Quartered neighbor method: A new distance method for density estimation

Quantitative data are essential to an appropriate characterization of vegetation. In the past few years, considerable attention has been paid to vegetation sampling techniques. A number of methods have been developed for plant density estimations that utilize spacing distances instead of fixed-area quadrats. In this paper, we review the main distance methods for estimating density and propose a new distance method denominated the quartered neighbor method. In this method, the sampling point is considered the center, and the area around it is divided into four quadrants. The distance from the closest individual in each quadrant to its closest neighbor in the same quadrant is measured, and the average of them is the distance we need. It is actually an integration of two old distance methods, the nearest neighbor method, and the point-centered quarter method. With our new method and an old distance method (the point-centered quarter method), we calculated the average spacing distances of the Larix principis-rupprechtii population in the larch forests of the Donglingshan Mountain. Comparing the two methods with the quadrat method, we found they were almost the same in accuracy, but the precision of the new one was better. Meanwhile, it is adequate in sampling intensity and adaptable for general use in rapid ecological survey work.     

象限法在热带山地雨林群落学调查中的应用研究

 本研究用象限法对海南岛尖峰岭地区一个山地雨林林分作了群落学调查,并将所得结果与78.5%面积取样比的记数样地法调查结果及实测结果进行比较。56个点的象限法调查所得密度、平均胸高断面积、优势度、组成种数量及组成种重要值序是令人满意的,而所花费时间最多为记数样地法的40%。但对该林分来说,样点数不能依照象限法的设计者Cottam和Curtis的结论来确定,即平均距离调查所需的点数即为群落调查所需的样点数,而要依据平均胸高断面积调查所需的点数来确定。     

亚热带常绿阔叶林调查中三种方法的比较

本文以昆明西山滇青冈为优势的亚热带常绿阔叶林为对象,介绍并比较了三种植被调查方法,即无样地取样法的中点象限法、记数样方法和样地记录法。按样地数目的代表性,采用6线90中点分别与两组3个400m2样地作比较。在各工作小组的人数和熟练程度基本一致条件下,记录完成时间,以对比速度。内业工作量也作了比较。从深入比较中清楚看到,对于亚热带常绿阔叶林的调查,中点象限法并不是一种可取的方法。     

Forest community analysis and the point-centered quarter method

The point-centered-quarter (PCQ) method has been applied in community analysis since the publication of the method nearly 50 years ago. This and other distance methods offer increased sampling efficiency over fixed-area plots (FAP), but have long been known to produce biased density estimates when plant distribution deviates from random spatial patterns. Spatial indices have been developed to quantify the direction of this bias when plant distributions are aggregated or evenly distributed. Its continued use, especially in community analysis, requires additional scrutiny in measurements of community structure. We measured 14 forest stands of varying age, elevation and disturbance regime using FAP and PCQ methods. Density estimates were biased, with the point-centered quarter method lower than fixed-area plot estimates when stems were aggregated and higher when stems were evenly spaced. In general the PCQ method underestimated species richness. The efficiency of the PCQ method makes it popular for ordination studies, although comparison of community structure varied from 18% to 90% similarity between the measurements of species basal area in the same stands using the two different methods. The bias observed in calculations of stem density, species abundance and community similarity indicate that use of the PCQ method should be approached with caution when used in community level analysis.     

Comparison of density and basal area estimation of mountain natural forests based on distance-based sampling methods in Zhejiang,China

ObjectiveThe sustainable development of forest ecology and forest management practices is inseparable from the support of forest surveys. Different sampling methods have an unavoidable impact on the collection of natural community characteristic information. An appropriate method reduces the cost of the investigation to the maximum degree under the premise of ensuring accuracy. Distance-based sampling methods are widely used because of their excellent performance in estimating forest population characteristics. The purpose of this study is to compare and find an efficient sampling method of natural broad-leaved forests in mountainous areas of Zhejiang, China, which is of great significance to large-scale field survey practice in similar areas.MethodOur study used census survey data from fixed monitoring sample plots of natural broad-leaved forest in Wuyanling National Nature Reserve, Zhejiang, China as an example and simulated different distance-based sampling methods, including n-tree distance (NTD), point-centered quarter (PCQ), and T-square (Ts), combined with several estimators to estimate the stand density and basal area. The results were compared with the actual mean values of the 100% survey.ResultWe found that different sampling methods and estimators significantly influenced the results. NTD1 overestimated both the stand density and basal area, while NTD2 performed the best, with the lowest RMSE. Secondary performance was obtained with Ts3, Ts5, and Ts6, with small RMSEs of density and basal area. The RMSEs of the PCQ and Ts sampling methods based on a single distance were all large.ConclusionThe NTD sampling method with the NTD2 estimator is recommended to estimate the stand density and basal area for field investigation of natural forests in the Zhejiang mountainous area.     

Bayes estimators for phylogenetic reconstruction

Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet, most reconstruction methods like maximum likelihood (ML) do not explicitly maximize this accuracy. To address this problem, we propose a Bayesian solution. Given tree samples, we propose finding the tree estimate that is closest on average to the samples. This "median" tree is known as the Bayes estimator (BE). The BE literally maximizes posterior expected accuracy, measured in terms of closeness (distance) to the true tree. We discuss a unified framework of BE trees, focusing especially on tree distances that are expressible as squared euclidean distances. Notable examples include Robinson-Foulds (RF) distance, quartet distance, and squared path difference. Using both simulated and real data, we show that BEs can be estimated in practice by hill-climbing. In our simulation, we find that BEs tend to be closer to the true tree, compared with ML and neighbor joining. In particular, the BE under squared path difference tends to perform well in terms of both path difference and RF distances.     

南亚热带森林种群分布格局取样技术研究

森林群落中植物种群分布格局测定和分析的结果,密切依赖于野外取样的技术手段及资料的可靠性。本文通过鼎湖山自然保护区三个不同森林群落类型的取样,比较了随机样方、相邻格子样方、中心点四分法、最近相邻法和最近个体法在野外操作、数据整理以及种群分布格局测定分析中的效用,对各方法在南亚热带森林群落中进行种群分布格局研究中的适用性予以客观评价。研究表明,同一样地中不同取样方法和测定方法会导致不同结果。随机样方取样数据的测定结果受样方大小影响,而几种无样地方法在种类复杂的群落中,应用受到限制。相邻格子样方适用于各群落类型中种群分布格局的测定与分析。     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance

Spatial point pattern is an important tool for describing the spatial distribution of species in ecology. Negative binomial distribution (NBD) is widely used to model spatial aggregation. In this paper, we derive the probability distribution model of event-to-event nearest neighbor distance (distance from a focal individual to its n-th nearest individual). Compared with the probability distribution model of point-to-event nearest neighbor distance (distance from a randomly distributed sampling point to the n-th nearest individual), the new probability distribution model is more flexible. We propose that spatial aggregation can be detected by fitting this probability distribution model to event-to-event nearest neighbor distances. The performance is evaluated using both simulated and empirical spatial point patterns.     

Properties of the nearest neighbor interchange metric for trees of small size

The crossover or nearest neighbor interchange metric has been proposed for use in numerical taxonomy to obtain a quantitative measure of distance between classifications that are modeled as unrooted binary trees with labeled leaves. This metric seems difficult to compute and its properties are poorly understood. A variant called the closest partition distance measure has also been proposed, but no efficient algorithm for its computation has yet appeared and its relationship to the nearest neighbor interchange metric is incompletely understood. I investigate four conjectures concerning the nearest neighbor interchange and closest partition distance measures and establish their validity for trees with as many as seven labeled vertices. For trees in this size range the two distance measures are identical. If a certain decomposition property holds for the nearest neighbor interchange metric, then the two distance measures are also identical at small distances for trees of any size.     

Kinetochore microtubules in PTK cells.

We have analyzed the fine structure of 10 chromosomal fibers from mitotic spindles of PtK1 cells in metaphase and anaphase, using electron microscopy of serial thin sections and computer image processing to follow the trajectories of the component microtubules (MTs) in three dimensions. Most of the kinetochore MTs ran from their kinetochore to the vicinity of the pole, retaining a clustered arrangement over their entire length. This MT bundle was invaded by large numbers of other MTs that were not associated with kinetochores. The invading MTs frequently came close to the kinetochore MTs, but a two-dimensional analysis of neighbor density failed to identify any characteristic spacing between the two MT classes. Unlike the results from neighbor density analyses of interzone MTs, the distributions of spacings between kinetochore MTs and other spindle MTs revealed no evidence for strong MT-MT interactions. A three-dimensional analysis of distances of closest approach between kinetochore MTs and other spindle MTs has, however, shown that the most common distances of closest approach were 30-50 nm, suggesting a weak interaction between kinetochore MTs and their neighbors. The data support the ideas that kinetochore MTs form a mechanical connection between the kinetochore and the pericentriolar material that defines the pole, but that the mechanical interactions between kinetochore MTs and other spindle MTs are weak.     

Trade-offs between social behaviour and foraging by sheep in heterogeneous pastures

In heterogeneous pastures, groups of sheep may have to alter their social behaviour in order to graze patches of preferred vegetation. In this event, patch size, inter-patch distance and the contrast between patch and background vegetation are likely to affect behaviour. In this experiment, groups of five female Scottish Blackface sheep grazed for 2-h periods in 0.1ha grass plots containing seven 1.5mx1.5m patches of improved vegetation, with inter-patch distances of 1.5, 6 or 11.5m. Background vegetation was of either medium or poor quality. Control plots contained no patches. On average, sheep spent 44% of the time grazing patches, although patches comprised only 1.6% of the total plot area. Inter-patch distance did not affect accumulated time spent grazing patches during the first 30min, but patch residence time and the number of sheep on a patch increased with inter-patch distance. The distribution of nearest neighbour distances was altered when patches were 6 or 11.5m apart, compared to no patches. Accumulated time spent grazing patches and the number of sheep on a patch were greater with poor than medium backgrounds. Sheep visited patches frequently and for short periods and it is suggested that sheep often moved off patches as a result of competition. The results provide evidence that sheep make trade-offs between social and foraging behaviour and demonstrate the importance of interactions between social spacing and the size and spacing of vegetation patches, when sheep forage in heterogeneous pastures.     

How Small is too Small? Camera Trap Survey Areas and Density Estimates for Ocelots in the Bolivian Chaco

Studies on carnivores, which are generally difficult to observe directly because they are elusive and nocturnal, are carried out through indirect methods, e.g. , camera trapping and radiotracking. The first method has been used to estimate population densities of species that can be differentiated as individuals using unique pelage patterns. However, the use of capture–recapture methodology has raised doubts regarding the estimation of the sampling area around the camera traps, which is obtained using maximum distances traveled by individuals photographed at two or more different locations. In this paper, the results from camera traps are compared with a radiotracking study carried out simultaneously with ocelots ( Leopardus pardalis ) to confirm whether maximum distances observed in camera traps coincide with ranging patterns determined from radio telemetry, and in turn whether the sampling areas estimated from camera traps are appropriate for estimating density. Mean maximum distance moved was 2880 m according to camera trap records during a 60-d survey period while, with radiotracking, the maximum distance moved was 3176 m during the same period. The difference is not significant, and the sampling areas estimated with camera traps to assess ocelot density are reliable. However, if the area covered by cameras is reduced to less than three to four times average home range for the target species, then density estimates from camera trapping are exaggerated because of the reduced observed distances and the fact that multiple individuals can overlap in relatively small areas.     

Genetic distance sampling: a novel sampling method for obtaining core collections using genetic distances with an application to cultivated lettuce

This paper introduces a novel sampling method for obtaining core collections, entitled genetic distance sampling. The method incorporates information about distances between individual accessions into a random sampling procedure. A basic feature of the method is that automatically larger samples are obtained if accessions are further apart and smaller samples if accessions are closer together. Genetic distance sampling can be used in conjunction with predefined stratifications of the accessions. Sample sizes are determined automatically; they depend on the distances between accessions within strata. The method is applied to the collection of cultivated lettuce of the Centre for Genetic Resources, the Netherlands. In this paper, genetic distances between accessions are obtained using AFLP marker data. However, genetic distance sampling can be applied using any measure of genetic distance between accessions. Some properties of genetic distance sampling are discussed.     

New combinatorial clustering methods

Sixteen clustering methods are compatible with the general recurrence equation of combinatorial SAHN (sequential, agglomerative, hierarchical and nonoverlapping) classificatory strategies. These are subdivided into two classes: the d-SAHN methods seek for minimal between-cluster distances the h-SAHN strategies for maximal within-cluster homogeneity. The parameters and some basic features of all combinatorial methods are listed to allow comparisons between these two families of clustering procedures. Interest is centred on the h-SAHN techniques; the derivation of updating parameters is presented and the monotonicity properties are examined. Three new strategies are described, a weighted and an unweighted variant of the minimization of the increase of average distance within clusters and a homogeneity-optimizing flexible method. The performance of d- and h-SAHN techniques is compared using field data from the rock grassland communities of the Sashegy Nature Reserve, Budapest, Hungary.Abbreviations CP = Closest pair - RNN = Reciprocal nearest neighbor - SAHN = Sequential, agglomerative, hierarchical and nonoverlapping     

Movement distances and density estimation of small mammals using the spool-and-line technique

Edge effect is an inherent problem when using trapping grids to estimate density of small mammals, resulting in a sampling area larger than the area of the grid. Distances between captures of individuals are used to estimateA(W), the effective sampling area of a trapping grid, but grid size sets a limit for the largest detectable distance. The spool-and-line technique is proposed here as a new method to estimateA(W). Movement distances based on the spool-and-line technique were compared to similar movement distances based on capture-recapture of three species of marsupials of the Atlantic Forest of Brazil. Distances based on the two methods were uncorrelated, and only ln-transformed distances based on the spool-and-line were normally distributed. The maximum distance moved (MaxD) estimated by the spool-and-line was chosen as the more accurate and practical distance to estimate edge effect. Estimates of the effective sampling area and densities for the common opossumDidelphis aurita (Wied-Neuwied, 1826), were compared using MaxD based on spool-and-line (MaxDs p o o l ) , capture-recapture (MaxD_cap), and also the distance between traps (DT). MaxD_spool reflected more accurately density variation between seasons. Movement distances of small mammals based on the spool-and-line technique permit more accurate estimates of density and its dynamics.     

分子系统发育树构建的简易方法

以系统发育树构建的原有距离方法为基础,吸取了NJ法和FM法中的部分理论,提出了以节点引入为手段的新的简易方法,通过该方法构建了分子系统发育树,结果表明这种方法更加快捷,而且所得结果与FM法完全一致。     

用距离取样技术估算森林生境中的梅花鹿密度

作者于 1999年 9、 10月在日本国日光国立公园的一个梅花鹿 (Cervusnippon)高密度区域实施了 16次夜间探照样带距离法取样调查。采用车载探照记数和激光测距仪测距 ,记录了梅花鹿的结群大小和距样带中心样线的垂直距离。应用距离取样技术 (Distancesamplingtechnique ,DST)计算的结果表明 ,梅花鹿的密度为12 5 8头 /km2 (95%CI 10 0 7-157 3 ) ,在两侧 80m宽度的调查样带内梅花鹿的总发现率为 52 5% ;对线样带法的传统动物密度计算方法 (King s ,Hayne s ,Leopold s ,Gates sⅠ ,Gates sⅡ ,Gates sⅢ和Frye s方法 )的结果验证表明 ,这些传统密度计算方法过高估算梅花鹿的密度 ,其结果为距离取样技术 (DST)计算结果的 1 76(Frye′s法 ) -6 10 (Hayne′s法 )倍。因此 ,作者建议在使用线样带法测定动物密度时应尽量避免使用这些传统计算方法 ;不同地区间及同一地区不同季节间应用线样带法调查得到的动物个体记数值之间的比较存在偏差 ,应该使用距离取样技术计算动物的密度     

The notion of minimum distance or why rare species are clumped

Summary The prevalence of statistical clumping in natural populations can sometimes obscure mutual avoidance behavior and the adaptive role of spacing out among population members. The problem is particularly severe in rare species where the inverse square relationship between expected nearest neighbor distance and population density demands mean distances between individuals be excessively large to maintain randomness or overdispersion. Realistically, individuals dispersing from a central nucleus might be expected to establish a minimum distance from neighbors to obtain a substantial gain in fitness but further dispersal would be undesirable due to increasing costs and decreasing gains. The result would be higher clumping at low densities. Data on clumping of rare species in an oak-cynipid gall wasp complex are interpreted in the context of the minimum distance notion, and the influence of parasitism on cynipid host population dispersion is discussed.     

Comparison of distance based density estimates for some arid rangeland vegetation

A method was required for determining the effect of management on extensive populations of trees and shrubs in central Australian rangelands. One useful indicator of change in these populations is the density of individuals, and there are several methods available based on distance measurement for density estimation. This study compared those procedures. Samples were drawn by computer from ground maps of actual plant distributions for Acacia aneura, Cassia nemophila and Atalaya hemiglauca and from a map generated at random. These samples were drawn to examine the properties of the nearest neighbour, point centred quarter, conditioned distance and compound T-square estimates of density. Samples were drawn by two methods: simple random sampling and semisystematic sampling. In general, there was a tendency for all estimators of density to underestimate the true density of naturally occurring populations with the compound T-square method (Byth 1982) being most robust. The compound T-square method was least biased but its variance increased for more aggregated spatial distributions. Estimates of density were not altered by the use of semisystematic sampling, when compared to simple random sampling. The spatial distributions examined in this study have not previously been studied as theoretical models. Acacia aneura and Cassia nemophila showed some aggregation of clusters, while the Atalaya hemiglauca showed a more extreme form of clustering due to its root suckering propagation.