Comparison of methods in analysis of the tree spatial distribution pattern

The L-function based on K-function, the pair-correlation function and the uniform angle index used in analyzing the tree spatial distribution pattern were compared on the basis of the data from 5 actual plots and 30 simulated plots. It was concluded that the pair-correlation function and the uniform angle index were more accurate than the L-function; the uniform angle index was more effective and feasible than the L-function and the pair-correlation function; the uniform angle index has an additional advantage that it could combine qualitative and quantitative analyses by using the distribution diagram of the uniform angle index and the average valueW .     

Comparison of methods in analysis of the tree spatial distribution pattern

The L-function based on K-function, the pair-correlation function and the uniform angle index used in analyzing the tree spatial distribution pattern were compared on the basis of the data from 5 actual plots and 30 simulated plots. It was concluded that the pair-correlation function and the uniform angle index were more accurate than the L-function; the uniform angle index was more effective and feasible than the L-function and the pair-correlation function; the uniform angle index has an additional advantage that it could combine qualitative and quantitative analyses by using the distribution diagram of the uniform angle index and the average valueW .     

Some Remarks on the Estimation of the Pair-Correlation Function for Point Processes

Doguwa (1990) proposed kernel based pair-correlation function estimators for Point processes. These estimators transport a part of the probability mass into the negative or left, to a hard-core distance. The reflection technique is used to provide an alternative estimator of the pair-correlation function, which drastically reduces the bias inherent in these estimators for the case of random and clustered point patterns. However, the drastic reduction in bias, is at the cost of a much larger variance.     

林木空间分布格局分析方法

采用5块实地调查样地和30块模拟样地,通过基于Ripley K-函数的L-函数、双相关函数和角尺度方法在林木空间分布格局研究中的比较分析,得出如下结论:双相关函数和角尺度在判断的准确性方面优于L-函数;角尺度在有效性和可行性方面比L-函数和双相关函数更强,并且它能利用角尺度分布图和均值同时作定性和定量分析,从而使其优势更加明显。     

Quantitative analysis of photoactivated localization microscopy (PALM) datasets using pair-correlation analysis

Pointillistic based super-resolution techniques, such as photoactivated localization microscopy (PALM), involve multiple cycles of sequential activation, imaging, and precise localization of single fluorescent molecules. A super-resolution image, having nanoscopic structural information, is then constructed by compiling all the image sequences. Because the final image resolution is determined by the localization precision of detected single molecules and their density, accurate image reconstruction requires imaging of biological structures labeled with fluorescent molecules at high density. In such image datasets, stochastic variations in photon emission and intervening dark states lead to uncertainties in identification of single molecules. This, in turn, prevents the proper utilization of the wealth of information on molecular distribution and quantity. A recent strategy for overcoming this problem is pair-correlation analysis applied to PALM. Using rigorous statistical algorithms to estimate the number of detected proteins, this approach allows the spatial organization of molecules to be quantitatively described.     

Statistical Analysis of Spatial Point Processes: A Soft-Core Model and Cross-Correlations of Marks

This paper suggests correlation characteristics for marked point processes with two marks for each point and describes statistical methods for their estimation. Its use is demonstrated by means of an example, where the points are locations of pine saplings, and the marks are their heights and ages. Furthermore, a soft-core point process model is presented. It is shown that a pattern of sites of beadlet anemones on a rock has a pair-correlation function and intensity which can be very well approximated by the model.     

Structure of Supercritical Fluid Krypton at Small Scattering Angle Using Parallel Molecular Dynamics Simulation

Abstract

We present a parallel algorithm for molecular dynamics involving short-range two- and three-body potentials and the pair-correlation function, g(r). The method is based on a spatial decomposition of the simulation box that takes advantage of a linked-cell list, and allows a load balanced partition of the computations of both the forces and g(r) over the processors. The tests of the program is conducted by evaluating the efficiency for both the thermalization phase and the production phase of the simulation. This method is successfully applied to the calculation of the direct correlation function of fluid krypton at small scattering angle along the T = 297 K supercritical isotherm.     

Measuring Actin Flow in 3D Cell Protrusions

Actin dynamics is important in determining cell shape, tension, and migration. Methods such as fluorescent speckle microscopy and spatial temporal image correlation spectroscopy have been used to capture high-resolution actin turnover dynamics within cells in two dimensions. However, these methods are not directly applicable in 3D due to lower resolution and poor contrast. Here, we propose to capture actin flow in 3D with high spatial-temporal resolution by combining nanoscale precise imaging by rapid beam oscillation and fluctuation spectroscopy techniques. To measure the actin flow along cell protrusions in cell expressing actin-eGFP cultured in a type I collagen matrix, the laser was orbited around the protrusion and its trajectory was modulated in a clover-shaped pattern perpendicularly to the protrusion. Orbits were also alternated at two positions closely spaced along the protrusion axis. The pair cross-correlation function was applied to the fluorescence fluctuation from these two positions to capture the flow of actin. Measurements done on nonmoving cellular protrusion tips showed no pair-correlation at two orbital positions indicating a lack of flow of F-actin bundles. However, in some protrusions, the pair-correlation approach revealed directional flow of F-actin bundles near the protrusion surface with flow rates in the range of ∼1 μm/min, comparable to results in two dimensions using fluorescent speckle microscopy. Furthermore, we found that the actin flow rate is related to the distance to the protrusion tip. We also observed collagen deformation by concomitantly detecting collagen fibers with reflectance detection during these actin motions. The implementation of the nanoscale precise imaging by rapid beam oscillation method with a cloverleaf-shaped trajectory in conjunction with the pair cross-correlation function method provides a quantitative way of capturing dynamic flows and organization of proteins during cell migration in 3D in conditions of poor contrast.     

Measuring Actin Flow in 3D Cell Protrusions

Actin dynamics is important in determining cell shape, tension, and migration. Methods such as fluorescent speckle microscopy and spatial temporal image correlation spectroscopy have been used to capture high-resolution actin turnover dynamics within cells in two dimensions. However, these methods are not directly applicable in 3D due to lower resolution and poor contrast. Here, we propose to capture actin flow in 3D with high spatial-temporal resolution by combining nanoscale precise imaging by rapid beam oscillation and fluctuation spectroscopy techniques. To measure the actin flow along cell protrusions in cell expressing actin-eGFP cultured in a type I collagen matrix, the laser was orbited around the protrusion and its trajectory was modulated in a clover-shaped pattern perpendicularly to the protrusion. Orbits were also alternated at two positions closely spaced along the protrusion axis. The pair cross-correlation function was applied to the fluorescence fluctuation from these two positions to capture the flow of actin. Measurements done on nonmoving cellular protrusion tips showed no pair-correlation at two orbital positions indicating a lack of flow of F-actin bundles. However, in some protrusions, the pair-correlation approach revealed directional flow of F-actin bundles near the protrusion surface with flow rates in the range of ∼1 μm/min, comparable to results in two dimensions using fluorescent speckle microscopy. Furthermore, we found that the actin flow rate is related to the distance to the protrusion tip. We also observed collagen deformation by concomitantly detecting collagen fibers with reflectance detection during these actin motions. The implementation of the nanoscale precise imaging by rapid beam oscillation method with a cloverleaf-shaped trajectory in conjunction with the pair cross-correlation function method provides a quantitative way of capturing dynamic flows and organization of proteins during cell migration in 3D in conditions of poor contrast.     

尖峰岭热带山地雨林优势树种白颜树空间分布格局

优势树种对群落的构建和形成起主要作用。该文以海南岛尖峰岭60 hm²样地内重要值第二大的树种白颜树(Gironniera subaequalis)为研究对象, 探索其种群分布格局特征, 讨论环境异质性、密度依赖死亡、扩散限制等机制在格局形成过程中所起的作用。将白颜树10022个植株分为6个径级, 分别归属于幼树、中龄树、成年树三个生活史阶段, 采用成对相关函数分析各径级的空间分布特征; 双变量成对相关函数和标签关联函数分析不同生活史阶段之间的空间关系; Berman检验方法检验3个地形因子分别对幼树、中龄树、成年树分布影响的显著度。结果表明: 白颜树种群内I、II、III、IV径级呈现聚集分布, 聚集程度随径级的增加减弱; V和VI径级小尺度上均匀分布, 大尺度上以随机分布为主。幼树与中龄树空间正关联; 幼树与成年树空间负关联; 成年树与中龄树在较小的尺度上负关联, 大尺度上微弱正关联。但是不同生活史阶段的个体之间彼此分离, 个体间无直接的促进作用。地形因子中, 坡度、海拔、凹凸度对幼树的分布影响显著; 坡度、凹凸度对中龄树的分布影响显著; 仅坡度对成年树的分布影响显著。从现有的空间格局可以推断出环境异质性和密度依赖死亡对格局形成起作用, 但是种子的扩散限制对空间格局的影响没有明确地表现出来。     

Some patterns of spatial-ontogenetic structure in populations of tuber orchids

Population dynamics, density, and aggregation size of tuberoid orchids have been identified based on mapping, electronic maps constructed with “point processes,” and Ripley function and pair-correlation function. Discrete and discrete-continuous types of spatial structure dominate in populations in optimal ecological conditions. The bounded aggregations of levels I (radius 0.45–0.75 m) and II (radius 1.2–2.5 m) are formed at 3 to 7.5 m². The spatial pattern depends on generative specimens which are related with the “group effect.” The microloci have full ontogenetic structure and may be regarded as elemental populations. They form larger aggregations of levels III and IV with random spatial distribution and continuous bounds. Aggregations of higher level are not formed under worse ecological conditions. Random spatial distribution and incomplete ontogenetic spectrum of microloci are indicators of critical population status.     

Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis

Photoactivated localization microscopy (PALM) is a powerful approach for investigating protein organization, yet tools for quantitative, spatial analysis of PALM datasets are largely missing. Combining pair-correlation analysis with PALM (PC-PALM), we provide a method to analyze complex patterns of protein organization across the plasma membrane without determination of absolute protein numbers. The approach uses an algorithm to distinguish a single protein with multiple appearances from clusters of proteins. This enables quantification of different parameters of spatial organization, including the presence of protein clusters, their size, density and abundance in the plasma membrane. Using this method, we demonstrate distinct nanoscale organization of plasma-membrane proteins with different membrane anchoring and lipid partitioning characteristics in COS-7 cells, and show dramatic changes in glycosylphosphatidylinositol (GPI)-anchored protein arrangement under varying perturbations. PC-PALM is thus an effective tool with broad applicability for analysis of protein heterogeneity and function, adaptable to other single-molecule strategies.     

湖北木林子保护区山矾属植物空间分布格局及其关联性

物种共存机制是生态学研究的重要问题。以同属物种山矾、光叶山矾为研究对象,分析其空间分布格局和种内、种间关联性特征。将山矾、光叶山矾分为4个径级,分别归属幼树、小树、中树和成年树4个生长阶段。采用单变量成对相关函数分析空间分布格局特征;双变量成对相关函数分析种内、种间关联性。结果显示：山矾和光叶山矾径级结构基本一致,均属增长型种群。在完全空间随机模型下,山矾和光叶山矾主要呈聚集分布,逐渐过渡为均匀分布;在异质泊松模型下,只在小尺度上聚集,较大尺度范围呈随机分布。种内关联上,山矾各生长阶段主要呈正关联,逐渐向无关联过渡,光叶山矾除小树与成年树外,其余均呈正关联;排除生境异质性影响后,小尺度呈正关联,其余尺度无关联。种间关联上,在幼树、小树物种对中主要呈负关联,中树、成年树物种对中多为无关联。研究表明,同属物种山矾和光叶山矾呈种内聚集、种间分离的空间构型,在竞争排除作用下实现同属共存,有利于亚热带常绿落叶阔叶混交林群落结构稳定和物种多样性维持。     

密度制约对宝天曼落叶阔叶林锐齿栎死亡前后分布格局的影响

为了在温带和亚热带的过渡带中验证森林树木死亡是否受密度制约的影响, 我们在宝天曼国家级自然保护区选择1个100 m×100 m的暖温带落叶阔叶林样地, 用双变量函数g(r)(the pair-correlation function)研究了锐齿栎(Quercus aliena var. acuteserrata)死亡前(活树和枯木统称为死亡前树木)和死亡后(活树为死亡后树木)的分布格局。把样地中的锐齿栎分为幼树(1 cm ≤ DBH<10 cm)、小树(10 cm ≤ DBH<20 cm)和成年树(DBH≥20 cm)3个不同的生长阶段来研究密度制约对空间分布格局的影响机制。结果表明: (1)死亡前锐齿栎在r>5 m尺度呈聚集分布, 死亡后幼树(1 cm≤DBH<10 cm)和成年树(DBH≥20 cm)在1-25 m尺度呈现随机分布, 死亡后小树(10 cm≤DBH< 20 cm)在r<1.5 m和2.5-4.5 m的尺度为随机分布, 在r>5 m的尺度呈聚集分布; (2)采用随机标签零模型和案例-对照设计的方法, 排除生境异质性影响后, 将幼树和小树的分布格局作为案例, 将成年树的分布格局作为对照, 并代表生境异质性的作用, 通过小径级树木与成年树分布格局的对比发现, 密度制约效应对死亡前后的锐齿栎分布格局均具有影响; (3)幼树和小树在成年树周围的分布死亡前为显著聚集分布格局, 死亡后剩余树木的聚集强度下降; 随着与成年树之间距离的增加, 死亡后的幼树(仅包括现存的活树)逐渐向随机分布格局演替。本研究初步表明锐齿栎空间格局受生境异质性的影响并呈现出显著的聚集效应, 排除生境异质性影响后, 锐齿栎死亡前后的空间格局受到密度制约的影响, 这一结果为Janzen-Connell假说提供了支持。     

Spatial patterns and competition of tree species in a Douglas-fir chronosequence on Vancouver Island

While the successional dynamics and large-scale structure of Douglas-fir forest in the Pacific Northwest region is well studied, the fine-scale spatial characteristics at the stand level are still poorly understood. Here we investigated the fine-scale spatial structure of forest on Vancouver Island, in order to understand how the three dominant species, Douglas-fir, western hemlock, and western redcedar, coexist and partition space along a chronosequence comprised of immature, mature, and old-growth stands. We quantified the changes in spatial distribution and association of the species along the chronosequence using the scale-dependent point pattern analyses pair-correlation function g(r) and Ripley's L-function. Evidence on intra- and inter-specific competition was also inferred from correlations between nearest-neighbor distances and tree size. Our results show that 1) the aggregation of Douglas-fir in old-growth was primarily caused by variation in local site characteristics, 2) only surviving hemlock were more regular than their pre-mortality patterns, a result consistent with strong intra-specific competition, 3) inter-specific competition declined rapidly with stand age due to spatial resource partitioning, and (4) tree death was spatially randomly distributed among larger overstory trees. The study highlights the importance of spatial heterogeneity for the long-term coexistence of shade-intolerant pioneer Douglas-fir and shade-tolerant western hemlock and western redcedar.     

Negative Density Dependence Regulates Two Tree Species at Later Life Stage in a Temperate Forest

Numerous studies have demonstrated that tree survival is influenced by negative density dependence (NDD) and differences among species in shade tolerance could enhance coexistence via resource partitioning, but it is still unclear how NDD affects tree species with different shade-tolerance guilds at later life stages. In this study, we analyzed the spatial patterns for trees with dbh (diameter at breast height) ≥2 cm using the pair-correlation g(r) function to test for NDD in a temperate forest in South Korea after removing the effects of habitat heterogeneity. The analyses were implemented for the most abundant shade-tolerant (Chamaecyparis obtusa) and shade-intolerant (Quercus serrata) species. We found NDD existed for both species at later life stages. We also found Quercus serrata experienced greater NDD compared with Chamaecyparis obtusa. This study indicates that NDD regulates the two abundant tree species at later life stages and it is important to consider variation in species'' shade tolerance in NDD study.     

长白山次生杨桦林种群空间点格局及密度制约效应

以长白山5.2 hm²次生杨桦林样地为研究对象,利用空间点格局分析的双相关函数g（r）以及随机标签零模型和案例-对照设计法,探讨了树木种群空间格局及其密度制约效应。研究结果表明：生境异质性对不同生活型以及不同树种的成熟个体在大尺度范围上具有强烈影响。剔除生境异质性带来的影响后,在14个常见树种中有12个树种在小尺度上呈显著的空间聚集分布格局;随着空间尺度的增加聚集性分布树种数量急剧下降,在18 m尺度上聚集率下降到0。全部14个常见树种均呈现出显著的密度制约效应,表明密度制约是调节温带森林树木种群空间结构的主要作用机制。此外,密度制约与物种多度呈负相关,与亚林层和灌木层树种的同种聚集强度呈正相关。并且随着空间尺度增大受密度制约影响的树种百分比逐渐减小,14个常见树种中有11个在0-1 m处达到最大的密度制约强度。     

Density dependence is prevalent in a heterogeneous subtropical forest

Although negative conspecific density dependence among neighbours is widely studied, the general prevalence of the effects is still poorly understood due to a lack of studies from zonal forests other than the tropics. In addition, the detection of density dependence may be confounded by the influence of habitat heterogeneity. Here we examined the spatial distributions of 47 common tree species (diameter at breast height≥1  cm) using the pair-correlation function g(r) in a fully mapped 24-ha subtropical forest in China. We first investigated whether habitat heterogeneity influenced tree distributions, and then examined the conspecific tree patterns and density dependence after removing the effects of habitat heterogeneity. We found that the forest plot exhibited strong large-scale heterogeneity in the distribution of both large adult trees of different growth forms and individual species. After the habitat heterogeneity was accounted for, 39 of the 47 species (83.0%) were found to exhibit density dependence predominantly at close distances among neighbors. Our findings highlight density dependence as a prevalent mechanism for regulating the population spatial structure of most tree species in the species-rich subtropical forest studied here. Furthermore, the occurrence of density dependence is closely associated with species abundance and the strength of conspecific aggregation at local scales. Abundant species with high strength of conspecific aggregation tend to show density dependence.     

Gap junction structures: Analysis of the x-ray diffraction data

Models for the spatial distribution of protein, lipid and water in gap junction structures have been constructed from the results of the analysis of X-ray diffraction data described here and the electron microscope and chemical data presented in the preceding paper (Caspar, D. L. D., D. A. Goodenough, L. Makowski, and W.C. Phillips. 1977. 74:605-628). The continuous intensity distribution on the meridian of the X-ray diffraction pattern was measured, and corrected for the effects of the partially ordered stacking and partial orientation of the junctions in the X-ray specimens. The electron density distribution in the direction perpendicular to the plane of the junction was calculated from the meridional intensity data. Determination of the interference function for the stacking of the junctions improved the accuracy of the electron density profile. The pair-correlation function, which provides information about the packing of junctions in the specimen, was calculated from the interference function. The intensities of the hexagonal lattice reflections on the equator of the X-ray pattern were used in coordination with the electron microscope data to calculate to the two-dimensional electron density projection onto the plane of the membrane. Differences in the structure of the connexons as seen in the meridional profile and equatorial projections were shown to be correlated to changes in lattice constant. The parts of the junction structure which are variable have been distinguished from the invariant parts by comparison of the X-ray data from different specimens. The combination of these results with electron microscope and chemical data provides low resolution three- dimensional representations of the structures of gap junctions.     

Calculation of DNA molecule packing in crystals by the method of atom-atom potentials I. B-form of DNA]

The van-der-Waals interaction of DNA molecules in the B-form has been studied by the method of atom-atom potentials. This study was carried out to clarify to what degree does this interaction determinate packing of DNA molecules in a crystal lattice. Interaction energy of two parallel molecules has been calculated as a function of 4 parameters (interaxial distance, axial shift, screw rotation of molecules). Energy as a function of these parameters is shown to have two minima, one of them exactly corresponding to mutual arrangement of DNA molecules in the lattice determined from X-ray data.