A systematic comparison of summary characteristics for quantifying point patterns in ecology

Many functional summary characteristics such as Ripley's K function have been used in ecology to describe the spatial structure of point patterns to aid understanding of the underlying processes. However, their use is poorly guided in ecology because little is understood how well single summary characteristics, or a combination of them, capture the spatial structure of real world patterns. Here, we systematically tested the performance of combinations of eight summary characteristics [i.e. pair correlation function g(r), K‐function K(r), the proportion E(r) of points with no neighbor at distance r, the nearest neighbor distribution function D(r), the spherical contact distribution H_s(r), the kth nearest‐neighbor distribution functions D_k(r), the mean distance nn(k) to the kth neighbor, and the intensity function λ( x )]. To this end we used point pattern data covering a wide range of spatial structures including simulated (stationary) as well as real, possibly non‐stationary, patterns on tree species in a tropical forest in Panamá. To measure the information contained in a given combination of summary characteristics we used simulated annealing to reconstruct the observed patterns based only on the limited information provided by this combination and assessed how well other characteristics of the observed pattern were recovered. We found that the number of summary characteristics required to capture the spatial structure of stationary patterns varied between one (for patterns with near random structures) and three (for patterns with complex cluster and superposition structures), but with a robust ranking g(r), D_k(r), and H_s(r) that was largely independent on pattern idiosyncrasies. Stationary summary characteristics [with ranking g(r), D_k(r), H_s(r), E(r)] captured small‐ to intermediate scale properties of non‐stationary patterns, but for describing large‐scale spatial structures the intensity function was required. Our finding revealed that the current practice in ecology of using only one or two summary characteristics bears danger that essential characteristics of more complex patterns would not be detected. The technique of pattern reconstruction presented here has wide applications in ecology.     

On the Uniqueness of the Reverse Monte Carlo Simulation for Molecular Liquids

Abstract

A careful analysis of the three dimensional structures of liquid Chlorine produced by the Reverse Monte Carlo (RMC) and Molecular Dynamics (MD) techniques is presented. The analysis allows us to measure the degree of uniqueness between the potential and the atom-atom distribution functions, g _aa(r), in the case of pairwise potentials formed by isotropic and anisotropic site-site interactions. The g _aa(r) obtained from MD simulations are used as ‘experimental’ input data in the RMC procedure and the constraint of rigid molecules is imposed. The particle configurations produced by RMC are then studied by using a recently proposed general method for analysing the local order in liquids. The same analysis applied to the particle configurations produced by the conventional MD simulation yields a set of partial distribution functions which relates the main features of the g _aa(r) to microscopic pair geometries. The comparison between the partial centre-centre g _cc(r) shows that the three dimensional structures, produced by MD and RMC simulations, agree very well when only isotropic site-site interactions act. In this case RMC produces the same radial distribution function g(r, ω₁, ω₂) as that obtained from the original MD configurations; it is therefore a valid tool for deriving a complete information on the physical properties of a fluid. For anisotropic site-site interactions the partial g _cc(r) of MD and RMC differ significantly and show that the three dimensional structures, produced by MD and RMC simulations, differ too. The discrepancies are particularly evident for the T shaped configurations and affect the values of the potential energy. Therefore, even if the potential is purely pairwise additive, the use of the atomic radial distribution function as input data and the imposition of atomic constraints which model the molecules as hard dumbbells are not sufficient to bring the RMC procedure towards the ‘true’ microscopic structure of the liquid; the presence of non central forces between sites disrupts the bijective correspondence between the potential and the g _aa(r).     

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.     

Competitive interactions of Persian oak coppice trees (<Emphasis Type="Italic">Quercus brantii</Emphasis> var. <Emphasis Type="Italic">persica</Emphasis>) in a pure dry woodland revealed through point pattern analysis

Understanding intraspecific interactions among Persian oaks is essential to predict the responses of Zagros dry woodlands purely covered by these coppice trees to environmental changes (such as drought) that have direct effects on the sustainability of these woodlands. This investigation attempted to explore the scale-dependent competition among Persian oaks and highlight the impacts of competitive interactions on their biophysical properties (i.e. tree height, diameter at root collar and crown attributes) via point pattern analysis. Structurally different summary statistics were implemented to analyse the spatial pattern of Persian oaks in a pure 9-ha study plot. Nearest neighbour distribution function D(r) indicated that these coppice trees had no nearest neighbours up to the spatial scale of 2 m, and they all had a nearest neighbour at distances shorter than 12 m. Furthermore, pair correlation function g(r) showed the significant dispersion of Persian oaks up to the scale of 5 m, which may be the outcome of intraspecific competition for resources such as soil nutrients and water. As explored by mark variograms γ _m (r), Persian oaks of the same size had significant spatial correlations that illustrated the competitive (not facilitative) interactions of these coppice trees in the study plot. Mark correlation function k _mm (r) additionally revealed negative correlations of height and radial growth up to large spatial scales. Consequently, the outcome of this study highlighted the significant effects of competitive intraspecific interactions among Persian oak coppice trees on their spatial pattern and biophysical properties.     

大兴安岭次生林区优势种落叶松分布格局及竞争作用

竞争是形成特定群落结构、构成分布格局的基本驱动力之一,树种的空间分布和大小并不是相互独立的,而是广泛受到竞争过程影响。在大兴安岭设置一块具有代表性的天然次生林恢复样地,采用点格局分析中的最近邻体距离G（r）函数、双关联函数g（r）和基于个体胸径标记的点格局分析方法同时结合4种点格局零模型（完全随机模型、均值托马斯模型、随机标签模型、先决条件零模型）研究分析大兴安岭次生林区优势种落叶松不同生活史阶段的分布格局、关联性及竞争作用。研究结果显示：落叶松不同发育阶段分布格局不同、同一发育阶段不同研究尺度分布格局也不同;落叶松种群内存在潜在的竞争、且竞争作用与龄级和研究尺度有关;落叶松幼龄个体在小尺度（r<5m）下的聚集分布是由扩散限制作用和竞争作用所导致;落叶松种群内成龄与幼龄个体间有较强的正关联性、成龄个体对幼龄个体在小尺度下有明显的庇护作用;标记点格局分析方法在检测植物群落中的竞争作用时敏感性较高。     

吉林蛟河针阔混交林树木生长的空间关联格局

以吉林蛟河21.12hm2(660m×320m)针阔混交林样地为对象,利用2009年和2014年森林生长观测数据,研究树木生长的空间自相关格局及其生境影响机制。在样地生境型划分结果的基础上,采用Ripley's L(r)函数分析不同生境型中树木种群空间分布特征;利用标记相关函数分析不同生境型中树木生长特征的空间关联格局。研究结果表明:(1)红松(生境型3:1—5m)、蒙古栎(生境型3:1—3m)、胡桃楸(生境型2:1—2m;生境型3:1—7m)、黄檗(生境型2:1—3m;生境型4:1—5m)、水曲柳(生境型3:1—2m;生境型4:1—2m)、瘤枝卫矛(生境型2:1—15m)在特定生境和空间尺度上呈随机分布,但空间格局仍以聚集性分布为主;其余10个物种则在全部0—30m尺度上呈聚集分布。(2)标记相关函数分析显示春榆、毛榛、色木槭、瘤枝卫矛和千金榆的径向生长至少在一个生境中表现出正相关格局;暴马丁香、胡桃楸、裂叶榆、瘤枝卫矛、水曲柳、紫椴、糠椴、毛榛、色木槭和白牛槭的径向生长至少在一个生境中表现出负相关格局;红松、黄檗、蒙古栎和簇毛槭的径向生长在全部尺度上均未检测到显著的空间关联格局。因此,不同树种径向生长的空间自相关特征不同,树种生长特征的空间关联格局具有明显的生境依赖性。     

Phylogeny contributes more than site characteristics and traits to the spatial distribution pattern of tropical tree populations

Dispersal mechanism, species height, sexual system, and wood density are potential drivers of the spatial distribution pattern of tropical tree populations. These traits are usually conserved among closely related species, thus populations of these species should have more similar spatial distribution patterns than populations of phylogenetically distant species. Additionally, variation in the abiotic and biotic environment might result in distinct spatial distribution patterns of local populations of the same species. We employed variation partitioning to determine the degree to which traits, shared evolutionary history, site characteristics, and their joint effects govern the degree of overdispersion or aggregation of tree populations at different spatial scales within fourteen 1‐ha plots of the Atlantic Rainforest in southeastern Brazil. We quantified the degree of overdispersion or aggregation with a new standardized index err(r) based on standardized effect sizes of the pair correlation function. Variation in err(r) was mostly explained by phylogenetic relationships among species (70–95%, depending on spatial scale), indicating that traits not included in our analysis are important drivers of the spatial distribution pattern. Site characteristics explained a smaller part of the variation, indicating context‐dependence. Finally, the traits studied here provided the smallest explanation of the variation, suggesting a minor role of seed dispersal. Residual variation in err(r) ranged from 5–29%, indicating that stochasticity and/or variables not included in the models (e.g. direct measures of post‐dispersal processes) also influence the spatial distribution pattern of the populations. Our results suggest that many ecological processes act in concert at the study site and that their importance changes with spatial scale. Additionally, the relative importance of these processes differs from that previously described for other tropical forests. Determining why a given ecological process is more important in some tropical tree communities than in others are promising venues for further research.     

Molecular dynamics and dissipative particle dynamics simulations for prediction of miscibility in polyethylene terephthalate/polylactide blends

The miscibility of polyethylene terephthalate (PET)/polylactide (PLA) blends is studied through atomistic molecular dynamics (MD) and mesoscale dissipative particle dynamics (DPD) simulation. Five PET/PLA blends (with the weight ratio at 90/10, 70/30, 50/50, 30/70 and 10/90) as well as pure PET and PLA are examined. The solubility parameter values obtained by using the MD simulation are in good agreement with the reference data. The Flory–Huggins parameters, χ, which are computed for different blends and determined from the cohesive energy densities, with the radial distribution functions g(r) of the inter-molecular atoms, suggest that PET is completely miscible with PLA over the entire composition range. This is further proved by the mesoscopic morphologies of PET/PLA blends. All the simulation results are qualitatively consistent with the experimental results, and demonstrate that the modelling strategies in this study may serve as a powerful tool for predicting miscibility and mesoscopic morphology of polymer blends.     

Analysis of local order in the spatial distribution of cell surface molecular assemblies.

Electron micrographs obtained from platinum-carbon replicas of freeze-cleaved or freeze-dried cells and exhibiting intramembranous or externally-disposed particles were analysed statistically for degree of non-random particle association. Analysis was based on use of an analogy to the radial distribution function, g(r), which provided the average density of neighbor particles around a particle in the micrograph at 30 Å increments from particle center. The ratio of average density of neighbors around a particle to overall particle density in the micrograph was then determined as a function of distance from particle center. For a random plot of 90 Å particles, the computed ratio deviated from 1 by less than 10% for a distance up to 900 Å from particle center. In a field of similarly-sized intramembranous particles within the freeze-cleaved surface membrane of a mouse fibroblast, there were indications of slight non-random particle associations at distances of 120–240 Å and 300–330 Å from particle center, while a significant association of particles comprising an intercellular gap junction was obtained at 90–120 Å. Virus-related molecular assemblies on the surfaces of fibroblasts infected with a temperature-sensitive mutant of murine luekemia virus and grown under conditions that did not permit virus assembly to occur were analysed similarly. Significant deviation from randomness was found at several distances from particle center, both on areas of membrane that were populated by large numbers of particles and on low-density areas.     

Nonlocal nature of the electron energy spectrum in a glow discharge in pure O2: I. Nonlocal character of the electron distribution function

Abstrac A study is made of the nonlocal nature of the electron energy distribution function in the positive column of a glow discharge in a tube filled with pure oxygen. The distribution function and the axial (E _z) and radial (E _r) electric fields as functions of radius are measured using an array of mobile probes. The experimentally obtained spatial profiles of the distribution function are used to test the applicability of the two-term approximation to the distribution function of the electrons with a nonlocal energy spectrum. The distribution function in a specified electric field E=E _z +E _r (where E _z ⊥ E _r) is calculated by solving the coordinate-dependent Boltzmann equation in the two-term approximation and by directly integrating the equations of electron motion using the Monte Carlo method. A comparison between the experimental data and the results of simulations carried out for a broad parameter range shows that, in the case of a highly nonlocal electron energy spectrum, the two-term approximation makes it possible to calculate the electron distribution function with a fairly good accuracy, in which case, however, in imposing the boundary conditions, the electron losses at the plasma surface should be treated in the kinetic approximation. It is shown that using the reflection coefficient of the plasma surface for electrons instead of the loss cone in space makes it possible to accurately calculate the electron energy distribution function over the entire parameter range under consideration, including the transient region in which the electron-energy relaxation length is comparable to the characteristic plasma dimension. __________ Translated from Fizika Plazmy, Vol. 26, No. 11, 2000, pp. 1038–1045. Original Russian Text Copyright ? 2000 by Ivanov, Klopovskii, Lopaev, Rakhimov, Rakhimova.     

川西米亚罗亚高山暗针叶林岷江冷杉和糙皮桦空间格局及其关联性分析

基于2019年9月完成的川西米亚罗亚高山暗针叶林9.6 hm~2动态样地的调查数据,分析了主要优势种岷江冷杉(Abies fargesii var.faxoniana)与糙皮桦(Betula utilis)的径级结构,并运用O-ring统计中的成对相关函数g(r)和g₁₂(r),研究了两个优势种的空间格局及其种内、种间的关联性。结果表明：岷江冷杉与糙皮桦径级分布连续,均呈倒“J”型。岷江冷杉与糙皮桦的不同径级个体主要呈现由聚集分布向随机分布发展的趋势。岷江冷杉的小树对幼树、中树对幼树、中树对小树以及大树对中树的种内相关性在所有空间尺度上均为显著正相关(P<0.05),而相同径级糙皮桦的种内相关性则表现为由显著正相关(P<0.05)逐渐向无显著相关(P>0.05)变化。随着空间尺度的增大,岷江冷杉的大树对幼树、大树和小树由无显著相关(P>0.05)逐渐向显著正相关(P<0.05)变化,糙皮桦的大树对幼树由显著负相关(P<0.05)逐渐向无显著相关(P>0.05)变化。岷江冷杉大树对糙皮桦所有径级个体的种间相关性主要呈现由为显...     

The time sequence of the relation between mean crowding and mean density with some population processes

Summary The theories of the stochastic processes are applied to construct mathematical models for describing the processes of population change as an ever changing the distribution of individuals in a space. These models consist of two mathematical expressions which are named the spatial distribution probability function (Q _n (t)) and the transition probability function (P _i,n (t)), respectively. The former gives the spatial distribution at any future time. Given an actual spatial distribution at any time, the latter function converts it to the spatial distribution at any future time. According to these models, we discussed the time sequence of the mean crowding-mean density relation (Iwao andKuno, 1971) in some population processes such as mortality, birth, immigration, growth, and their combined processes.     

Spatial patterns and interspecific associations among trees at different stand development stages in the natural secondary forests on the Loess Plateau,China

Quercus wutaishansea populations on the Loess Plateau are currently becoming more dominant in natural secondary forests, whereas Pinus tabulaeformis is declining. In the present paper, the diameter class (instead of age) was used to classify the different growth stages as juvenile, subadult, or adult, and the univariate function g(r) was used to analyze the dynamic changes in spatial patterns and interspecific associations in three 1‐ha tree permanent plots on the Loess Plateau, NW China. Our results suggested that the niche breadth changed with the development stage. The diameter distribution curve was consistent with the inverted “J” type, indicating that natural regeneration was common in all three plots. There was a close relationship between the spatial pattern and scale, which showed significant aggregation at small distances, and became more random as distance increased, but in the Pinus + Quercus mixed forests, the whole species were aggregated at distances up to 50 m. The degree of spatial clumping decreased from juvenile to subadult and from subadult to adult. The spatial pattern also differed at different growth stages, likely due to strong intraspecific competition. Associations among different growth stages were positively correlated at small scales. Our study is important to the understanding of the development of the Q. wutaishansea forests; thus, the spatial dynamic change features should be received greater attention when planning forest management and developing restoration strategies on the Loess Plateau.     

Dosimetric parameters of the new design 103Pd brachytherapy source based on Monte Carlo study

In this study version 5 of the MCNP photon transport simulation was used to calculate the dosimetric parameters for new palladium brachytherapy source design following AAPM Task Group No. 43U1 report. The internal source components include four resin beads of 0.6 mm diameters with ¹⁰³Pd uniformly absorbed inside and one cylindrical copper marker with 1.5 mm length. The resin beads and marker are then encapsulated within 0.8 mm in diameter and 4.5 mm long cylindrical capsule of titanium. The dose rate constant, Λ, line and point-source radial dose function, g_L(r) and g_P(r), and the anisotropy function, F(r,θ) of the IR01-¹⁰³Pd seed have been calculated at distances from 0.25 to 5 cm. All the results are in good agreement with previously published thermoluminescence-dosimeter measured values [3] for the source. The dosimetric parameters calculated in this work showed that in dosimetry point of view, the IR01-¹⁰³Pd seed is suitable for use in brachytherapy of prostate cancer.     

Extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor

The extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor were studied. The spatial distribution of the transmembrane potential was obtained by integrating the system of partial differential equations characterizing the electric processes in the active myelinated nerve fiber. The spatial distribution of the extracellular potentials at various radial distances in the volume conductor were calculated using the line source model. Up to a certain radial distance (500 m) the discontinuity of the action potential propagation is reflected in the extracellular potentials, while further in the volume conductor the potentials are smooth. The effect of the fiber diameter and the internodal distance on the volume conductor potentials as well as the changes in the magnitude of the extracellular potential (in the time domain) between two adjacent nodes at various radial distances were studied. The radial decline of the peak-to-peak amplitude of the extracellular potential depends on the radial coordinater of the field point and increases with the increase ofr.     

江西武夷山珍稀濒危植物南方铁杉种群动态与空间分布

明晰江西武夷山国家级自然保护区内180年生的珍稀濒危植物南方铁杉(Tsuga chinensis var.tchekiangensis)的种群特征,并提出针对性的保护策略,对南方铁杉种群的就地保护具有现实意义。通过分析保护区内6.4 hm~2动态监测固定样地的南方铁杉种群数据,编制了静态生命表,绘制了存活曲线、死亡率和消失率曲线、生存函数曲线,采用了时间序列模型对种群数量特征进行未来预测;同时,运用点格局分析Ripley′s K函数中的成对相关函数g(r)判断不同生长阶段的南方铁杉种群在不同尺度下的空间分布格局。结果表明：(1)南方铁杉种群的年龄结构呈“金字塔”型,属于衰退型种群;各龄级间的数量变化动态关系显示该种群在当前阶段呈增长型,但是种群的天然更新能力较差;(2)南方铁杉种群的存活曲线表现为Deevey-I型,种群个体在进入生理死亡阶段后产生一定的波动;(3)南方铁杉种群的生存率随龄级增加而逐渐下降,累积死亡率逐渐递增;死亡密度整体偏低,在第1—2龄级较高,总体波动幅度较小;危险率曲线总体呈现上升的趋势;(4)在经过不同龄级的时间后,南方铁杉幼龄树数量降低,中龄树和老龄树数量持平...     

Carbon use efficiency depends on growth respiration, maintenance respiration, and relative growth rate. A case study with lettuce

Carbon use efficiency (C_UE, the ratio between the amount of carbon incorporated into dry matter to the amount of carbon fixed in gross photosynthesis) is an important parameter in estimating growth rate from photosynthesis data or models. It previously has been found to be relatively constant among species and under different environmental conditions. Here it is shown that C_UE can be expressed as a function of the relative growth rate (r_GR) and the growth (g_r) and maintenance respiration coefficients (m_r): 1/C_UE = 1 + g_r + m_r/r_GR. Net daily carbon gain (C_dg), r_GR, and C_UE were estimated from whole‐plant gas exchange measurements on lettuce (Lactuca sativa L.) ranging from 24 to 66 d old. Carbon use efficiency decreased from 0.6 to 0.2 with increasing dry mass, but there was no correlation between C_UE and C_dg. The decrease in C_UE with increasing dry mass was correlated with a simultaneous decrease in r_GR. From the above equation, g_r and m_r were estimated to be 0.48 mol mol^?1 and 0.039 g glucose g^–1 dry matter d^?1, respectively. Based on the g_r estimate, the theoretical upper limit for C_UE of these plants was 0.68. The importance of maintenance respiration in the carbon balance of the plants increased with increasing plant size. Maintenance accounted for 25% of total respiration in small plants and 90% in large plants.     

大兴安岭林区南、北部天然樟子松生长对气候变化的响应差异

利用树木年代学方法,建立大兴安岭林区南、北部樟子松(Pinus sylvestris var.mongolica)年轮宽度年表,探讨樟子松径向生长对气候变化的响应差异。结果表明,南部(阿尔山、海拉尔)树轮宽度主要与当年4—9月的平均标准化降水蒸散指数SPEI(Standardized Precipitation Evapotranspiration Index)极显著正相关(r=0.639,P0.01),而北部(漠河、塔河)树轮宽度主要与同时期的平均最低温极显著正相关(r=0.488,P0.01)。说明南部樟子松径向生长主要受当年4—9月的水分限制,北部主要受同期平均最低温调控。两个地区树木生长对降水的响应一致,对当年4—9月(6月除外)的温度响应相反。近几十年来随着温度显著升高(P0.01),南部树木生长对4—9月平均最高温的负响应不断增强,而北部树木对同时段平均最低温的正响应更加明显。同时,南部樟子松生长量快速下降(r=0.612,P0.001),而北部生长量显著增加(r=0.474,P0.001)。研究发现,高温加剧干旱胁迫是南部樟子松生长量下降的主要原因,而北部樟子松生长量增加是受到4—9月平均最低温和降水量的相互作用。如果持续变暖,未来樟子松分布区可能北移。     

Lumbricus terrestris hemoglobin: A comparison of small-angle X-ray scattering and cryoelectron microscopy data

The quaternary structure of Lumbricus terrestris hemoglobin was investigated by small-angle x-ray scattering (SAXS). Based on the SAXS data from several independent experiments, a three-dimensional (3D) consensus model was established to simulate the solution structure of this complex protein at low resolution (about 3 nm) and to yield the particle dimensions. The model is built up from a large number of small spheres of different weights, a result of the two-step procedure used to calculate the SAXS model. It accounts for the arrangement of 12 subunits in a hexagonal bilayer structure and for an additional central unit of cylinder-like shape. This model provides an excellent fit of the experimental scattering curve of the protein up to h = 1 nm⁻¹ and a nearly perfect fit of the experimental distance distribution function p(r) in the whole range. Scattering curves and p(r) functions were also calculated for low-resolution models based on 3D reconstructions obtained by cryoelectron microscopy (EM). The calculated functions of these models also provide a very good fit of the experimental scattering curve (even at h > 1 nm⁻¹) and p(r) function, if hydration is taken into account and the original model coordinates are slightly rescaled. The comparison of models reveals that both the SAXS-based and the EM-based model lead to a similar simulation of the protein structure and to similar particle dimensions. The essential differences between the models concern the hexagonal bilayer arrangement (eclipsed in the SAXS model, one layer slightly rotated in the EM model), and the mass distribution, mainly on the surface and in the central part of the protein complex. © John Wiley & Sons, Inc. Biopoly 45: 289–298, 1998     

Hierarchical Classification I: Single-Linkage Method

This is the first part of a survey of hierarchical clustering algorithms using joining methods: the Single-Linkage algorithm. Complete-Linkage and general algorithms defined by d(A_i, B) = = α,d(A_i, A_r)±α_sd(A_i, A_s)±βd(A_r, A_s) will be discussed in two subsequent papers.