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.

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,

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

‘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.

Tree survival and maximum density of planted forests–Observations from South African spacing studies

Background：Among the most important aspects of risk and hazard studies relating to forest ecosystems are maximum forest density and density-dependent tree survival.Methods：Long-term observations about the maximum density of unthinned Pinus patula and P.elliottii field plots based on the Correlated Curve Trend（CCT）spacing studies which were established almost 8 decades ago by O’Connor（Forest Research with Special Reference to Planting Distances and Thinning,1935）in South Africa.Three specific approaches were introduced for analysing maximum density and tree survival,namely the‘limiting line’,Nilson’s sparsity and tree survival with the Weibull function.Results：The main results are：a）Maximum densities differ greatly among the two species grown on the same site and within the same species grown on different sites;it is possible to relate these differences to site index in both species.b）The relationship between the quadratic mean diameter and the minimum average spacing of surviving trees（known as Nilson’s Sparsity）appears to be surprisingly similar in both species.c）An analysis of tree survival in response to different initial planting espacements shows that the Weibull survival function parameters can be estimated if the initial planting density is known.This result is presented for each of the eight large experiments used in this study.Conclusions：This study contributes to a better understanding of tree survival and maximum density which are the key factors required for estimating risk and uncertainty.The risk of tree mortality is not constant,but varies with tree species,planting density,tree age and growing site.For estimating that risk,therefore,continuous long-term observation on different sites and with varying planting densities,as provided by the unthinned CCT series,are essential.

Exogenous and endogenous determinants of spatial aggregation patterns in tibetan Plateau meadow vegetation

Aims We aim to quantify the relative importance of various endogenous and exogenous processes influencing the spatial distribution of the individuals of plant species at different temporal and spatial scales in a species-rich and high-cover meadow in the eastern tibetan Plateau.Methods We calculated green’s index of dispersion to infer the spatial dis-tribution patterns of 73 herbaceous species at two scales(0.25 and 1.0 m2).We constructed a series of generalized linear models to test the hypotheses that different species traits such as mean plant stem density,per capita dry biomass,maximum plant height and mean seed mass contribute to their spatial distribution.We used the first principal component of soil C,N and P to explain abundance vari-ation across quadrats and sub-plots.Important Findingsthe individuals of the species studied were highly spatially aggregated.at both spatial scales,biomass and stem density explained the most variation in aggregation,but there was no evidence for an effect of mean seed mass on aggregation intensity.the effects of soil carbon,nitrogen and phosphorus at different depths affected plant abundance mostly at the broader spatial scale.our results demonstrate that self-thinning and habitat heterogeneity all contribute to determine the spatial aggregation patterns of plant individuals in alpine meadow vegetation in the eastern tibetan Plateau.