Fitting and Calibrating a Multilevel Mixed-Effects Stem Taper Model for Maritime Pine in NW Spain

Stem taper data are usually hierarchical (several measurements per tree, and several trees per plot), making application of a multilevel mixed-effects modelling approach essential. However, correlation between trees in the same plot/stand has often been ignored in previous studies. Fitting and calibration of a variable-exponent stem taper function were conducted using data from 420 trees felled in even-aged maritime pine (Pinus pinaster Ait.) stands in NW Spain. In the fitting step, the tree level explained much more variability than the plot level, and therefore calibration at plot level was omitted. Several stem heights were evaluated for measurement of the additional diameter needed for calibration at tree level. Calibration with an additional diameter measured at between 40 and 60% of total tree height showed the greatest improvement in volume and diameter predictions. If additional diameter measurement is not available, the fixed-effects model fitted by the ordinary least squares technique should be used. Finally, we also evaluated how the expansion of parameters with random effects affects the stem taper prediction, as we consider this a key question when applying the mixed-effects modelling approach to taper equations. The results showed that correlation between random effects should be taken into account when assessing the influence of random effects in stem taper prediction.     

基于抚育间伐效应的长白落叶松人工林两阶段枯死模型

1972和1974年分别在黑龙江省江山娇林场及孟家岗林场设置10块长白落叶松人工林固定样地(8块抚育间伐样地、2块对照样地),采用连年复测数据,分析抚育间伐对人工长白落叶松样地枯死与单木枯死的影响.基于二分类变量Logistic回归,建立了样地枯死及样地内单木枯死概率的两阶段模型(Ⅰ:抚育间伐后样地水平枯死概率模型;Ⅱ:枯死样地中单木水平枯死概率模型),采用广义估计方程(GEE)方法对模型参数进行估计.根据敏感度和特异度曲线相交点确定枯死概率最优临界点.结果表明: 样地数据按照抚育间伐次数分为4组分别建模(模型1～模型4).在模型1中,地位指数、林分年龄的自然对数、抚育间伐年龄及强度为显著自变量;模型2～模型4采用主成分分析法建模,主成分包含林分年龄、每公顷株数、平均胸径及抚育间伐因子,说明抚育间伐因子对样地枯死概率有显著影响.抚育间伐对枯死样地中单木枯死概率无显著影响,单木枯死概率模型中显著性自变量为林分初植密度、年龄、林木胸径的倒数及林分中大于对象木的所有林木断面积之和.样地枯死概率模型及单木枯死概率模型Hosmer和Lemeshow拟合优度检验均不显著,模型AUC均在0.91以上,估计正确率均超过80%,说明模型拟合效果较好.     

平地无风条件下蒙古栎阔叶床层的火行为Ⅰ.蔓延速率影响因子与预测模型

以东北林业大学帽儿山实验林场蒙古栎次生林下的蒙古栎凋落叶片为材料,根据研究地区同类可燃物的野外条件,在实验室内构建了不同载量、高度和含水率的可燃物床层,进行100次平地无风条件下的点烧试验.结果表明：平地无风条件下蒙古栎阔叶床层的林火蔓延速率不超过0.5 m·min^-1;可燃物含水率、床层载量和高度对蒙古栎阔叶床层的林火蔓延速率具有显著影响;含水率对林火蔓延速率的影响与可燃物床层高度、载量等无显著关系,而可燃物床层高度对林火蔓延速率的影响与可燃物床层载量有关.可燃物床层压缩比对蒙古栎阔叶床层的林火蔓延速率影响不大.以可燃物含水率、床层载量和高度为预测因子的林火蔓延速率预测模型能解释83%的林火蔓延速率变差,模型的平均绝对误差为0.04 m·min^-1,平均相对误差不超过17%.     

樟子松人工林树冠表面积及体积预估模型的研究

基于樟子松(Pinus sylvestris var. mongolica)人工林6块固定标准地30株枝解析数据,在分析树冠表面积和树冠体积与林分变量和林木变量的基础上,利用幂函数建立了树冠表面积（CSA）和树冠体积(CV)的预估模型,同时还对林木材积生长量与CSA和CV进行了相关分析。研究结果表明：樟子松人工林树冠表面积和树冠体积随着林木胸径、树高和冠长的增大而增大,林木材积生长量与树冠表面积和树冠体积均明显呈线性关系。不同林分条件的樟子松人工林CSA和CV随林分年龄和胸径的增大而增大,CSA随林分密度的增大而减小,而CV与林分密度相关不紧密。林分树冠表面积和树冠体积预估模型的检验结果表明,两个模型的平均相对误差都在±8%之内,预估精度均大于91%,说明所建模型可以很好地预估樟子松人工林不同林分条件下的林木树冠表面积和树冠体积。     

Leaf area index development in temperate oak and beech forests is driven by stand characteristics and weather conditions

Using data from 20 even-aged and homogeneous mature beech and oak study plots in Flanders (Northern Belgium), an analysis of the empirical relationships between the rates of leaf area index (LAI) change throughout the leaf development of 2008 and stand, site and meteorological variables was performed. Species-specific multiple linear regressions were fitted between the rates of LAI change and the predictors for two distinct periods from April until August. After a sharp increase in LAI following budburst, the seasonal LAI development for both species showed a marked period of stationary LAI development over all study plots. The cause for the cessation of LAI growth was assumed to be the decline of air temperature and radiation during this period. Later on, the rate of LAI development restarted similarly in every plot. The influence of weather on LAI development was high and its effects were different between species, with beech mostly affected by radiation and oak negatively related to minimal and maximal values of air temperature. Furthermore, our analysis suggested that stand structural (tree density and stand basal area for both species) and tree growth characteristics (average tree-ring width ratio for oak) variables were major drivers of the LAI development during early spring. Later during the growth period, stand variables became less predominant in affecting LAI development. Site quality variables affected LAI development to a lesser extent. The seasonal LAI development was found very similar among stands. This study adds a more accurate and comprehensive approach to the modelling of LAI development during leaf growth of two important European temperate deciduous forest species.     

Linear Mixed-Effects Models to Describe Individual Tree Crown Width for China-Fir in Fujian Province,Southeast China

A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike’s information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R ²). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.     

帽儿山阔叶混交林天然更新幼苗幼树地径-树高模型

基于黑龙江省东北林业大学帽儿山实验林场48块天然阔叶林幼苗幼树调查数据,在8个备选模型中为主要更新树种选择最佳地径(D₀)-树高(H)模型作为基本模型,通过再参数化在基础模型中引入林分因子,并建立样地水平混合效应模型,最后分别对基础模型和混合效应模型进行独立样本检验.结果表明:各树种幼苗幼树的地径-树高关系存在明显的正相关,幂函数或包含幂函数的模型能较好地拟合幼苗幼树地径和树高的关系;基础模型中引入林分因子[林分优势高(H_T)、林分平均胸径(D_g)、林分胸高断面积(BA)]能提高模型的拟合效果,各树种剩余均方根误差(RMSE)下降1.3%～7.4%(平均3.8%),但调整后的决定系数(R_a²)仅仅提高0.1%～1.1%(平均0.6%),赤池信息准则(AIC)下降3.2%～35.2%(平均下降11.4%).对春榆、椴树、水曲柳等10个树种建立混合效应模型,混合效应模型的R_a²比基础模型有所提高,增幅为0.5%～3.5%(平均增加2.2%);RMSE和AIC比基础模型的小,RMSE下降的幅度很大,为3.9%～20.3%,平均下降13.9%,AIC减少4.0%～44.4%(平均减少22.3%).模型检验结果显示,相对于基础模型,混合效应模型的平均绝对误差(MAE)减小0.0001～0.46 m,平均减小0.08 m;平均预测误差百分比(MPSE)降幅较大,为0.1%～6.2%,平均降幅2.0%.说明混合效应模型既能提高模型的拟合效果,又能提高模型的预测能力.本研究构建的阔叶混交林主要更新树种幼苗幼树地径-树高模型为天然阔叶林结构分析和林分生长预测提供了参考.     

基于抚育间伐效应的落叶松人工林直径分布动态模拟

基于黑龙江省孟家岗林场长白落叶松人工林5块固定样地(其中1块为对照样地,4块为抚育间伐样地,断面积强度为3.7%~49.7%)1974—2014年(林龄为19～59 a)复测的31次胸径数据,采用三参数Weibull分布函数拟合5块样地各年份直径分布,研究了直径分布曲线随林龄的动态变化规律,并分析了抚育间伐对林分直径分布曲线及Weibull分布参数的动态影响.构建了基于抚育间伐效应的Weibull分布参数预测的联立方程组模型,分别采用三阶段最小二乘法及度量误差法估计了模型的参数.结果表明: 未间伐林分(对照)直径分布曲线随林龄增加由“高峰狭窄”(林木直径分布集中)状态逐渐向“低峰宽广”(林木直径分布分散)状态过渡;抚育间伐后,林木直径分布曲线均较抚育间伐前右偏加剧,峰度变高,径阶变窄,对称性下降;间伐强度越大,伐除的中小径阶树木越多,直径分布曲线较间伐前左侧截尾明显,峰度增高,径阶分布范围变小.低强度抚育间伐使得参数a值变大,b值变小,对参数c的影响不明显;高强度抚育间伐使得参数a的增量变大,b值变小,参数c值变小.参数预测联立方程组模型的拟合结果表明,参数b的预测模型拟合效果最好,R²>0.98;参数c预测模型拟合效果稍差,但R²>0.91;三阶段最小二乘法拟合结果与度量误差联立方程组方法区别不大,两种方法检验结果均较好,模型精度都>97%,拟合效率均>0.92.所建立的模型能够较好地模拟抚育间伐效应下落叶松人工林直径分布动态变化,为科学合理经营森林提供了依据.     

基于混合效应的大别山地区杉木树高-胸径模型比较

基于安徽省大别山区马鬃岭林场杉木人工林30块样地1087组数据,选用7个常用树高-胸径(H-D)模型(线性模型、Chapman-Richards模型、Logistic模型等),采用最小二乘法拟合并选出最优基础模型(式11,只含D变量的Chapman-Richards模型),然后基于该模型构建含林分变量优势木平均高度、密度的H-D模型(式12),同时考虑样地水平的随机效应,分别基于式11、12构建混合模型(式13、14),并用幂函数、指数函数消除误差异方差,利用决定系数(R²)、均方根误差(RMSE)、平均绝对误差(MAE)和平均相对误差绝对值(MAPE)等指标来评价模型的拟合与预测能力,最终获取最优树高预测模型.结果表明:含林分变量的模型的拟合精度(式12,R²=0.863、RMSE=1.381、MAE=0.971)优于基础模型(式11,R²=0.827、RMSE=1.554、MAE=0.101).对于误差方差,幂函数、指数函数均能较好地消除异方差,但幂函数相对最好.混合模型的拟合与预测能力均优于式11、12,但混合模型(式13、14)之间的拟合与预测精度相差不大.基于混合效应的H-D模型(式13)能够较好地描述不同林分间H-D关系的差异,实际运用中可选用该模型来预测杉木树高,具有较高的预测精度.     

人工红松树干内部节子体积预测模型

基于黑龙江省林口林业局林场和东京城林业局林场29块标准地中49株人工红松1207个节子数据,使用图片处理软件Digimizer对节子纵剖面图片数据进行提取,将节子形状用一个二维散点图表示。根据节子二维形状散点图,把人工红松节子分为3种类型: 活节(整个节子为健全节)、未包藏死节(节子由健全节和疏松节组成)和包藏死节(节子的健全节和疏松节部分被树干包藏)。3个类型节子的健全节体积通过对健全节形状参数方程求积得到;疏松节体积利用圆柱体的体积计算得到;节子总体积等于健全节体积与疏松节体积之和。最后,基于节子变量(节子直径、节子相对高、节子总长度)和树木变量(胸径),采用样地和树木水平的线性混合模型建立了红松人工林健全节体积、疏松节体积和节子总体积的预测模型。与基础模型相比,考虑样地和树木水平的混合效应所建立的健全节体积、疏松节体积和节子总体积预测模型,其参数估计更精准,残差分布更均匀,拟合精度明显提高。检验结果表明,基础模型预估精度均在90%以上,引入样地和树木效应的混合模型的预估精度均在93%以上,说明所建模型可以很好地预测红松人工林节子体积大小。     

Modelling Variable Fire Severity in Boreal Forests: Effects of Fire Intensity and Stand Structure

It is becoming clear that fires in boreal forests are not uniformly stand-replacing. On the contrary, marked variation in fire severity, measured as tree mortality, has been found both within and among individual fires. It is important to understand the conditions under which this variation can arise. We integrated forest sample plot data, tree allometries and historical forest fire records within a diameter class-structured model of 1.0 ha patches of mono-specific black spruce and jack pine stands in northern Québec, Canada. The model accounts for crown fire initiation and vertical spread into the canopy. It uses empirical relations between fire intensity, scorch height, the percent of crown scorched and tree mortality to simulate fire severity, specifically the percent reduction in patch basal area due to fire-caused mortality. A random forest and a regression tree analysis of a large random sample of simulated fires were used to test for an effect of fireline intensity, stand structure, species composition and pyrogeographic regions on resultant severity. Severity increased with intensity and was lower for jack pine stands. The proportion of simulated fires that burned at high severity (e.g. >75% reduction in patch basal area) was 0.80 for black spruce and 0.11 for jack pine. We identified thresholds in intensity below which there was a marked sensitivity of simulated fire severity to stand structure, and to interactions between intensity and structure. We found no evidence for a residual effect of pyrogeographic region on simulated severity, after the effects of stand structure and species composition were accounted for. The model presented here was able to produce variation in fire severity under a range of fire intensity conditions. This suggests that variation in stand structure is one of the factors causing the observed variation in boreal fire severity.     

红松人工林优势木竞争指数影响因子

在温带湿润气候区东段不同立地条件下的红松人工林内设置面积为600 m~2(20 m×30 m)的70块矩形固定样地。在每个样地内,选取5颗最高且长势较好的优势木作为研究的对象木,用Voronoi图确定优势木相应的竞争木,测定每一块样地内优势木与竞争木之间的距离。采用Hegyi单木竞争指数模型,分析优势木在不同样地水平上的种内竞争强度,探讨林分生长因子、地形因子、土壤养分因子对优势木竞争指数的影响,并对这3类因子与优势木竞争指数进行相应的拟合和相关性分析。结果表明：红松人工林优势木竞争强度随着优势木胸径的增大而变小,并且两者之间的关系服从幂函数;红松优势木的竞争指数与其树高、胸径、冠幅呈极显著的相关关系(P<0.01);坡向、坡位、海拔对竞争指数影响极显著(P<0.01);红松人工林优势木竞争指数的大小与土壤氮磷钾含量均呈极显著的相关关系(P<0.01);pH值对优势木竞争指数的影响不显著。当红松人工林优势木平均胸径达到45cm,优势木平均树高和冠幅大于周围竞争木时,其对周围资源的利用程度增大,林木会发生自然稀疏现象,其所受的竞争压力减小。红松喜光性强,对水分的要求高,...     

Epiphytic lichen diversity in old-growth and managed Picea abies stands in southern Finland

Abstract. Epiphytic and epixylic lichens were surveyed on 15 1-ha plots in mature Picea abies-dominated boreal forests in southern Finland. The sample plots were classified into three groups according to the age of the dominant tree stand and recent signs of cutting: (1) early mature managed, ‘EM’ (95 -109 yr), (2) late mature managed, ‘LM’ (126 - 145 yr) and (3) old-growth, ‘OG’ (129 - 198 yr). Two data sets on epiphytic and epixylic lichens were recorded from each plot: (1) species on basal trunks and branches of Picea abies and (2) species on all available woody substrates, including basal parts of all tree species, saplings, snags, logs and stumps. 142 epiphytic and epixylic lichen species were found, of which 83 (58%) occurred on P. abies. Mean total numbers of species per sample plot were 69 in EM, 78 in LM and 88 in OG plots, species number on P. abies were 47, 56, and 54 respectively. The LM plots had lower species numbers than OG plots, mainly due to the lack of old Populus tremula trees, but they had higher species number than the EM plots mainly due to the higher age of Picea abies. Differences in species composition, both within and between the three groups, were small. The results suggest that the epiphytic and epixylic lichen diversity in a managed stand can be increased by prolonging the rotation of the stand to >120 yr and by increasing the diversity of habitats in the stand.     

Windstorm damage and forest recovery: accelerated succession, stand structure, and spatial pattern over 25?years in two Minnesota forests

We evaluated 25?years of change in wind-impacted oak and pine-dominated sites in the Cedar Creek Ecosystem Science Reserve, Minnesota, USA. We address the question: how did the storm alter stand architecture and spatial pattern and how did this affect recovery and recruitment? We mapped and marked all stems greater than 1?cm in diameter in a 0.25?ha oak-dominated plot and a 0.30?ha pine-dominated plot. After the initial sampling in 1983, plots were resurveyed four times in the 25?years following the windstorm. We used ordination and diameter distributions to describe compositional and structural characteristics of the sites. The stands are compositionally converging after the windstorm with both moving towards a late-successional forest type dominated by shade-tolerant tree species. The architecture in both sites is similar through time; sites have transitioned from bimodal diameter distributions to reverse-J distributions. We used Ripley??s K point pattern analysis to assess spatial patterns of tree mortality and recruitment within each site. In the pine site, surviving trees were significantly clumped, but mortality and recruitment patterns did not significantly differ from random. In the oak site, the storm did not substantially alter the spatial pattern of surviving trees, but subsequent recruitment was significantly associated with trees killed by the storm at scales within 6?C8?m and significantly dissociated with surviving trees at scales greater than 1?m. The dynamics of accelerated succession observed here are mediated by the damage and mortality initially sustained and its corresponding effects on spatial patterns of surviving and recruiting trees.     

Predicted genetic gain and realised gain in stand volume of Eucalyptus globulus

Realised gains in stand volume of Eucalyptus globulus Labill. families at 7–9 years were compared with gains predicted at 3.5 years. Gain predictions were based on height, diameter at breast height (DBH), sectional area, and stem volume for 153 full-sib families and 18 commercial checks in five-tree line plots on three West Australian sites. Single-site narrow-sense heritability estimates were 0.12–0.24 for height, 0.08–0.12 for DBH, 0.09–0.13 for sectional area, and 0.14–0.19 for stem volume. Genetic dominance effects were significant (p?<?0.05) in most cases, and the estimated dominance/additive genetic variance ratio was heterogeneous for height and DBH. Stand volume was measured for 93 of the same families and checks in 40-tree block plots on four sites. Heritability of stand volume was 0.25–0.76, with an across-sites estimate of 0.41. Dominance effects were statistically absent at two sites. Estimated region-wide additive genetic correlations between selection traits (in line plots) and stand volume (in block plots) ranged from 0.86 to 0.90. Estimated stand volume gain was 23 % of the mean for the best 12 % of families and 14 % of the mean for the best 24 % of families. Realised gain was under-estimated by predictions based on height, DBH, and sectional area, which had smaller coefficients of additive variation than did stem volume. It is concluded that although BLUP analysis of early-age height and DBH can provide for indirect selection on E. globulus stand volume, analysis of stem volume is required to predict genetic gain at an appropriate scale.     

山坡退化林地林木生长对微地形人工干预的响应

为探究水土保持微地形人工干预措施(等高反坡阶)对坡面退化林地林木生长的影响,在昆明市松华坝水源区内选取典型山坡退化林地,通过动态观测和对比分析不同样地林木胸径、树高、新枝生长量及样地叶面积指数(LAI)的变化差异,再结合土壤水分有效性分析以探讨差异原因.结果表明:等高反坡阶样地云南松胸径和树高的最大值和均值均大于对照样地(CK),退化林群落中小径阶和低矮的植株占更大比例,表明等高反坡阶样地中优势木新生植株和退化严重植株的生长潜力得到激发,不同样地云南松植株新枝平均枝长和枝径的年变化差异率达到了72.4%和39.1%.等高反坡阶样地云南松植株新枝生长量和样地LAI的变化及新枝生长的速度大于CK.土壤含水率和新枝生长量与LAI均呈显著相关,对水分有效性分析后得到等高反坡阶样地易效水比例(64.2%)整体高于CK(54.7%),5月至9月雨季中,等高反坡阶样地易效水存在时间更长,这有利于林木的生长,进而改变退化林地植物群落结构.     

Selection system efficiencies for computer simulated progeny test field designs in loblolly pine

Summary Six simulated progeny test field designs in combination with three within-family selection systems were tested on three loblolly pine (Pinus taeda L.) progeny test sites in southeastern Oklahoma and southwestern Arkansas, to compare genetic gains for the single trait, height. Residual deviations obtained by subtraction of family and plantation mean effects for each plantation were combined with simulated genetic effects with known family variance structure. The simulated genetic populations, arranged in the following progeny test field designs — large square or almost square plots, five- and ten-tree row plots, five-tree noncontiguous plots, two tree row plots, and single-tree plots — were superimposed on the residual data for each plantation. Within-family selection methods based on deviations from block means, deviations from neighborhood means and deviations from plot means were built into the model. Realized genetic gain attained by each design — selection system combination was compared with the genetic gain theoretically possible if selection accuracy were perfect, and with expected gain estimated using the general linear model. In general, average realized genetic gain compared well with expected gain. Differences between designs with large versus small plots were generally lower than expected, although the single-tree plot design always yielded highest realized gain. Realized gain was generally higher than expected when within-family selection was based on deviations from block or neighborhood means, but equal to or lower than expected when selection was based on deviations from plot means.     

5种红树林植物叶片SPAD值比较

以5种红树林植物为研究材料,分析测试其叶片相对叶绿素含量(SPAD值),并比较红树林树种、样区对其叶片SPAD值的影响。结果表明,各样区、各树种以及单株之间SPAD值均存差异,对不同样区进行多重比较,可将其分为7类,5个红树林树种在叶绿素含量上差异较明显。各树种中以秋茄Kandelia obvolata最大(70.4),其次是红海榄Rhizophora stylosa (65.9)和木榄Bruguiera gymnorrhiza (62.9),白骨壤Avicennia marina为51.9,最小为桐花树Aegiceras corniculatum(48.6),树种平均为60.5。试验分析表明,树种因子效应极显著(P<0.01),强于样区因子效应,说明红树林树种是影响其叶片SPAD值的重要因子,同时也表明不同的立地环境条件对叶绿素含量存在影响。5种红树林植物叶片SPAD值均与其树高、基径生长性状存在显著正相关。     

Tree species diversity influences herbivore abundance and damage: meta-analysis of long-term forest experiments

Plant monocultures are commonly believed to be more susceptible to herbivore attacks than stands composed of several plant species. However, few studies have experimentally tested the effects of tree species diversity on herbivory. In this paper, we present a meta-analysis of uniformly collected data on insect herbivore abundance and damage on three tree species (silver birch, black alder and sessile oak) from seven long-term forest diversity experiments in boreal and temperate forest zones. Our aim was to compare the effects of forest diversity on herbivores belonging to different feeding guilds and inhabiting different tree species. At the same time we also examined the variation in herbivore responses due to tree age and sampling period within the season, the effects of experimental design (plot size and planting density) and the stability of herbivore responses over time. Herbivore responses varied significantly both among insect feeding guilds and among host tree species. Among insect feeding guilds, only leaf miner densities were consistently lower and less variable in mixed stands as compared to tree monocultures regardless of the host tree species. The responses of other herbivores to forest diversity depended largely on host tree species. Insect herbivory on birch was significantly lower in mixtures than in birch monocultures, whereas insect herbivory on oak and alder was higher in mixtures than in oak and alder monocultures. The effects of tree species diversity were also more pronounced in older trees, in the earlier part of the season, at larger plots and at lower planting density. Overall our results demonstrate that forest diversity does not generally and uniformly reduce insect herbivory and suggest instead that insect herbivore responses to forest diversity are highly variable and strongly dependent on the host tree species and other stand characteristics as well as on the type of the herbivore.