 2001, 58(2): 193-202. doi: 10.1051/forest:2001118
[7] Zhao D H, Kane M, BoRders B E. Crown ratio and relative spacing relationships for loblolly pine plantations[J]. Open Journal of Forestry, 2012, 2(3): 107-112.
[8] Dickinson Y L, Battaglia M A, Asherin L A. Evaluation of the FVS-CR diameter growth model in structurally-heterogeneous ponderosa pine ( Pinus ponderosa Douglas ex C. Lawson) stands in the Southern Rockies, and potential modifications[J]. Forest Ecology and Management, 2019, 448: 1-10. doi: 10.1016/j.foreco.2019.05.031
[9] Sterba H, Blab A, Katzensteiner K. Adapting an individual tree growth model for Norway spruce (Picea abies L. Karst. ) in pure and mixed species stands[J]. Forest Ecology and Management, 2002, 159(1-2): 101-110. doi: 10.1016/S0378-1127(01)00713-7
[10] Leites L P, Robinson A P, Crookston N L. Accuracy and equivalence testing of crown ratio models and assessment of their impact on diameter growth and basal area increment predictions of two variants of the Forest Vegetation Simulator[J]. Canadian Journal of Forest Research, 2009, 39(3): 655-665. doi: 10.1139/X08-205
[11] Temesgen H, Lemay V, Mitchell S J. Tree crown ratio models for multi-species and multi-layered stands of southeastern British Columbia[J]. Forestry Chronicle, 2005, 81(1): 133-141. doi: 10.5558/tfc81133-1
[12] Hasenauer H, Monserud R A. A crown ratio model for Austrian forests[J]. Forest Ecology and Management, 1996, 84(1): 49-60.
[13] 覃阳平, 张怀清, 陈永富, 等. 基于简单竞争指数的杉木人工林树冠形状模拟[J]. 林业科学研究, 2014, 27(3):363-366. doi: 10.13275/j.cnki.lykxyj.2014.03.011
[14] Thorpe H C, Astrup R, Trowbridge A, et al. Competition and tree crowns: A neighborhood analysis of three boreal tree species[J]. Forest Ecology and Management, 2010, 259(8): 1586-1596. doi: 10.1016/j.foreco.2010.01.035
[15] 韩大校, 金光泽. 地形和竞争对典型阔叶红松林不同生长阶段树木胸径生长的影响[J]. 北京林业大学学报, 2017, 39(1):9-19. doi: 10.13332/j.1000-1522.20160218
[16] Sharma R P, Vacek Z, Vacek S. Generalized nonlinear mixed-effects individual tree crown ratio models for Norway spruce and European beech[J]. Forests, 2018, 9(9): 555-555. doi: 10.3390/f9090555
[17] Fu L Y, Zhang H Y, Lu J, et al. Multilevel nonlinear mixed-effect crown ratio models for individual trees of Mongolian oak (Quercus mongolica) in Northeast China[J]. Plos One, 2015, 10(8): e0133294. doi: 10.1371/journal.pone.0133294
[18] 王金池, 邓华锋, 冉啟香, 等. 基于哑变量的云南松蓄积生长模型[J]. 森林与环境学报, 2017, 37(4):453-458.
[19] 石振威, 曾思齐, 刘发林, 等. 基于地形与竞争因子的青冈栎次生林树高哑变量模型研究[J]. 西北林学院学报, 2020, 35(1):196-202 + 272. doi: 10.3969/j.issn.1001-7461.2020.01.30
[20] 曹 梦, 潘 萍, 欧阳勋志, 等. 基于哑变量的闽楠天然次生林单木胸径和树高生长模型研究[J]. 北京林业大学学报, 2019, 41(5):88-96. doi: 10.13332/j.1000-1522.20190026
[21] 段光爽, 王秋燕, 宋新宇, 等. 竞争环境下红松单木树高与胸径的相对生长关系[J]. 林业科学, 2020, 56(10):105-112. doi: 10.11707/j.1001-7488.20201011
[22] 段光爽, 李学东, 冯 岩, 等. 华北落叶松天然次生林树高曲线的混合效应模型[J]. 南京林业大学学报(自然科学版), 2018, 42(2):163-169.
[23] Popoola F S, Adesoye P O. Crown ratio models for Tectona grandis (Linn. f) stands in Osho Forest Reserve, Oyo State, Nigeria[J]. Journal of Forest & Environmental Science, 2012, 28(2): 63-67.
[24] Dyer M E, Burkhart H E. Compatible crown ratio and crown height models[J]. Canadian Journal of Forest Research, 1987, 17(6): 572-574. doi: 10.1139/x87-096
[25] Holdaway M R. Modeling tree crown ratio[J]. The Forestry Chronicle, 1986, 62(5): 451-455. doi: 10.5558/tfc62451-5
[26] 袁 慧, 杜超群, 赵小涛, 等. 基于混合效应的湖北杉木冠长率模型[J]. 中国农学通报, 2021, 37(4):31-37. doi: 10.11924/j.issn.1000-6850.casb2020-0023
[27] Adame P, Hynynen J, Cañellas I, et al. Individual-tree diameter growth model for rebollo oak ( Quercus pyrenaica Willd. ) coppices[J]. Forest Ecology and Management, 2007, 255(3): 1011-1022.
[28] 段仁燕, 王孝安, 黄敏毅. 太白红杉径向生长的预测模型[J]. 广西植物, 2009, 29(2):212-216. doi: 10.3969/j.issn.1000-3142.2009.02.015
[29] 陈东升, 孙晓梅, 李凤日. 落叶松人工林枝条直径和长度的非线性混合模型[J]. 南京林业大学学报(自然科学版), 2015, 39(6):74-80.
[30] Carr S, Larocque G R, Luckai N, et al. Effect of competition on individual white spruce production in young boreal mixedwood forests[J]. Canadian Journal of Forest Research, 2020, 50(8): 726-735. doi: 10.1139/cjfr-2019-0395
[31] 郭明辉. 森林培育措施对红松人工林径向生长性质的影响[J]. 林业科学, 2003, 39(5):100-104. doi: 10.3321/j.issn:1001-7488.2003.05.015
[32] 严恩萍, 林 辉, 洪奕丰, 等. 杉木人工林叶面积指数估测及影响因子分析[J]. 水土保持研究, 2013, 20(4):75-81.
[33] Mäkelä A, Valentine H T. Crown ratio influences allometric scaling in trees.[J]. Ecology, 2006, 87(12): 2967-2972. doi: 10.1890/0012-9658(2006)87[2967:CRIASI]2.0.CO;2