基于分位数回归的长白落叶松人工林最大密度线

基于东北地区378块固定样地和415块临时样地的调查数据和Reineke方程,利用线性分位数回归技术建立了不同分位点(τ=0.90、0.95、0.99)下的长白落叶松人工林最大林分密度与林木平均胸径的关系模型,选出拟合长白落叶松人工林最大密度线的最优模型. 利用人为选取最大的拟合数据,采用最小二乘(OLS)和最大似然(ML)回归同时建立最大密度线模型. 采用极值统计理论的广义Pareto模型推算现实林分特定径阶的极限最大株数,进一步建立极限密度线模型. 将线性分位数回归模型与其他方法进行对比.结果表明: 在全部径阶范围内选取5个最大数据点拟合的方法能够得到现实林分的最大密度线,选取的样点过多会使模拟结果偏离最大密度线,且ML法要优于OLS法. 分位点为0.99的线性分位数回归模型能够取得与ML接近的拟合结果,但分位数回归模型参数的估计结果更稳定. 人为选取拟合数据具有一定的人为性,最终选取分位点为0.99的分位数回归模型为拟合最大密度线的最优模型,参数估计结果为k=11.790、β=-1.586,极限密度线模型的参数估计结果为k=11.820、β=-1.594. 所确定的极限密度线位置略高于最大密度线,但二者差异不明显. 由固定样地数据的验证结果可知,所建立的最大林分密度线及极限密度线能够对现实林分的最大密度及极限密度进行预测,为长白落叶松人工林的合理经营提供依据.     

基于线性分位数混合效应的辽东山区红松冠幅模型

冠幅是反映单木生长状态及构建林木生长收获模型的重要变量。本研究以辽东山区大边沟林场10～55年生红松人工林为对象,基于66块固定样地的2763株红松的每木检尺数据,选取冠幅基础模型,采用再参数化的方法引入单木竞争指标(R_d),利用哑变量的方法引入了林分密度、林层变量,构建不同分位点(0.50、0.90、0.93、0.95、0.96、0.99)的冠幅分位数回归模型,并与传统方法进行比较,选取模拟林分最大冠幅的最优分位点。为反映林分中单木冠幅在林木个体之间的差异,建立了基于样地水平的最优分位点的线性混合效应分位数回归冠幅模型,分析各变量对单木冠幅的影响。结果表明: 基于F统计检验,不同林分密度和林层的冠幅模型具有显著差异,在基础模型中引入林层、林分密度和竞争后,模型R_a²提高0.0104,均方根误差降低0.0115,均方误差降低为7.4%;与最小二乘法比较,分位数回归模型能够较好地模拟林分状态下的单木最大冠幅,并选出0.96分位点和0.93分位点作为上林层和下林层的分位数回归模型的最优分位点。引入混合效应的线性分位数回归模型的赤池信息准则、贝叶斯信息准则、HQ信息准则等评价指标优于传统分位数回归,参数标准误显著降低,混合效应的引入很好地解释了样地之间的差异。就上林层和下林层而言,林分密度越大,最大冠幅越小;相对直径越大,最大冠幅越大,其中林分密度对下林层的冠幅影响大于上林层,当林分密度足够大时,冠幅随着胸径的增大先增大后降低。本研究构建的基于混合效应的分位数回归模型能有效提高模型的拟合优度,今后可通过调控林分密度、适度抚育间伐等措施,实现对辽东山区红松人工林的科学营建和可持续发展。     

基于混合效应模型和分位数回归的长白落叶松枝下高模型构建

枝下高是反映树冠特征的重要指标,准确预测枝下高对森林的经营管理和提高林分生产具有重要意义。本研究采用非线性回归构建枝下高广义基础模型,再进一步扩展到混合效应模型和分位数回归模型,通过“留一法”检验对模型的预测能力进行评价和比较。此外,使用4种抽样设计和不同抽样大小对枝下高模型进行校正,选择最佳的模型校正方案。结果表明：基于包含树高、胸径、林分每公顷断面积和优势木平均高的枝下高广义模型、扩展后的混合效应模型以及三分位数组合模型的预测精度均显著提高,混合效应模型略优于三分位数组合模型,最佳抽样校正方案为抽5株平均木。因此,推荐在实践应用中使用混合效应模型,抽5株样地平均木校正预测枝下高。     

基于8hm2样地的天山云杉林蒸腾耗水从单株到林分的转换

为准确地估算天山北坡中部雪岭云杉森林的林分蒸腾耗水量,本研究设置了8hm2固定样地,在每木调查的基础上,通过对7株标准木连续晴天液流的观测,分别得到胸径与液流速率和边材面积的拟合方程,最终计算得到了林分的蒸腾耗水量,确定了估算该森林群落蒸腾耗水的最小取样面积,并且讨论了最小取样面积随样地位置的变化。结果表明：①在自然生长系,雪岭云杉林分最大蒸腾耗水量、平均蒸腾耗水量同植株密度呈Extrem函数分布;当种植密度达到1200株/hm2时,林分最大蒸腾耗水量达到最大,为77.27 t/hm2d;②对林分蒸腾耗水量的测算存在明显的最小取样面积,最小取样面积随取样点的不同而略有差异,取样起始点在本样地的海拔上边界和下边界处时最小取样面积为4 hm2,取样起始点在本样地的中部时最小取样面积为2.56hm2。本研究为更精确地估算天山北坡雪岭云杉森林的蒸腾耗水量提供了理论依据。     

同龄纯林自然稀疏过程的经验模型研究

应用-3/2法则及广义Schumacher生长方程导出同龄纯林自然稀疏过程中密度随时间变化规律新模型,采用遗传算法对非线性模型参数进行最优估计.以山杨、云南松、杉木等树种同龄纯林自疏过程中密度随时间变化资料对新模型进行了验证,并与前人提出的主要森林自疏过程密度随时间变化规律模型进行了对比.结果表明,所提出的同龄纯林自疏规律模型能很好地拟合实际观测资料,具有良好的使用价值;新模型拟合效果较前人提出的自疏规律模型效果均更佳,说明新模型是一个描述同龄纯林自疏过程密度随时间变化规律的理想经验模型,可在森林自疏规律研究中应用.杉木林自疏过程密度变化规律的研究可为南方林区杉木林经营管理提供参考.     

基于哑变量和分位数回归的兴安落叶松更新幼树的树高-胸径模型

本研究以大兴安岭地区翠岗林场2018—2019年55块固定样地2054株兴安落叶松幼树为对象,采用四分位数法将林分密度指数(SDI)划分为4个等级,即等级Ⅰ(SDI₁<1863株·hm^-2)、等级Ⅱ(1863≤SDI₂<2155株·hm^-2)、等级Ⅲ(2155≤SDI₃<2459株·hm^-2)和等级Ⅳ(SDI₄≥2459株·hm^-2),并采用哑变量方法引入SDI构建兴安落叶松幼树树高-胸径的哑变量模型和分位数回归模型。结果表明：选取的5个代表性非线性树高曲线模型中,Richards模型的拟合效果最好,其R_a²、RMSE、MAE分别为0.7637、0.8250 m、0.5696 m;基于Richards模型构建的包含SDI的哑变量模型,其R_a²较基础模型提高了1.3%,而RMSE、MAE、AIC分别降低了2.1%、1.5%和11.2%;当分位点τ=0.5时,分位数回归模型的R_a²最大,RMSE、MAE、AIC最小,分别为0.7612、0.8294 m、0.5657 m、-767.19。相较于SDI₁,SDI₂～SDI₄林分内幼树的树高分别增加5.6%、5.6%和11.3%。因此,合理调控兴安落叶松林的林分密度有利于增加更新幼树的高生长。     

基于自稀疏理论的杉木人工林密度指标研究

量化林分密度是精准林业实现的基础。选择合适的林分密度指标用于杉木人工林的模拟和预测研究。基于同一套数据构建3个林分密度指标,根据这些指标的理论分析和动态变化规律进行选优。理论上,Reneike林分密度指数(SDI)和Curtis相对密度(RD)可互相转换,SDI可作为Nilson密度(SD)指标的特例;杉木人工林分的实证结果表明,SD指标的动态变化规律优于传统的SDI和RD密度,更能反映林分的生长规律;而且具有与立地质量不相关的比较优势。Nilson密度指标可用来模拟和预测杉木人工林的生长和收获。     

海南铜鼓岭灌木林稀疏规律

以海南省文昌市铜鼓岭国家级自然保护区160m?160m的山麓灌木林固定样地中胸径(DBH)31.5cm的所有木本植物为对象,并根据DBH划分为7个径级,研究其稀疏规律,结果表明：1）群落中Ⅰ级（DBH＜4.5cm）个体数所占百分比最大,占64%,群落结构为“倒J型”,林分密度是幼树＞小树＞成年树,该群落正处于稳定状态,且个体间为争夺更多的生存空间和资源发生强烈的自疏和它疏作用,存在明显的稀疏现象。2）各径级地上生物量随着密度增加呈幂函数增加,幂函数方程为：AGB=6?107N0.4626或lnAGB=0.4626lnN 17.855,在较小的密度范围内,随林分密度的增加,群落地上总生物量增加较快,但当密度趋于0.6株/m2时,地上生物量变化缓慢,趋于恒定值。3）林分密度与各径级平均胸径呈负相关关系(密度越大,平均胸径越小),其幂函数关系式为：N=70.1d-3.5506,R2=0.8808。4）选择Yoda提出的幂函数方程对天然灌木林自然稀疏规律进行模拟,林分密度与平均生物量之间具有显著相关性,其关系式为：W=2219.1N-0.5374或 lnW=7.7048-0.5374lnN;自疏指数α值为0.5374,这与Yoda所提出的3/2指数相差甚远,并不满足-3/2自疏定律。5）此次调查的物种有常见种（0.2hm2样地中个体数≥5的种为常见种）41种,非常见种53种。天然灌木林在物种层面的稀疏也有一定的规律。     

马尾松林天敌昆虫群落对马尾松毛虫控制作用的研究

本文通过对马尾松林松毛虫天敌昆虫群落优势种的选择及功能表述、用典型相关分析选择关键林分因子进行林地分类,研究了表示天敌昆虫群落对松毛虫控制作用的途径。结果表明,用天敌昆虫群落功能指标选择的重要林分因子为郁闭度、灌木层高度及盖度、草木层高度及总盖度。用这些林分因子可以把常灾区林地划分为4种类型,且这4类林地在天敌昆虫群落多样性、种数、个体数及松毛虫密度上都存在明显差异。最后分别建立了4类林地松毛虫密度变化率与多样性等功能指标及郁闭度等林分因子间的回归模型,回归相关性进一步表明用林分因子代替天敌昆虫的作用是合适的,这样代替的结果克服了生产应用时数据调查的困难,增加了实用性。     

落叶松人工林树干形状模型和可变参数

对以往树木干形的一系列可变参数削度方程进行比较,根据模型拟合统计量(残差平方和及相关指数),选出其中对落叶松干形拟合效果较好(残差平方和较小、相关指数较高)的模型,并根据模型中可变参数的意义提出了5种描述干形的指数.结果表明:Lee等提出的削度方程的拟合效果较好,可以用来描述落叶松人工林的树干形状;5种描述干形的指数分别为根部梢头削度率、影响点、圆柱体和抛物线体范围值、最小可变参数、最小可变参数所在的相对高度,这些指数可以作为比较干形的方法和工具.较大密度(870株.hm-2)和较小密度林分(275株.hm-2)的林木干形质量都较差,只有适中密度林分(487株.hm-2)的落叶松干形质量较好.     

A method of selecting data points for fitting the maximum biomass-density line for stands undergoing self-thinning

Abstract A problem that has always existed in self-thinning studies is the lack of objectivity in determining which data points to include when fitting the maximum biomass-density line. This paper demonstrates a more objective method of selecting data points using data from 12 even-aged Pinus radiata stands undergoing self-thinning. The method involves the division of a cluster of data points into a specified number of intervals. From each interval, that point having the maximum stand biomass is selected to contribute to the fitting process. This process is repeated a specified number of times using an increasing number of intervals. Each time an estimate of the line is obtained. From these estimates, one can be chosen to represent the maximum biomass-density line. The method may also be useful in other areas involving the definition of a boundary condition.     

Relationship between the virtual dynamic thinning line and the self-thinning boundary line in simulated plant populations

The self-thinning rule defines a straight upper boundary line on log-log scales for all possible combinations of mean individual biomass and density in plant populations. Recently, the traditional slope of the upper boundary line, -3/2, has been challenged by -4/3 which is deduced from some new mechanical theories, like the metabolic theory. More experimental or field studies should be carried out to identify the more accurate self-thinning exponent. But it＇s hard to obtain the accurate self-thinning exponent by fitting to data points directly because of the intrinsic problem of subjectivity in data selection. The virtual dynamic thinning line is derived from the competition-density （C-D） effect as the initial density tends to be positive infinity, avoiding the data selection process. The purpose of this study was to study the relationship between the virtual dynamic thinning line and the upper boundary line in simulated plant stands. Our research showed that the upper boundary line and the virtual dynamic thinning line were both straight lines on log-log scales. The slopes were almost the same value with only a very little difference of 0.059, and the intercept of the upper boundary line was a little larger than that of the virtual dynamic thinning line. As initial size and spatial distribution patterns became more uniform, the virtual dynamic thinning line was more similar to the upper boundary line. This implies that, given appropriate parameters, the virtual dynamic thinning line may be used as the upper boundary line in simulated plant stands.     

In Defence of the -3/2 Boundary Rule: a Re-evaluation of Self-thinning Concepts and Status

The -3/2 power rule, or -3/2 self-thinning rule, was accepted10 years ago as an important generalization, but has recentlybeen questioned by a number of authors. This paper assesseswhat remains of the rule. While it has been empirically establishedthat size-density trajectories followed by self-thinning plantpopulations do not necessarily follow a -3/2 slope, a more generalpower rule describing a density-dependent upper limit to meanshoot biomass per plant (the '-3/2 boundary rule') remains largelyintact. Principal component analysis (PCA) overestimates the steepnessof the thinning slope if y:x variance ratio is greater than1:1. Lonsdale's (Ecology 71: 1373-1388) overall mean PCA slopeof -0·6 for biomass-density suggests a true mean slopeclose to the theoretical value of -0·5. Reduced majoraxis (RMA) regression appears a reasonable approximation forthe -3/2 but not the -1/2 formulation of the rule. Fitting ofa linear functional relationship (LFR) is a more appropriateslope estimation procedure, not previously used for data onthinning. None of these procedures estimates a boundary linethat is not transgressed by any data point except through errorsof measurement. Mortality due to overcrowding ensues when a small, suppressedplant no longer holds its leaves high enough in the canopy tomaintain a positive carbon balance. It follows that LAI shouldremain constant during thinning, and that self-thinning theoryshould be developed in terms of maximum leaf area index andthe biomass required to support it. A derivation is presentedand some of its consequences are examined.Copyright 1995, 1999Academic Press Self-thinning, -3/2 power rule, -3/2 self-thinning rule, boundary line, size-density compensation, regression methods     

How does fertility of the substrate affect intraspecific competition? Evidence and synthesis from self-thinning

When dense populations of even-aged plant monocultures are subject to intense competition, mortality can occur in a process known as self-thinning, in which changes in biomass are accompanied by decreases in density. On a plot of log biomass versus log density, self-thinning populations show a linear relationship called the self-thinning line. Variations in the fertility level of the substrate are known to affect self-thinning in a number of ways. Populations from substrates with different fertility levels have been observed to self-thin along the same line, or along different lines. A review of several experiments using the one species grown at different fertility levels was undertaken to look for any mechanisms that might account for the different patterns observed. It was postulated that the critical difference between whether populations followed a common or different line was the way in which competition developed in the stands as biomass accumulated. For the common-line pattern, data on the canopy volume required to support a given biomass showed that biomass packing did not differ between fertility levels, supporting the model of a common competitive mechanism operating at all fertility levels. When different lines were observed, the development of competition differed as plants increased in size and biomass accumulated at each fertility level. Over the upper range of fertility levels, biomass packing values per plant increased as fertility declined and the position of self-thinning lines followed predictions from biomass packing data. At the low end of the fertility scale, biomass packing values still decreased with fertility level, but the position of self-thinning lines was not linked to the biomass packing of individual plants: root interactions were presumed to dominate competition and the trajectory of self-thinning lines.     

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.)Hook.) plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF). Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc.) on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.     

Self-thinning lines differ with fertility level

The effect of variations in fertility level of the substrate on the self-thinning lines followed by populations of Ocimum basilicum L. was investigated experimentally by establishing populations over a range of densities at two fertility levels. Populations from each fertility level followed different self-thinning lines for shoot biomass. Self-thinning began at a lower biomass in populations grown at the higher fertility level; the subsequent slope of the thinning line was –0.5 for these stands on a log shoot biomass versus log density plot. The slope of the self-thinning line was flatter (–0.29) at the lower fertility level. Fitting the self-thinning line by the Structural Relationship rather than the Major Axis made little difference to line estimates. Biomass packing differed with fertility level, with plants from the higher fertility stands requiring more canopy volume for given shoot biomass than plants from lower fertility levels. Biologically, this would mean shoot competition intensified more rapidly at the higher fertility level as biomass accumulated in stands. The difference in slope between fertility levels was associated with changes above- and belowground. The radial extension of the canopy versus shoot mass relationships of individual plants differed with fertility level. Plants at the lower fertility level allocated more biomass to root growth, and had less leaf area per unit root length. The differences in slope of the self-thinning lines may have been because of differences in the radial extension of the canopy versus shoot mass relationships of individual plants at each fertility level, and/or to an increase in root competition at the lower fertility level.     

Effect of Localized Placement of Nutrients on Root Competition in Self-thinning Populations

The hypothesis that increased root competition can lower theslope and/or intercept of the self-thinning line traversed byplant populations was tested using localized placement of nutrientsto increase root competition. Localized placement of nutrientswill result in increased root competition, if average inter-rootdistances are reduced, and if nutrients are in limiting supply.It was predicted that high-density, nutrient-limited populationsof Ocimum basilicum L. grown with localized placement of nutrientswould self-thin along a lower biomass–density line thannon-localized controls. This was tested at two fertility levelson a soil-based potting medium in expt 1, and at one fertilitylevel on washed sand in expt 2. Localized placement of nutrients significantly reduced the elevation(intercept) of the self-thinning line for both shoot and rootbiomass in expt 2. In expt 1, at the higher-fertility level,localized placement of nutrients had no significant effect;at the lower fertility level, localization had no significanteffect on thinning lines for shoot biomass, and resulted ina zero slope of the thinning line for root biomass. Canopy-based models of self-thinning failed to account for thereduction in the thinning-line intercept observed in expt 2.In both experiments, localized placement of nutrients resultedin a higher proportion of total root length being located inthe localization zone, which would result in a reduction inthe average inter-root distance. This would intensify root competitionunder conditions of nutrient limitation. The hypothesis thatintensified root competition would lower the self-thinning lineis supported by the results of expt 2. Localized placement of nutrients; root competition; shoot competition; root–shoot allocation; self-thinning; Ocimum basilicum ; sweet basil     

Layering, the effective density of mussels and mass-density boundary curves

Overall intraspecific mass-density patterns have seldom been explored in animals. Instead, self-thinning studies have predominated. The analysis of 253 samples in a multilayered mussel showed that the classical approach is biased by layering or crowding effects, suggesting a transition zone between density independence and self-thinning, without a C–D effect. However, when the effective density (density corrected by layer effect) is used, space/allometric constraint expectations are met. Layering and crowding effects on self-thinning and the mass-density boundary should be common in mussels and other taxa showing aggregated distributions.     

The effects of salt stress and arbuscular mycorrhiza on plant neighbour effects and self-thinning

Abiotic and biotic factors can alter the nature and strength of plant–plant interactions and therefore self-thinning (density-dependent mortality), but few studies have looked at how such factors interact. We investigated how salt stress and arbuscular mycorrhizal fungi (AMF) influence plant neighbour effects and self-thinning in experimental populations of Medicago sativa. We obtained two mycorrhizal levels by applying the fungicide benomyl (low AMF) or not (high AMF) at three salinity levels (0.05%, 0.2% and 0.5%). In experiment 1, we investigated how salinity and AMF interact to influence plant interaction intensity using a neighbour removal treatment. In experiment 2, we investigated how self-thinning dynamics vary under salinity conditions and different AMF levels at two initial plant densities (6000 and 17,500 seeds m^?2). Shoot biomass and plant density were measured 30, 60 and 90 days after sowing. Standardized major axis regression was used to estimate self-thinning parameters. In experiment 1, AMF increased competitive plant neighbour effects when there was no salinity stress, but this enhancement was not significant with increasing salinity. In experiment 2, there were effects of salinity and AMF on the self-thinning trajectory. The slope of the log (mean shoot biomass per unit area) vs. log density relationship was significantly steeper for the high AMF treatment than for the low AMF treatment without salinity, but the effect of AMF level on the self-thinning exponent was not significant under the two higher salinity levels. The effect of AMF treatments on the intercept of the self-thinning line was not significant at 0.2% salinity but was significant at 0.5% salinity, higher elevation for high AMF treatment. In self-thinning populations, AMF decreased the survival rate without salinity, but increased the survival rate at the highest salinity level. Our results support the hypothesis that salinity and AMF interact to influence plant neighbour effects and self-thinning. Under no-salinity conditions, AMF increased competition, steepened the self-thinning line and decreased survival rate, but these effects of AMF were not significant in the presence of salinity.     

Comparison of self-thinning models: an exercise in reasoning

Self-thinning of forest stands is one of the clearest and best-documented examples of natural selection. Besides their theoretical interest, understanding of self-thinning is important for forest practice because it produces estimates of stand density and stocking. There is a considerable diversity of views on the processes causing self-thinning, predicting variables, and analytical form of models. The most popular model was proposed by Reineke (J Agric Res 46(7):627–638, 1933) over 70 years ago. This study compares existing models of self-thinning and provides evidence that the virtually unknown model developed by Artur Nilson describes self-thinning more realistically than Reineke’s. While in the Reineke model the rate of mortality (the slope of self-thinning line) is assumed to be constant, it changes from 0 to −2 in Nilson’s model. As a result, Nilson’s model is slightly but consistently more accurate than Reineke’s. Although both models are empirical, their analysis suggests several general conclusions about self-thinning.