Density effects and self-thinning in even-aged pure stands ofEucalyptus camaldulensis Dehn

The competition density effect and changes of mean total tree weight (w) and stand density (ρ) during course of self-thinning were examined in even-aged pure stands ofEucalyptus camaldulensis Dehn. which were planted in the tropical monsoon region. The level of competition was controlled by changing the initial stand density from 625 trees ha⁻¹ to 40,000 trees ha⁻¹. Hozumi's model was used to describe thew-ρ trajectory with aging of each stand and thew-ρ relation between stands of different densities at each time. The higher density produced trees of smaller mean tree sizes. The higher the density, the sooner self-thinning began. The growth curve ofE. camaldulensis followed the logistic growth curve where both maximum size and intrinsic growth rate change with time. Mean intrinsic growth rate was maximized at initiation of growth after lag time and then gradually decreased as time progressed. Hozumi's model was considered to be the best model with wide applicability for describing and comparing the growth characteristics during the course of self-thinning among different species, especially in tropical forest plantations, in which many diverse species were used for reforestation.     

Density effect, self-thinning and size distribution in Pinus densiflora Sieb. et Zucc. stands

The competition-density (C-D) effect for given times and self-thinning over time in even-aged, natural, pure stands of Pinus densiflora Sieb. et Zucc. were analyzed with the reciprocal equation of the C-D effect in self-thinning stands, and the equation describing the time-trajectory of mean stem volume and stand density. The C-D effect and self-thinning were consistently well explained by the two equations. Differences in mean stem volume and in stand density among the stands tended to merge with increasing stand age. The self-thinning line with a slope of approximately –3/2 was reached by the higher density stand prior to the medium and lower density stands. The skewness of tree height distribution showed positive values, which means that the distribution is more or less L-shaped, and in addition the skewness decreased with increasing mean tree height, which indicates that smaller trees died as the stands grew. This trend is consistent with the asymmetric (one-sided) competition hypothesis that self-thinning is driven by competition for light. The tree height distribution was analyzed using the Weibull distribution. The location parameter h _min of the Weibull distribution increased with increasing stand age, and the scale parameter a tended to increase slightly with increasing stand age. The range of the shape parameter b of the Weibull distribution corresponded to that of the skewness.     

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.     

白石砬子国家级自然保护区天然林的自然稀疏

以白石砬子自然保护区14个天然林为研究对象,利用近30 a间14次的连续定位观测数据,分析了各林分自然稀疏过程中Reineke方程指数β值的变化范围,阐明了β值恒定的机制与影响因素。结果表明,白石砬子自然保护区天然林随着林分密度的降低,林分平均胸径逐年提高;14个天然林中,平均胸径与林分密度的幂函数相关性均达到极显著水平,其中9个天然林的幂指数β值约为1.5;5个天然林β值变化范围较大,在0.44-1.80之间。对β值波动的5个林分进一步分析,1、9、56号林分受到明显的人为干扰;22、23号林分分别在林分密度较大和胸径生长量较高的时间范围内,β值约为1.5。在天然林的自然稀疏过程中,枯损林木呈左偏单峰状分布,大径阶木死亡数量较低,中小径阶的被压木死亡数量较大,形成了树木间的负反馈关系。综合本研究表明,白石砬子自然保护区天然林的自然稀疏是连续的过程,符合-3/2自疏法则,β值恒定,约为3/2;而β值是否恒定,与立地、树种组成等因素无关,与人为干扰有关;林木之间的负反馈机制是发生自然稀疏的根本原因,光是影响自然稀疏的主要因子。     

Maintenance cost, toppling risk and size of trees in a self-thinning stand

Wind routinely topples trees during storms, and the likelihood that a tree is toppled depends critically on its allometry. Yet none of the existing theories to explain tree allometry consider wind drag on tree canopies. Since leaf area index in crowded, self-thinning stands is independent of stand density, the drag force per unit land can also be assumed to be independent of stand density, with only canopy height influencing the total toppling moment. Tree stem dimensions and the self-thinning biomass can then be computed by further assuming that the risk of toppling over and stem maintenance per unit land area are independent of stand density, and that stem maintenance cost is a linear function of stem surface area and sapwood volume. These assumptions provide a novel way to understand tree allometry and lead to a self-thinning line relating tree biomass and stand density with a power between −3/2 and −2/3 depending on the ratio of maintenance of sapwood and stem surface.     

A long-term study of Pinus banksiana population dynamics

Abstract. The long-term population dynamics of a pure, naturally-established stand of Pinus banksiana (jack pine) in southeastern Manitoba, Canada is described. The study was initiated at stand age 15, when all 468 trees in a plot were mapped and their trunk diameter at breast height (DBH) measured. The plot was remeasured eight times — every five years (six years in one case) — and mortality and DBH changes recorded. Total mortality over the 41-yr study period was ca. 84 %. Mortality was initially very low, increased once the stand entered the self-thinning stage from ages 25–46, and declined at ages 46–56. Mortality was restricted to the smallest size classes throughout. The stand reached the self-thinning line at ca. age 30. The self-thinning slope was significantly less steep than the theoretically expected value of ?0.5. The distribution of DBH values was initially symmetric, showed increasing positive skewness during the period of highest mortality, and became symmetric again at later stages. Size (DBH) inequality was highest just prior to the onset of density-dependent mortality, and subsequently declined. Tree DBH values were positively autocorrelated both initially and at later stages of stand development, but were spatially independent during the period of highest density-dependent mortality. The stand initially had a strongly clumped pattern at all spatial scales. Patterns of mortality were non-random during stand development, however, resulting in increased spatial regularity over time. Mortality was initially restricted to high density patches of the stand, but occurred throughout the plot once the self-thinning line was reached. Mortality during the self-thinning stage deviated from random expectation at local spatial scales (1–2m radius), suggesting that individuals were competing with their immediate neighbours. It is argued that an integrated approach, incorporating both population size and spatial structures, is essential in improving our understanding of long-term plant population dynamics.     

Modeling forest stand dynamics from optimal balances of carbon and nitrogen

We formulate a dynamic evolutionary optimization problem to predict the optimal pattern by which carbon (C) and nitrogen (N) are co-allocated to fine-root, leaf, and wood production, with the objective of maximizing height growth rate, year by year, in an even-aged stand. Height growth is maximized with respect to two adaptive traits, leaf N concentration and the ratio of fine-root mass to sapwood cross-sectional area. Constraints on the optimization include pipe-model structure, the C cost of N acquisition, and agreement between the C and N balances. The latter is determined by two models of height growth rate, one derived from the C balance and the other from the N balance; agreement is defined by identical growth rates. Predicted time-courses of maximized height growth rate accord with general observations. Across an N gradient, higher N availability leads to greater N utilization and net primary productivity, larger trees, and greater stocks of leaf and live wood biomass, with declining gains as a result of saturation effects at high N availability. Fine-root biomass is greatest at intermediate N availability. Predicted leaf and fine-root stocks agree with data from coniferous stands across Finland. Optimal C-allocation patterns agree with published observations and model analyses.     

Ecological and mathematical considerations on self-thinning in even-aged pure stands

It is emphasized in growth analysis of self-thinning populations that relative mortality rate pertains to the difference between relative growth rates and net assimilation rates, each of which are definable on a mean plant size basis or on a biomass basis. The time trends of the ratio of relative mortality rate to relative growth rates to be expected according to Tadaki's, Shinozaki's and Hozumi's models are compared with that of the eastern white pine population, and a good agreement is exhibited. As an alternative to Hozumi's model, a new model is constructed to unite the logistic theory of plant growth and the 3/2 power law concerning self-thinning, which so far have usually been applied independently to growth analysis. To construct the model the following assumptions are made: the fundamental equation to relate mean plant weight with density in self-thinning population proposed by Shinozaki, and a special population with a specific initial density which follows thew-p trajectory of the 3/2 power law type and has an exponential decrease in its density with biological time. Properties of the model are examined from ecological and mathematical viewpoints.     

水杉人工林建植50年后的分化特征

通过种群统计学、格局分析和树干解析等对50 a生水杉人工林林分的分化特征进行了研究.结果表明:小个体林木占有相对多数(>50.4%);林木分化现象显著,特别是树高与材积的分化十分突出,林分已出现一定强度的自然稀疏;基于TSTRAT程式的林木分级结果表明,亚优势木占绝对优势(45.7%),其树冠构成该林分的主林冠;竞争指数依次为优势木级<亚优势木级<中庸木级<被压木级,各级的基尼系数基本上低于全林总计;优势木绝对生长率和相对生长率在林分成熟期以前均大于标准木,且胸径速生期持续时问较标准木长;林分高度生长受压抑程度低于胸径生长;林木分布格局总体呈均匀型,与造林初始基本一致;优势木和被压木为聚集分布,中庸木和枯死木为随机散布,亚优势木的分布型则介于随机和聚集之间.林木种群分化既表现在个体大小的不均等性上,也表现在空间分布的非匀质性上.目前林分结构特征的主要成因可以归结为密度压力下的种内竞争.     

Non-Homogeneous Gibbs Process Models for Forestry — A Case Study

Forestry statistics needs realistic models for non-homogeneously distributed trees in forests. For elder trees, non-homogeneous Poisson or Cox processes are not realistic models. Instead, non-homogeneous Gibbs processes are suggested, which are described by a fixed pair potential describing the short-range interaction of trees and a location dependent intensity function describing long-range variation of tree density. The application of this model is demonstrated for a hickory forest in North Carolina and an artificial forest stand.     

How to measure stand density

Foresters have produced many measures of stand density. Yet, none of these is entirely satisfactory. A majority of the measures (stand density index, basal area, and leaf area) present number of trees per unit area as a function of one factor: average tree size. This paper identifies the second factor driving self-thinning: the accumulation of gaps between tree crowns inevitable even in dense stands with a sizeable overlap of crowns. A model accounting for both factors allows us to quantify stand density and find a single number characterizing the density of undisturbed stands. The number changes with species, being higher for more shade tolerant ones. It is found that the second factor affects survival of trees but not their growth. This means that there are two kinds of stand density.     

Derivation and analysis of new stand-level mortality models based on existing growth equations

Considering that, the temporal trend in stocking, expressed as number of trees per unit area, is the opposite of that of growth, and that both trajectories are sigmoidal, we derived a temporal trajectory of density decrease by reversing the temporal trend of a generalized growth function. We derived and analysed twelve stand-level mortality models by using four data sets from monospecific even-aged stands. Stand dominant height rather than stand age was incorporated as an indicator of the growth stage and a careful examination of the models conformity with the essential logical properties of the stand-level survival models was conducted. We first tested the models adequacy and general predictive performance by fitting them to parameterization data sets and subsequently assessing them with validation data. The regression equations were re-fitted afterwards over the total data sets to make use of all available information in the final parameter estimates. Nine model formulations were successfully fitted and four of them were the most adequate in describing stand density decrease with dominant height growth. The site-specific effect was incorporated in the newly derived models through the predictor variable and the stand-specific starting density was accounted for through a specific model parameter. These new dominant height-dependent mortality equations can be considered for inclusion in the framework of stand-level growth models as transition functions.     

The self-thinning process in mangrove <Emphasis Type="Italic">Kandelia obovata</Emphasis> stands

The self-thinning process was monitored in crowded Kandelia obovata Sheue, Liu & Yong stands over four years. The frequency distribution of tree phytomass was an L-shape, which was kept over the experimental period. Spearman’s rank correlation coefficient for phytomass decreased as the time span of the comparison became longer, a result which indicates that the rank of phytomass changes as stands grow. Death of trees resulted from one-sided competition, i.e., death occurred in lower-rank trees. Surviving trees continued to grow. Whatever the current spatial distribution of the trees, death occurred randomly and the spatial distribution gradually became close to random as stands grew. The self-thinning exponent was 1.46, which can be regarded as evidence in favor of the 3/2 power law of self-thinning. Relative growth rate, RGR, decreased in proportion to decreasing relative mortality rate, RMR, with a proportionality constant of 1.57, which was not significantly different from the slope of the self-thinning exponent. This experimental result probably justifies the assumption that the ratio of RGR to RMR in the mean phytomass-density trajectory for any self-thinning population with different densities becomes constant as the growth stage progresses.     

Testing a method for reconstructing structural development of even-aged Abies sachalinensis stands

Accuracy of a stand reconstruction technique was examined by comparing the estimated values of the aboveground biomass, total stem volume, stem volume growth, and stand density of Abies sachalinensis stands to those observed between 1980 and 1998 in Hokkaido, northern Japan. Census data from two stands established in 1973, one fertilized and the other unfertilized, were used for the examination. The stand statistics in the past were estimated from the DBH and height of individual trees measured in 1998, data on the aboveground biomass and stem volume with bark for nine living trees of various sizes harvested in each plot in 1998 or in 1999, and data from the stem analysis of the same harvested trees. We showed that the reconstructed patterns of the frequency distribution in aboveground biomass and in stem volume were generally the same as those observed in both plots and in any year in the past (except for 1982 and/or 1980), and that the reproduced patterns of stand development over time were similar to those observed directly in the past. Accuracy in predicting stand statistics was generally in the order of ±10% relative error. We consider that the present method of stand reconstruction could be used to estimate aboveground biomass, total stem volume, and stem volume growth of a stand in the past. Interpretation of results for the early years (1982 and 1980) and for the stand density requires caution.     

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.     

Intraspecific Competition in a Natural Stand of Betula ermanii

Density and size of naturally regenerated Betula ermanii weremonitored for six years in a 100 m² plot located in Hokkaido,northern Japan. Natural thinning of 10- to 15-year-old treesoccurred at a negative exponential rate related to tree volume,demonstrating the –3/2 power rule of self-thinning. Diameterdistributions were unimodal at ages 10–13 years and bimodalat 14 and 15 years. Changes in diameter distribution were accompaniedby changes in structure, from a one- to two-storied stand. Mortalitywas highest among smaller trees and where density was greatest.The spatial distribution of trees changed from random to uniformwith increased stand age. Betula ermanii Cham., Self-thinning, mortality, spatial distribution, size distribution     

Population structure and dynamics of Pinus massoniana Lamb. on mount Jinyun,Sichuan, China

Masson Pine (Pinus massoniana Lamb.) is a pioneer in forest succession in the subtropics of East Asia. However, the species persits, though with decreasing abundance, throughout the various successional phases. Agestructure, spatial pattern, density, population biomass, and their dynamics are described for a population in Sichuan, China, on the basis of a census of all individuals in the population while substituting space with time. In the course of succession, the population density increases and its rate of growth decreases until self-thinning starts; during the phase of self-thinning density decrease and continues to decrease even afterwards, but the rate of growth increase markedly after self-thinning has stopped. The development of population biomass (Bp) during the early succession from shrub-grassland to the early stages of mixed pine and broad-leaved forest can be described by a logistic equation. Later, Bp decrease rapidly. These changes are governed partly by inherent biological features of P. massoniana and partly by the invasion, establishment and development of shade-tolerant evergreen broad-leaved trees. Both self- and alien-thinning occur. Soil conditions affect the rates of these processes.     

Early growth of environmental plantings in relation to site and management factors

In extensively cleared areas of temperate Australia, large‐scale mixed‐species environmental revegetation is often recommended to address land and water degradation in rural landscapes. Although survival and growth are central to the success of revegetation, there is very limited information on this aspect of practice. We investigated how site and management practices influence early growth by surveying 29 planted or direct‐seeded sites, covering ages from 3–6 years, in north central Victoria, Australia. We measured heights and crown widths of trees and shrubs at each site and estimated average growth over time at the scale of: (i) individual trees or shrubs (mean height increment) and (ii) stand (vegetation cover increment and a ‘height integral’ increment variable, which integrates differences in both height and stand density). Relationships between growth increment variables and site factors, including climate, site preparation and land‐use history, were investigated to identify the main factors influencing early growth rates. Mean annual increment in height of individual trees was significantly higher for trees established from tubestock than those from direct seeding. Multiple linear regression models for two growth variables, cover increment and height integral increment, explained 61% and 38% of the variation, respectively, but with high uncertainty. Ploughing, pre‐establishment weed control and fertiliser addition improved growth rates. Revegetation method had a significant effect on early growth; at the scale of individuals, growth rates were higher for planted tubestock than for direct seeding, while at the stand scale, growth rates were higher for direct seeding than for planted tubestock.     

Banded vegetation patterning in a subantarctic forest of Tierra del Fuego,as an outcome of the interaction between wind and tree growth

Banded patterns have been investigated in a Nothofagus betuloides primeval forest from Bahía del Buen Suceso, on the eastern edge of Tierra del Fuego island (Argentina). These forests grow on spodosols developed upon silicic shales, in a cold oceanic climate, with 5 °C mean annual temperature and 600 mm mean annual rainfall. Bands are oriented perpendicular to the prevailing wind direction, with older and dying trees in the windward edge and a seedling regrowth in the lee side of each band. Forest structure, species composition and relevant soil properties were sampled in a wind-affected forest and in an undisturbed stand. In the former, samples were obtained in transects across the banding and along a hill-slope gradient. Results show that wind causes about 50 % reduction of stand basal area and of size of overstorey trees. Stand growth processes, such as self-thinning, basal area and height growth, and specific composition of the understorey, occur in a windward direction, as well as changes in soil properties such as C/N ratio and redox potential increase. Based on field observations, we have developed an hypothesis of how wind is able to generate this pattern. Its core is that bands develop when vulnerability of trees to wind damage increases with age and with lack of protection from older windward trees. In such conditions, bands are the outcome of a tuning between tree growth rates and wind killing capacity. On the basis of this hypothesis, a simulation model, based on the cellular automata approach, was constructed. Simulated patterns that arise from heterogeneous forests with random age distributions match successfully with those observed in nature. Increasing tree growth rates lead to longer wavelengths and higher wave propagation rates, while increasing wind killing potential leads to shorter wavelengths and lower propagation rates. This interpretation of banded patterning involves a resonance between a directional disturbance and an oscillatory process, such as stand regeneration, growth and decay.     

An Individual Stand Growth Model for Mean Plant Size Based on the Rule of Self-thinning

A growth model for pure, even-aged stands of plants is asymptoticallybounded above by the self-thinning rule that relates maximumplant size to stand density. The model characterizes accretionin mean size as a deviation from the limiting size. It consistsof a function relating mean size to time and density and a companionsurvival model. The growth model is obtained by substitutingthe survival model for density in the mean size relationship.Model flexibility is demonstrated by fitting it to annual remeasurementsof mean size and number of plants per unit area in a stand ofPinus taeda L. 3/2-power rule, mortality, survival, stand dynamics, plant growth model, loblolly pine