不同林火烈度对大兴安岭兴安落叶松天然林林木空间分布格局的影响

王烁; 韩大校; 王千雪; 丛日征; 王晓红; 杨光; 王立中; 张吉利

doi:10.12171/j.1000-1522.20210367

不同林火烈度对大兴安岭兴安落叶松天然林林木空间分布格局的影响

1.
中国林科院寒温带林业研究中心，黑龙江哈尔滨 150086
2.
东北林业大学林学院，黑龙江哈尔滨 150040
3.
大兴安岭农林科学研究院，黑龙江加格达奇 156000

基金项目: 中国林业科学研究院中央级公益性科研院所基本科研业务费专项（CAFYBB2019MA007），国家自然科学基金青年基金项目（31600524）

详细信息

作者简介:
王烁，助理研究员。主要研究方向：森林经理学。Email：2529853280@qq.com　地址：150086 黑龙江省哈尔滨市南岗区学府路374号中国林科院寒温带林业研究中心

责任作者:
张吉利，副研究员。主要研究方向：森林生态学。Email：xtafktj@126.com　地址：同上

中图分类号: S758.5
计量
- 文章访问数: 681
- HTML全文浏览量: 130
- PDF下载量: 86
出版历程
- 收稿日期: 2021-09-14
- 修回日期: 2022-03-01
- 录用日期: 2022-11-14
- 网络出版日期: 2022-11-16
- 发布日期: 2023-02-24

Effects of different forest fire intensities on the spatial distribution pattern of natural Larix gmelinii forests in the Great Xing’an Mountains of northeastern China

1.
Research Center of Cold Temperate Forestry, Chinese Academy of Forestry, Harbin 150086, Heilongjiang, China
2.
College of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, China
3.
Research Institute of Agriculture and Forestry of Daxing’anling Forestry Group, Jiagedaqi 156000, Heilongjiang, China

摘要

摘要:
目的林木空间分布格局对于评估森林是否需要经营至关重要，判断林木处于哪种分布状态（聚集分布、随机分布或者均匀分布）是制定合理的森林经营方案的前提。中重度林火会直接导致林木大量死亡，进而改变林分直径分布特征及林木空间分布格局。本文主要研究了达尔滨湖国家森林公园林火发生一年后，不同火烧烈度下兴安落叶松林的林分状态。
方法通过比较林分直径分布、不同类别树木空间格局及其关联性，分析林火对林木空间格局的影响。
结果火烧烈度高的区域，小径级林木存活数量少，小死树的聚集半径相对小。与未过火样地相比，发生火烧的区域，中活树均出现中等尺度的聚集。中度火烧样地内的中树和小树存在关联性，中死树与周围的小死树在4 ~ 8 m范围内呈正相关，中活树与周围的小死树在8 ~ 20 m范围内呈负相关。
结论火烧烈度会影响树木的空间格局以及不同大小不同存活状态树木之间的关联性。针对不同火烧烈度下林木的聚集尺度选择适合的抚育措施对火后森林恢复具有重要意义。本研究可为兴安落叶松林的火后恢复提供科学依据。
- 空间分布格局 /
- 兴安落叶松 /
- 火烈度 /
- O-ring 统计
Abstract:
Objective The spatial distribution pattern of trees is important for evaluating whether the forest needs to be managed, and judging which distribution state (aggregated distribution, random distribution, or uniform distribution) of trees is a prerequisite for developing suitable management plans. Moderate and high severity forest fires can kill a large number of trees, and then change the distribution characteristics of stand diameter and the spatial distribution pattern of forest trees. We investigated natural Larix gmelinii forests in the Da’erbinhu National Forest Park, Inner Mongolia of northern China one year following a mixed-severity wildfire.
Method By comparing the distribution of stand diameter, the spatial distribution pattern of different types of trees and their association, we analyzed the influence of fire on the spatial distribution pattern of trees.
Result The results showed that in high severity areas, the number of small living trees and the gathering radius of small dead trees were relatively small. Compared with the unburned sample plots, the medium living trees presented a clustered distribution at the medium scale in the burned areas. The middle trees and the small trees were associated in the moderate severity burned sample plots. The medium dead trees and the surrounding small dead trees were positively associated within a radius of 4 to 8 m, while the medium living trees and the surrounding small dead trees were negatively associated within a radius of 8 to 20 m.
Conclusion The spatial pattern of trees and the association between trees of different sizes and different status are affected by the fire severity. Choosing suitable afforestation measures according to the aggregation scale of trees for different fire severities is of great significance to forest restoration after a fire. This study can provide a scientific basis for the protection and rational use of nature larch forests in the Great Xing’an Mountains of northeastern China.
- spatial distribution pattern /
- Larix gmelinii /
- fire severity /
- O-ring statistics

HTML全文

图 1 达尔滨湖国家森林公园地理位置

Figure 1. Geographic location of Da’erbinhu National Forest Park

下载: 全尺寸图片幻灯片

图 2 不同火烧烈度下林分的直径分布

U.未火烧；L.轻度火烧；M.中度火烧；H.重度火烧。虚线用于划分小树、中树和大树所在区域；蓝线代表样地中活树的平均胸径；红线代表样地中死树的平均胸径。U, unburned; L, low fire severity; M, moderate fire severity; H, high fire severity. The dotted lines are used to divide small trees, medium trees and large trees. The blue lines represent the mean DBH of live trees in the sample plot. The red lines represent the mean DBH of dead trees in the sample plot.

Figure 2. Stand diameter distribution under different fire severities

下载: 全尺寸图片幻灯片

表 1 不同火烧烈度样地内不同状态和大小的树木数量

Table 1 Number of trees by status and size in different fire severity sample plots

状态 Status	大小 Size	未火烧 Unburned		轻度火烧 Low severity burned		中度火烧 Moderately burned		重度火烧 Severely burned
状态 Status	大小 Size	树木数量 Number of trees	占比 Proportion/%	树木数量 Number of trees	占比 Proportion/%	树木数量 Number of trees	占比 Proportion/%	树木数量 Number of trees	占比 Proportion/%
	树木总量 All trees	148.00 ± 3.29	100	149.00 ± 7.78	100	175.00 ± 7.87	100	176.00 ± 9.97	100
活 Live	活树总量 Total live trees	148.00 ± 3.29	100	123.00 ± 3.74	82.65 ± 2.16	85.00 ± 4.49	48.88 ± 3.76	10.00 ± 4.49	6.12 ± 2.59
	小树 Small tree	50.00 ± 2.49	34.09 ± 1.68	42.00 ± 6.79	28.49 ± 3.08	17.00 ± 1.24	10.09 ± 0.56	3.00 ± 0.81	1.71 ± 0.48
	中树 Medium tree	80.00 ± 3.26	53.79 ± 1.29	51.00 ± 4.54	34.44 ± 4.53	56.00 ± 3.39	32.32 ± 3.19	5.00 ± 2.44	2.86 ± 1.39
	大树 Large tree	18.00 ± 0.81	12.11 ± 0.61	29.00 ± 3.29	19.71 ± 2.32	11.00 ± 1.69	6.46 ± 0.85	2.00 ± 1.24	1.53 ± 0.72
死 Dead	死树总量 Total dead trees			26.00 ± 4.54	17.34 ± 2.16	89.00 ± 9.84	51.11 ± 3.76	165.00 ± 12.39	93.87 ± 2.59
	小树 Small tree			24.00 ± 4.11	16.46 ± 1.94	76.00 ± 7.71	43.74 ± 3.22	108.00 ± 6.94	61.41 ± 0.91
	中树 Medium tree			1.00 ± 0.47	0.88 ± 0.26	11.00 ± 1.88	6.44 ± 0.76	39.00 ± 4.89	22.03 ± 1.56
	大树 Large tree			0	0	1.00 ± 0.94	0.93 ± 0.48	18.00 ± 1.69	10.43 ± 1.12

下载: 导出CSV

表 2 不同火烧烈度样地内不同类别树木的空间分布格局

Table 2 Spatial distribution pattern of different types of trees in different fire severity sample plots

类型 Type	尺度 Scale/m
类型 Type	0 ~ 4	4 ~ 8	8 ~ 12	12 ~ 16	16 ~ 20	20 ~ 24	24 ~ 28	28 ~ 32	32 ~ 36	36 ~ 40
未火烧−小活树 Unburned-small live trees	r	r	r	r	r	r（−）	r（+）	r	r	r
未火烧−中活树 Unburned-medium live trees	r（−）	r（−）	+（r）	r	r	r（+）	r	r	r	r（−）
轻度火烧−小活树 Low severity-small live trees	r	r	r	r	r	r（−）	r	r（+）	r	r
轻度火烧−中活树 Low severity-medium live trees	r	r（+）	r	+（r）	r	r（+）	r	r（−）	r	r（−）
轻度火烧−大活树 Low severity-large live trees	r	r	r	r	r（+）	r	r	r（+）	r	r
轻度火烧−小死树 Low severity-small dead trees	r	r	+（r）	r	r	r	r	r	r（+）	r
中度火烧−中活树 Moderate severity-medium live trees	r	r	r	+	+（r）	r	r（+）	r	r（+）	r（+）
中度火烧−小死树 Moderate severity-small dead trees	r	+（r）	r	r（+）	r	r（+）	r	r（+）	r	r
重度火烧−小死树 High severity-small dead trees	+（r）	r	r	r	r（+）	r	r（−）	r	r	r
重度火烧−中死树 High severity-medium dead trees	r	r	r	r	r	r（−）	r（+）	r	r	r
注：+代表聚集分布，−代表均匀分布，r代表随机分布，−（r）为均匀分布多于随机分布；r（−）表示随机分布多于均匀分布，+（r）、（r）+同理。Notes: + stands for clustering distribution, − for regular distribution, r for random distribution, − (r) for more regular distribution than random distribution, r(−) for more random distribution than regular distribution, the same as +(r) and (r)+.

下载: 导出CSV

表 3 不同火烧烈度样地内不同类别树木的关联性

Table 3 Association of different types of trees in different fire severity sample plots

类型 Type	尺度 Scale/m
类型 Type	0 ~ 4	4 ~ 8	8 ~ 12	12 ~ 16	16 ~ 20	20 ~ 24	24 ~ 28	28 ~ 32	32 ~ 36	36 ~ 40
未火烧−大活树与周围的中活树 Unburned-medium live trees around large live trees	r	r	r	r	r	r	r（+）	r（+）	r	r（+）
未火烧−大活树与周围的小活树 Unburned-small live trees around large live trees	r	r	r	r	r	r	r	r	r	r
未火烧−中活树与周围的小活树 Unburned-small live trees around medium live trees	r	r	r	r（−）	r	r（−）	r	r	r（+）	r
轻度火烧−大活树与周围的中活树 Low severity-medium live trees around large live trees	r	r	r	r	r	r	r	r	r	r
轻度火烧−大活树与周围的小活树 Low severity-small live trees around large live trees	r	r	r	r	r	r	r	r	r	r
轻度火烧−大活树与周围的小死树 Low severity-small dead trees around large live trees	r	r	r	r（−）	r	r	r	r	r	r
轻度火烧−中活树与周围的小活树 Low severity-small live trees around medium live trees	r	r	r（+）	r	r（+）	r	r（+）	r	r	r
轻度火烧−中活树与周围的小死树 Low severity-small dead trees around medium live trees	r	r	r	r	r	r（−）	r	r	r	r
中度火烧−大活树与周围的中活树 Moderate severity-medium live trees around large live trees	r	r（+）	r	r	r（−）	r	r	r	r	r
中度火烧−大活树与周围的小死树 Moderate severity-small dead trees around large live trees	r	r	r（+）	r	r	r（+）	r（+）	r	r（−）	r（−）
中度火烧−中活树与周围的小活树 Moderate severity-small live trees around medium live trees	r（+）	r	r	r	r	r	r	r	r	r（+）
中度火烧−中活树与周围的小死树 Moderate severity-small dead trees around medium live trees	r（−）	r（−）	−	−	−	r（−）	r	r（−）	r（−）	r
中度火烧−中死树与周围的小活树 Moderate severity-small live trees around medium dead trees	r	r	r	r	r	r	r	r	r	r
中度火烧−中死树与周围的小死树 Moderate severity-small dead trees around medium dead trees	r	+	r	r	r	r（+）	r	r	r	r
重度火烧−大活树与周围的小死树 High severity-small dead trees around large living trees	r	r	r	r（−）	r	r	r	r（−）	r	r
重度火烧−大死树与周围的中死树 High severity-medium dead trees around large dead trees	r	r	r	r（+）	r	r	r	r（+）	r	r
重度火烧−大死树与周围的小死树 High severity-small dead trees around large dead trees	r	r（−）	r	r	r	r	r	r	r	r
重度火烧−中活树与周围的小死树 High severity-small dead trees around medium live trees	r	r（−）	r（−）	r	r	r	r（+）	r	r	r
重度火烧−中死树与周围的小活树 High severity-small live trees around medium dead trees	r	r（+）	r	r	r	r	r	r	r	r（+）
重度火烧−中死树与周围的小死树 High severity-small dead trees around medium dead trees	r（+）	r	r	r（−）	r	r（−）	r	r	r	r
注：+代表正相关，−代表负相关，r 代表不相关，−（r）表示负相关多于不相关；r（−）表示不相关多于负相关，+（r）、（r）+同理。Notes: + represents positive association, − represents negative association, r represents non-association, −（r） represents more negative association than non-association, and r（−） represents more non-association than negative association , the same as +（r） and （r）+.

下载: 导出CSV

参考文献(34)

[1]	杨慧, 娄安如, 高益军, 等. 北京东灵山地区白桦种群生活史特征与空间分布格局[J]. 植物生态学报, 2007, 31(2): 272−282. doi: 10.3321/j.issn:1005-264X.2007.02.010 Yang H, Lou A R, Gao Y J, et al. Life history characteristics and spatial distribution of the Betula platyphylla population in the Dongling Mountain Region, Beijing, China[J]. Journal of Plant Ecology, 2007, 31(2): 272−282. doi: 10.3321/j.issn:1005-264X.2007.02.010
[2]	马芳, 王顺忠, 冯金朝, 等. 北京东灵山优势种群树木死亡对空间格局与生境的影响[J]. 生态学报, 2018, 38(21): 7669−7678. Ma F, Wang S Z, Feng J Z, et al. The study of the effect of tree death on spatial pattern and habitat associations in dominant populations of Dongling Mountains in Beijing[J]. Acta Ecologica Sinica, 2018, 38(21): 7669−7678.
[3]	Zenner E K, Hibbs D E. A new method for modeling the heterogeneity of forest structure[J]. Forest Ecology and Management, 2000, 129(1−3): 75−87. doi: 10.1016/S0378-1127(99)00140-1
[4]	Lydersen J M, Collins B M, Miller J D, et al. Relating fire-caused change in forest structure to remotely sensed estimates of fire severity[J]. Fire Ecology, 2016, 12(3): 99−116. doi: 10.4996/fireecology.1203099
[5]	Stevens C S, Sieg C H, Hunter M E. Ten years after wildfires: how does varying tree mortality impact fire hazard and forest resiliency[J]. Forest Ecology and Management, 2012, 267: 199−208. doi: 10.1016/j.foreco.2011.12.003
[6]	Sparkle M. Mixed-severity fire fosters heterogeneous spatial patterns of conifer regeneration in a dry conifer forest[J]. Forests, 2018, 9(1): 1−17.
[7]	Sparks A M, Talhelm A F, Partelli F R, et al. An experimental assessment of the impact of drought and fire on western larch injury, mortality and recovery[J]. International Journal of Wildland Fire, 2018, 27: 1−8. doi: 10.1071/WF16221
[8]	李艳丽, 杨华, 邓华锋. 蒙古栎−糠椴天然混交林空间格局研究[J]. 北京林业大学学报, 2019, 41(3): 33−41. Li Y L, Yang H, Deng H F. Spatial distribution patterns of Quercus mongolica and Tilia mandshurica natural mixed forests[J]. Journal of Beijing Forestry University, 2019, 41(3): 33−41.
[9]	Zhang L Y, Dong L B, Liu Q, et al. Spatial patterns and interspecific associations during natural regeneration in three types of secondary forest in the central part of the Greater Khingan Mountains, Heilongjiang Province, China[J]. Forests, 2020, 152(11): 1−18.
[10]	倪瑞强, 唐景毅, 程艳霞, 等. 长白山云冷杉林主要树种空间分布及其关联性[J]. 北京林业大学学报, 2013, 35(6): 28−35. doi: 10.13332/j.1000-1522.2013.06.013 Ni R Q, Tang J Y, Cheng Y X, et al. Spatial distribution patterns and associations of main tree species in spruce-fir forest in Changbai Mountains, northeastern China[J]. Journal of Beijing Forestry University, 2013, 35(6): 28−35. doi: 10.13332/j.1000-1522.2013.06.013
[11]	白小军, 贾琳, 谷会岩. 大兴安岭次生林区优势种落叶松分布格局及竞争作用[J]. 生态学报, 2021, 41(10): 4194−4202. Bai X J, Jia L, Gu H Y. Spatial distribution pattern and competition relationship of the dominantLarix gmelinii species in Greater Khingan Mountains’ secondary forest area[J]. Acta Ecologica Sinica, 2021, 41(10): 4194−4202.
[12]	胡海清, 魏书精, 孙龙. 1965—2010年大兴安岭森林火灾碳排放的估算研究[J]. 植物生态学报, 2012, 36(7): 629−644. Hu H Q, Wei S J, Sun L. Estimation of carbon emissions due to forest fire in Daxing’an Mountains from 1965 to 2010[J]. Chinese Journal of Plant Ecology, 2012, 36(7): 629−644.
[13]	Ban Y, Xu H, Kneeshaw B D. Gap regeneration of shade-intolerant Larix gmelini in old-growth boreal forests of northeastern China[J]. Journal of Vegetation Science, 1998, 9(4): 529−536. doi: 10.2307/3237268
[14]	Cai W, Yang J, Liu Z, et al. Post-fire tree recruitment of a boreal larch forest in Northeast China[J]. Forest Ecology and Management, 2013, 307: 20−29. doi: 10.1016/j.foreco.2013.06.056
[15]	刘志华, 常禹, 贺红士, 等. 火控制政策对大兴安岭森林景观、可燃物动态及火险的长期影响[J]. 生态学杂志, 2009, 28(1): 70−79. doi: 10.13292/j.1000-4890.2009.0055 Liu Z H, Chang Y, He H S, et al. Long-term effects of fire suppression policy on forest landscape, fuels dynam ics, and fire risks in Great Xing’an Mountains[J]. Chinese Journal of Ecology, 2009, 28(1): 70−79. doi: 10.13292/j.1000-4890.2009.0055
[16]	Chang Y, He H S, Hu Y, et al. Historic and current fire regimes in the Great Xing’an Mountains, northeastern China: implications for long-term forest management[J]. Forest Ecology and Management, 2008, 254(3): 445−453. doi: 10.1016/j.foreco.2007.04.050
[17]	Hu T, Zhou G. Drivers of lightning- and human-caused fire regimes in the Great Xing’an Mountains[J]. Forest Ecology and Management, 2014, 329: 49−58. doi: 10.1016/j.foreco.2014.05.047
[18]	刘树超, 陈小中, 覃先林, 等. 内蒙古毕拉河林场森林火灾受害程度遥感评价[J]. 林业资源管理, 2018(1): 90−95. Liu S C, Chen X Z, Qin X L, et al. Remote sensing assessment of forest fire damage degree in Bilahe Forest Farm, Inner Mongolia[J]. Forest Resources Management, 2018(1): 90−95.
[19]	李文辉. 浅谈毕拉河林业局立地类型分布特点[J]. 内蒙古林业调查设计, 2010, 33(3): 48−50. doi: 10.3969/j.issn.1006-6993.2010.03.021 Li W H. Elementary discussion on the distribution characteristics of site types of Bilahe Forestry Bureau[J]. Inner Mongolia Forestry Investigation and Design, 2010, 33(3): 48−50. doi: 10.3969/j.issn.1006-6993.2010.03.021
[20]	Keeley J E. Fire intensity, fire severity and burn severity: a brief review and suggested usage[J]. International Journal of Wildland Fire, 2009, 18: 116−126. doi: 10.1071/WF07049
[21]	王睿智, 国庆喜. 小兴安岭阔叶红松林木本植物种−面积关系[J]. 生态学报, 2016, 36(13): 4091−4098. Wang R Z, Guo Q X. Woody plants species-area relationships in a broad-leaved Korean pine forest in the Xiaoxing’an Mountains[J]. Acta Ecologica Sinica, 2016, 36(13): 4091−4098.
[22]	赵广东, 熊凯, 许格希, 等. 川西米亚罗亚高山暗针叶林主要优势种岷江冷杉和糙皮桦的空间格局及其关联性分析[J]. 生态学报, 2022, 42(8): 1−12. Zhao G D, Xiong K, Xu G X, et al. Spatial patterns and associations of main dominant species Abies fargesii var. faxoniana andBetula utilis in Miyaluo subalpine dark coniferous forest of western Sichuan, China[J]. Acta Ecologica Sinica, 2022, 42(8): 1−12.
[23]	张春雨, 赵秀海, 夏富才. 长白山次生林树种空间分布及环境解释[J]. 林业科学, 2008, 44(8): 1−8. doi: 10.3321/j.issn:1001-7488.2008.08.001 Zhang C Y, Zhao X H, Xia F C. Spatial distribution of tree species and environmental interpretations of secondary forest in Changbai Mountains[J]. Scientia Silvae Sinicae, 2008, 44(8): 1−8. doi: 10.3321/j.issn:1001-7488.2008.08.001
[24]	Condit R, Ashton P S, Baker P, et al. Spatial patterns in the distribution of tropical tree species[J]. Science, 2000, 288: 1414−1418. doi: 10.1126/science.288.5470.1414
[25]	Wiegand T, Moloney K A. Rings, circles, and null-models for point pattern analysis in ecology[J]. Oikos, 2004, 104(2): 209−229. doi: 10.1111/j.0030-1299.2004.12497.x
[26]	孙云霞, 刘兆刚, 董灵波. 帽儿山地区1983—2016年森林景观空间点格局及其关联动态性[J]. 应用生态学报, 2018, 29(8): 2601−2614. Sun Y X, Liu Z G, Dong L B. Spatial point patterns and their association dynamics of forest landscapes in Maoershan Region, Northeast China between 1983 and 2016[J]. Chinese Journal of Applied Ecology, 2018, 29(8): 2601−2614.
[27]	舒兰, 刘兆刚, 董灵波. 帽儿山天然次生林内主要木本植物空间格局及更新特点[J]. 应用生态学报, 2019, 30(6): 1945−1955. doi: 10.13287/j.1001-9332.201906.026 Shu L, Liu Z G, Dong L B. Spatial pattern and forest regeneration characteristics of natural secondary forest in Maoershan, Northeast China[J]. Chinese Journal of Applied Ecology, 2019, 30(6): 1945−1955. doi: 10.13287/j.1001-9332.201906.026
[28]	祝燕, 白帆, 刘海丰, 等. 北京暖温带次生林种群分布格局与种间空间关联性[J]. 生物多样性, 2011, 19(2): 252−259. Zhu Y, Bai F, Liu H F, et al. Population distribution patterns and interspecific spatial associations in warm temperate secondary forests, Beijing[J]. Biodiversity Science, 2011, 19(2): 252−259.
[29]	Yu H, Wiegand T, Yang X, et al. The impact of fire and density-dependent mortality on the spatial patterns of a pine forest in the Hulun Buir Sandland, Inner Mongolia, China[J]. Forest Ecology and Management, 2009, 257(10): 2098−2107. doi: 10.1016/j.foreco.2009.02.019
[30]	胡海清. 大兴安岭原始林区林木火疤的研究[J]. 自然灾害学报, 2003, 12(4): 68−72. doi: 10.3969/j.issn.1004-4574.2003.04.012 Hu H Q. Study on fire scar of trees in Daxing’an Mountains’ virgin forest region[J]. Journal of Natural Disasters, 2003, 12(4): 68−72. doi: 10.3969/j.issn.1004-4574.2003.04.012
[31]	Stephens S L, Fry D L, Vizcaíno E F. Wildfire and spatial patterns in forests in northwestern Mexico: the United States wishes it had similar fire problems[J]. Ecology and Society, 2008, 13(2): 1−12.
[32]	Mantgem P J, Stephenson N L, Knapp E B, et al. Long-term effects of prescribed fire on mixed conifer forest structure in the Sierra Nevada, California[J]. Forest Ecology and Management, 2011, 261(6): 989−994. doi: 10.1016/j.foreco.2010.12.013
[33]	Fulé P Z, Covington W W. Spatial patterns of Mexican pine-oak forests under different recent fire regimes[J]. Plant Ecology, 1998, 134: 197−209. doi: 10.1023/A:1009789018557
[34]	Andrew J L, Derek C. Tree spatial patterns in fire-frequent forests of western North America, including mechanisms of pattern formation and implications for designing fuel reduction and restoration treatments[J]. Forest Ecology and Management, 2012, 267: 74−92. doi: 10.1016/j.foreco.2011.11.038