Based on density theory of plant growth and related biological hypothesis, a theoretical model describing the whole change process of plant population density was derived, i.e. \%N\%=exp(\%a\%ln\+2\%v+b\%ln\%v+c\%), w...Based on density theory of plant growth and related biological hypothesis, a theoretical model describing the whole change process of plant population density was derived, i.e. \%N\%=exp(\%a\%ln\+2\%v+b\%ln\%v+c\%), where \%N\% and \%v\% represent population density and mean volume of a plant, and \%a,b,c\% are parameters. Thereby, the authors proposed a self\|thinning mechanism model which can be used in different sites and different growth stages of Chinese fir plantation, the model was described as \%N\%=exp(5 895932H 0 01351034 -0 9225263H -0 002829299\}ln\%v\%-0 1148481H -0 01018257\}ln\+2\%v\%).The simulating result showed that the mechanism model fitted the data observed from Chinese fir plantation very well. Therefore it is very useful in practice, which will provide a scientific basis for sustainable management of Chinese fir plantation.展开更多
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 exp...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.展开更多
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...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.展开更多
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 fir...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 ca展开更多
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 b...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.展开更多
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 calcul...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.展开更多
文摘Based on density theory of plant growth and related biological hypothesis, a theoretical model describing the whole change process of plant population density was derived, i.e. \%N\%=exp(\%a\%ln\+2\%v+b\%ln\%v+c\%), where \%N\% and \%v\% represent population density and mean volume of a plant, and \%a,b,c\% are parameters. Thereby, the authors proposed a self\|thinning mechanism model which can be used in different sites and different growth stages of Chinese fir plantation, the model was described as \%N\%=exp(5 895932H 0 01351034 -0 9225263H -0 002829299\}ln\%v\%-0 1148481H -0 01018257\}ln\+2\%v\%).The simulating result showed that the mechanism model fitted the data observed from Chinese fir plantation very well. Therefore it is very useful in practice, which will provide a scientific basis for sustainable management of Chinese fir plantation.
文摘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.
基金The 12th and 13th Five-Year Plan of the National Scientific and Technological Support Projects(2015BAD09B01,2016YFD0600302)Jiangxi Scientific and Technological innovation plan(201702)National Natural Science Foundation of China(31570619,31370629)
文摘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.
文摘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 ca
基金the National Natural Science Foundation of China (30270243).
文摘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.
基金supported by Foundation of Guangdong Forestry Bureau (Nos.4400-F11031,4400-F11055)
文摘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.
