MAXIMUM DENSITY LINE AND MODEL OF SELF-THINNINGFOR PLANTATION

The method to determine the maximum density line of self-thinning is discussed and a self-thinning model is developed by using long term observed data of spacing study plots. According to traditional method, the slope of the maximum density line was result of average, which was determined by different stand sites and densities Therefore the slope determined by the previolls inethod poorly describes the sclf-thinning procedure of the maximum density stand. The self-thinning line (NDg curve) of plantation is reverse sigmoid, which can be simulated by modified Korf equation. It is concluded that the minimum asymptotic number of trees (Nmin) of self-thinning in plantation are positively correlated with initial density (N0), While curve shape is related to site and initial density,

Self-thinning lines and allometric relation in Chinese fir(Cunninghamia lanceolata) stands

We calculated a self-thinning exponent of 1.05 for tree mass using the 3/2 power equation in 93 Cunninghamia lanceolata plots.According to Weller’s allometric model,the self-thinning exponent for tree mass was calculated as 1.28 from the allometric exponents h and d.The both self-thinning exponents were significantly lower than 3/2.The self-thinning exponent of organs was estimated to be 1.42 for stems,0.93 for branches,0.96 for leaves,1.35 for roots and 1.28 for shoots,respectively.The self-thinning exponent of stem mass was not significantly different from 3/2,whereas thinning exponents of trees,branches,leaves and roots were significantly lower than 3/2.The stand leaf mass and stand branch mass were constant regardless of the stand density.The scaling relations among branch,leaf,stem,root and shoot mass（MB,ML,MS,MR and MA,respectively） showed that MB and ML scaled as the3/4 power of MS,whereas MS or MA scaled isometrically with respect to MR.

Density effect and self-thinning in Eucalyptus urophylla stands

Density effects on the growth and self-thinning of Eucalyptus urophylla stands were examined for 7 years.The reciprocal equation of the competition-density(C–D)effect was used to describe the C–D effect in even-aged pure stands of E. urophylla during course of self-thinning and showed a good fit to the data. The time trajectories of mean stem volume-density nearly paralleled the y-axis during early growth stages of stands, and then began to curve left. Finally, the mean stem volume-density trajectories of the low-, middle-and high-density stands tended to follow the self-thinning lines with slopes of-2.01,-1.90 and-1.99, respectively. With increasing physical time t, the biological time s increased rapidly during early growth stages and became slow gradually during later growth stages. Realized density-initial density curves tended to become more or less flat with increasing initial density, indicating the existence of an asymptotic value for density at a given time. The coefficient e, the reciprocal of which represents the asymptotic density at a given time,increased with increasing biological time s, indicating that the asymptotic density decreased with increasing stand age.Final yield Y(t) increased gradually with increasing stand age.

Bayesian inference of biomass growth characteristics for sugi(C.japonica)and hinoki(C.obtusa)forests in self-thinned and managed stands

Background:Forests are an important sink for atmospheric carbon and could release that carbon upon deforestation and degradation.Knowing stand biomass dynamic of evergreen forests has become necessary to improve current biomass production models.The different growth processes of managed forests compared to self-managed forests imply an adaptation of biomass prediction models.Methods:In this paper we model through three models the biomass growth of two tree species(Japanese cedar,Japanese cypress)at stand level whether they are managed or not(self-thinning).One of them is named self-thinned model which uses a specific self-thinning parameterαand adapted to self-managed forests and an other model is named thinned model adapted to managed forests.The latter is compared to a Mitscherlich model.The self-thinned model takes into account the light competition between trees relying on easily observable parameters(e.g.stand density).A Bayesian inference was carried out to determine parameters values according to a large database collected.Results:In managed forest,Bayesian inference results showed obviously a lack of identifiability of Mitscherlich model parameters and a strong evidence for the thinned model in comparison to Mitscherlich model.In self-thinning forest,the results of Bayesian inference are in accordance with the self-thinning 3/2 rule(α=1.4).Structural dependence between stand density and stand yield in self-thinned model allows to qualifying the expression of biological time as a function of physical time and better qualify growth and mortality rate.Relative mortality rate is 2.5 times more important than relative growth rate after about 40 years old.Stand density and stand yield can be expressed as function of biological time,showing that yield is independent of initial density.Conclusions:This paper addressed stand biomass dynamic models of evergreen forests in order to improve biomass growth dynamic assessment at regional scale relying on easily observable parameters.These models can be used to dynamically estimate forest biomass and more generally estimate the carbon balance and could contribute to a better understanding of climate change factors.

马尾松人工林碳储量密度控制图研建及应用研究

[目的]马尾松是我国重要的人工林树种,不但发挥着重要的经济效益,而且在固碳释氧,应对气候变化等生态服务方面发挥着重要的作用。开展抚育间伐,调控林分密度是人工林经营过程中的重要手段,而当前马尾松人工林抚育间伐存在“定性”不“定量”的问题,制约着经营目标的实现。本研究拟构建马尾松人工林碳储量密度控制图,实现马尾松人工林抚育间伐过程中的精准化。[方法]首先,以湖南省马尾松人工纯林为研究对象,基于森林资源连续清查(一类清查)数据,以Reineke自然稀疏模型为基础,构建湖南省马尾松基本密度控制图。其次,将碳储量等高线加入到基本密度控制图上,构建了碳储量密度控制图,增加了以碳储量调控为目标的密度调控功能。再次,基于所构建的密度控制图,以湖南慈利县为例,对马尾松人工林的林分密度合理性进行诊断,生成密度诊断图,并提出相关经营建议。[结果]湖南省慈利县(1)绝大部分马尾松人工林的密度高于合理密度区间,林木对有限的光照、温度、水分等自然资源产生强烈竞争,甚至有些林分会产生严重的自然枯死现象,亟待开展抚育间伐,降低林分密度;(2)少部分林分位于合理密度区间范围内,此时的林分能够充分利用自然资源,林木个体之间处于互相促进的状态;(3)少部分林分密度低于最优密度下限,此时的林地空间没有得到充分的利用,造成林地资源的浪费,亟待开展林下补植作业。[结论]本研究所构建的马尾松林分密度控制图,能够精准指导森林抚育,此外还能够对森林经营单位的林分密度合理性进行诊断,形成林分密度诊断图,进而为合理经营措施的制定提供依据。

北京市油松林碳储量密度控制图研制及应用

为了提升北京市油松林经营质量,实现林分密度调控精准化和数量化,本研究以北京市油松林为研究对象,基于北京市国家森林资源连续清查(一类清查)数据,以Reineke自然稀疏模型为基础,基于最优密度上下限及自然稀疏线、林分蓄积等值线、林分优势高等值线和林分碳储量等值线,构建北京市油松林碳储量密度控制图。根据密度控制图和林分实际情况,模拟林分自然稀疏、合理抚育间伐和对照抚育间伐(重度疏伐)3种抚育间伐措施下的林分碳储量,发现在科学密度下经营比自然稀疏或者无规则经营的碳储量高,合理抚育间伐时的碳储量增长是自然稀疏和重度间伐的1倍多;林分总收获量的增长也明显高于自然稀疏和重度疏伐。应用林分密度控制图可直观地展示不同经营情景下碳储量、蓄积量的变化,将不同经营目标下抚育间伐的时间、采伐木株树、采伐木蓄积量及碳储量等信息数量化,为以碳汇提升为目标的量化经营措施制定提供决策依据,有助于森林质量精准提升,实现森林经营的精细化和差异化管理。

福建杉木人工林密度控制图研制及应用

林分密度管理是通过控制造林时初植株行距以及后继的疏伐管理,对林分密度的控制,进而实现特定的经营目标。为了实现福建杉木人工林密度量化调控,基于Reineke自然稀疏方程,构建福建杉木密度控制图。结果表明:1)构建了杉木人工林最优生长密度上下限以及杉木林分郁闭线;2)构建了杉木优势高模型、杉木材积模型、立地指数模型作为密度控制图的辅助方程;3)基于密度控制图,模拟了3种常见密度下,对杉木林分进行的3种不同经营措施(不进行任何经营措施,合理抚育间伐,对照性抚育间伐),获得不同经营措施下林分总收获量、林分总枯损量、林分年平均收获量等林分参数以及对相应的林分年龄,为合理安排经营密度提供参考。

基于极值理论的落叶松人工林自稀疏线估计

为研究林分自稀疏线,应用极值统计方法,从现实林分数据出发,通过设计一个阈值,采用广义Pareto模型拟合阈值超出值并进行外推,获得了林分在各个给定径阶下的极限最大株数。利用最大株数与直径关系进行回归分析,得到林分自稀疏线。应用该方法分析了黑龙江省1 511块落叶松人工林固定样地数据,得到黑龙江省落叶松人工林林分自稀疏线,结果与Reineke公式估算结果相一致。

用Reinecke盐液曝光计检测树冠内的光合有效辐射

1 引言 传统的植物光合生理生态研究中,多用照度计来测定光照指标,它以人眼对光亮度的响应特性为基础,与植物叶片对光照的响应曲线差异很大;

Competition-density effect in plant populations

The competition-density effect of plant populations is of significance in theory and practice of forest management and has been studied for long time. The differences between the two reciprocal equations of the competition-density effect in nonself-thinning populations and self-thinning populations were analyzed theoretically. This supplies a theoretical basis for analyzing the dynamics of forest populations and evaluating the effect of forest management.

Nonlinear versus linearised model on stand density model fitting and stand density index calculation: analysis of coefficients estimation via simulation

The stand density index,one of the most important metrics for managing site occupancy,is generally calculated from empirical data by means of a coefficient derived from the“self-thinning rule”or stand density model.I undertook an exploratory analysis of model fitting based on simulated data.I discuss the use of the logarithmic transformation(i.e.,linearisation)of the relationship between the total number of trees per hectare(N)and the quadratic mean diameter of the stand(QMD).I compare the classic method used by Reineke(J Agric Res 46:627–638,1933),i.e.,linear OLS model fitting after logarithmic transformation of data,with the“pure”powerlaw model,which represents the native mathematical structure of this relationship.I evaluated the results according to the correlation between N and QMD.Linear OLS and nonlinear fitting agreed in the estimation of coefficients only for highly correlated(between-1 and-0.85)or poorly correlated([-0.39)datasets.At average correlation values(i.e.,between-0.75 and-0.4),it is probable that for practical applications,the differences were relevant,especially concerning the key coefficient for Reineke’s stand density index calculation.This introduced a non-negligible bias in SDI calculation.The linearised log–log model always estimated a lower slope term than did the exponent of the nonlinear function except at the extremes of the correlation range.While the logarithmic transformation is mathematically correct and always equivalent to a nonlinear model in case of prediction of the dependent variable,the difference detected in my studies between the two methods(i.e.,coefficient estimation)was directly related to the correlation between N and QMD in each simulated/disturbed dataset.In general,given the power law as the“natural”structure of the N versus QMD relationship,the nonlinear model is preferred,with a logarithmic transformation used only in the case of violation of parametric assumptions(e.g.data distributed non-normally).

A derivation of the generalized Korf growth equation and its application

Based on the biological hypothesis of tree growth, the generalized Korf growth equation, was derived theoretically. From a standpoint of applications, the equation can be used in two ways associated with the power exponent ofp, and two types of growth equations: the Korf-A (p>1) and the Korf-B (O<p<1) were developed and between them, there is the Gompertz equation (p=1) to separate each other. All of the three types of equations are independent. It was concluded that the Korf-A equation could be used to describe the growth of trees, of which inflection point is between 0 andA/e, while the Korf-B equation with the inflection point betweenA/e andA could be applied to describe the biological population growth. It was found that the Korf-A equation had a better property in describing the growth process of a tree or a stand and its applications to predicting height growth and stand self-thinning showed general good fitness.

Self-thinning Rules at Chinese Fir(Cunninghamia lanceolata) Plantations——Based on a Permanent Density Trial in Southern China

Data selection and methods for fitting coefficients were considered to test the self-thinning law. TheChinese fir (Cunninghamia lanceolata) in even-aged pure stands with 26 years of observation data were applied tofit Reineke's (1933) empirically derived stand density rule (No∝d^-1.605, N = numbers of stems, d= mean diameter),Yoda's (1963) self-thinning law based on Euclidian geometry (v ∝ N^-3/2, v= tree volume), and West, Brown andEnquist's (1997, 1999)(WBE) fractal geometry (w ∝ d^-8/3). OLS, RMA and SFF algorithms provided observedself-thinning exponents with the seven mortality rate intervals (2%--80%, 5%--80%, 10%- 80%, 15%--80%,20%- 80%, 25%--80% and 30%- 80%), which were tested against the exponents, and expected by the rules con-sidered. Hope for a consistent allometry law that ignores species-specific morphologic allometric and scale differ-ences faded. Exponents a of N ∝ d^α, were significantly different from -1.605 and -2, not expected by Euclidianfractal geometry;exponents β of w ∝ N^β varied around Yoda's self-thinning slope - 3/2, but was significantly differentfrom - 4/3;exponent Y of w ∝ d^γ tended to neither 8/3 nor 3.

Growth and form of Quercus robur and Fraxinus excelsior respond distinctly different to initial growing space: results from 24-year-old Nelder experiments

Initial growing space is of critical importance to growth and quality development of individual trees. We investigated how mortality, growth （diameter at breast height, total height）, natural pruning （height to first dead and first live branch and branchiness） and stem and crown form of 24-year-old pedunculate oak （Quercus robur [L.]） and European ash （Fraxinus excelsior [L.]） were affected by initial spacing. Data were recorded from two replicate single-species Nelder wheels located in southern Germany with eight initial stocking regimes varying from 1,020 to 30,780 seedlings·ha？1. Mortality substantially decreased with increasing initial growing space but significantly differed among the two species, averaging 59% and 15% for oak and ash plots, respectively. In contrast to oak, the low self-thinning rate found in the ash plots over the investigated study period resulted in a high number of smaller intermediate or suppressed trees, eventually retarding individual tree as well as overall stand development. As a result, oak gained greater stem dimensions throughout all initial spacing regimes and the average height of ash significantly increased with initial growing space. The survival of lower crown class ashes also appeared to accelerate self-pruning dynamics. In comparison to oak, we observed less dead and live primary branches as well as a smaller number of epicormic shoots along the first 6 m of the lower stem of dominant and co-dominant ashes in all spacing regimes. Whereas stem form of both species was hardly affected by initial growing space, the percentage of brushy crowns significantly increased with initial spacing in oak and ash. Our findings suggest that initial stockings of ca. 12,000 seedlings per hectare in oak and 2,500 seedlings per hectare in ash will guarantee a sufficient number of at least 300 potential crop trees per hectare in pure oak and ash plantations at the end of the self-thinning phase, respectively. If the problem of epicormic shoots and inadequate self-pruning can be controlled with trainer species, the initial stocking may be reduced significantly in oak.

Variation in individual biomass decreases faster than mean biomass with increasing density of bamboo stands

The total biomass of a stand is an indicator of stand productivity and is closely related to the density of plants. According to the self-thinning law, mean individual biomass follows a negative power law with plant density. If the variance of individual biomass is constant, we can expect increased stand productivity with increasing plant density. However, Taylor's power law(TPL) that relates the variance and the mean of many biological measures(e.g. bilateral areal differences of a leaf, plant biomass atdifferent times, developmental rates at different temperatures, population densities on different spatial or temporal scales), affects the estimate of stand productivity when it is defined as the total biomass of large plants in a stand.Because the variance of individual biomass decreases faster than mean individual biomass, differences in individual biomass decline with increasing density, leading to more homogeneous timbers of greater economic value. We tested whether TPL in plant biomass holds for different species and whether the variance of individual biomass changes faster than the mean with increasing stand density.The height, ground diameter and fresh weight of 50 bamboo species were measured in 50 stands ranging from 1 m by 1 m to 30 m by 30 m to ensure more than 150 bamboos in every stand. We separately examined TPL in height,ground diameter, and weight, and found that TPL holds for all three biological measures, with the relationship strongest for weight. Using analysis of covariance to compare the regression slopes of logarithmic mean and variance against the logarithm of density, we found that the variance in individual biomass declined faster than the mean with increasing density. This suggests that dense planting reduced mean individual biomass but homogenized individual biomass. Thus, there exists a trade-off between effective stand productivity and stand density for optimal forest management. Sparse planting leads to large variation in individual biomass, whereas dense planting reduces mean individual biomass. Consequently, stand density for a plantation should be set based on this trade-off with reference to market demands.

The relationships among structure variables of larch forests in China

Background:Larch(Larix Mill.)forests are widely distributed in the upper parts of mountainous areas in China,playing vital roles in constructing mountain landscapes and maintaining mountain environments.Despite their importance,our knowledges on the large-scale patterns of structure characteristics and the relationships between different structure variables are unclear.In this paper,we investigated 155 plots from 11 natural larch forest types across the country to explore the biogeographic patterns of the structure characteristics and the allometric relationships between different structure variables for Chinese larch forests.Results:The structure characteristics were significantly different among larch forest types.For different larch forest types,the power function fits the relationships between tree height and diameter at breast height(DBH),average DBH and stem density,and taper and stem density well,but with different exponents among larch forest types.The power exponents of the allometric relationships between tree height and DBH for different larch forest types varied from 0.61 to 0.93(mean=0.86)by standard major axis regression(SMA),and from 0.51 to 0.78(mean=0.56)by ordinary least square regression(OLS).The 50%,75%and 95%quantile regression(QR)and OLS indicated that the average DBH and taper of the L.gmelinii forests,L.gmelinii var.principis-rupprechtii forests,and L.sibirica forests were significantly correlated with stem density.Conclusions:The relationship between tree height and DBH showed a power function relationship for all larch forest types in China,but with different exponents.Overall,stem density was negatively correlated with average DBH and taper.The Sect.Larix forests exhibited stand density effect.Our findings provide an important basis for recognizing the biogeographic patterns of structure factors and for the management of larch forests in China.

Effects of different land-use systems (grazing and understory cultivation) on growth and yield of semi-arid oak coppices

The present study examines the extent of negative eff ects of traditional multiple land-use systems on oak coppices,from a forest management point of view.The study area was located in approximately 10,000 ha of hilly Brant’s oak(Quercus brantii Lindl.)woodlands in the central Zagros Mountains.In the same site-quality class,three land-use systems were compared:simple coppice(Co),coppice in conjunction with small ruminant grazing(CoG),and coppice with understory rain-fed wheat cultivation plus grazing(CoCG).Data on total wood volume of trunk and major branches,and annual ring growth,were collected and analyzed from 74 stands in 15 coppiced woodland patches.The results showed the advantage of Co over CoG and CoCG land-uses by 43 and 60 m 3 of mean accumulated wood volume per hectare,respectively.The diameter growth analysis also revealed an annual increase in wood production of trees in Co land-uses over 43 years,with an exception of the recent decade,when growth coincided with a severe drought.Using a back-extrapolation method,the minimum rotation age of woodlands in Co land-use was found to be 23.6 years,5 and 7 years shorter than those of CoG and CoCG land-uses,respectively.Unlike CoCG,woodlands located in Co and CoG land-use systems demonstrated a high level of agreement with self-thinning rule of−3/2.Values for the stand density index for coppiced oak woodlands were between more than 1000 for the least disturbed(Co)and less than 400 for the most disturbed woodlands(CoCG).The structure and growth rate of the coppiced oak woodlands were irreversibly disrupted by understory tillage plus grazing and in less extent by grazing alone.It was concluded that ending undergrowth cultivation in semi-arid oak coppices should be addressed as a priority by adopting minimum regulations.

Effect of Water Deficit on Self-thinning Line in Spring Wheat （Triticum aestivum L.） Populations

Monocultures of spring wheat （Triticum aestivum L.） were grown at overcrowded densities （10 000 and 3 000 plants per m^2） under well-watered and water-stressed conditions to investigate the effects of water deficits on self-thinning. The results showed that density reduction in water-stressed populations was delayed compared with that In well-watered populations. Populations grown In well-watered conditions conformed to the -3/2- power law. Compared with the well-watered condition, there was no significant decrease of the self-thinning line under water-stressed conditions In this experiment, although the rate of average shoot blomass accumulatlon decreased. This result Implied that the exponent of the -3/2-power equation Is not as sensitive as the rate of average shoot blomass accumulation to water stress. Further analysis indicated that, In each density treatment, the lines of the height versus shoot blomass relationships did not differ significantly between the two water conditions. However, the Intercepts of the height versus shoot blomass relationships were greater In the higher-density populations （10 000/m^2） than those In the lower-density populations （3 000/m^2）. These results showed that water deficit did not change plant geometry In this experiment. That Is to say, shoot competition for light remains constant at a given blomass, although root competition for water becomes more serious In water deficit conditions. Based on these results and previous reports we propose that, to affect the thinning line slope, changes In symmetric competition are not as efficient as changes In asymmetric competition.

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.

‘Relationships between relationships’ in forest stands: intercepts and exponents analyses

Relationships between diameter at breast height(dbh) versus stand density, and tree height versus dbh(height curve) were explored with the aim to find if there were functional links between correspondent parameters of the relationships, exponents and intercepts of their power functions. A geometric model of a forest stand using a conic approximation suggested that there should be interrelations between correspondent exponents and intercepts of the relationships. It is equivalent to a type of ‘relationship between relationships’ that might exist in a forest stand undergoing self-thinning, and means that parameters of one relationship may be predicted from parameters of another. The predictions of the model were tested with data on forest stand structure from published databases that involved a number of trees species and site quality levels. It was found that the correspondent exponents and intercepts may be directly recalculated from one another for the simplest case when the total stem surface area was independent of stand density. For cases where total stem surface area changes with the drop of density, it is possible to develop a generalization of the model in which the interrelationships between correspondent parameters(exponents and intercepts) may be still established.