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.     

LabKey Server: An open source platform for scientific data integration, analysis and collaboration

Background

This paper is devoted to distance measures for leaf-labelled trees on free leafset. A leaf-labelled tree is a data structure which is a special type of a tree where only leaves (terminal) nodes are labelled. This data structure is used in bioinformatics for modelling of evolution history of genes and species and also in linguistics for modelling of languages evolution history. Many domain specific problems occur and need to be solved with help of tree postprocessing techniques such as distance measures.

Results

Here we introduce the tree edit distance designed for leaf labelled trees on free leafset, which occurs to be a metric. It is presented together with tree edit consensus tree notion. We provide statistical evaluation of provided measure with respect to R-F, MAST and frequent subsplit based dissimilarity measures as the reference measures.

Conclusions

The tree edit distance was proven to be a metric and has the advantage of using different costs for contraction and pruning, therefore their properties can be tuned depending on the needs of the user. Two of the presented methods carry the most interesting properties. E(3,1) is very discriminative (having a wide range of values) and has a very regular distance distribution which is similar to a normal distribution in its shape and is good both for similar and non-similar trees. NFC(2,1) on the other hand is proportional or nearly proportional to the number of mutation operations used, irrespective of their type.     

Spatial pattern,regeneration and growth rates of Brachystegia spiciformis and Julbernardia globiflora

Past work on tree-to-tree interactions in semi-arid savannas, through the use of nearest neighbour analysis, has shown both a regular dispersion pattern and a positive correlation between the size of a tree and the distance to its nearest neighbour. From these results, the importance of competition has been inferred. In the present study, tree-to-tree interactions in a mesic savanna woodland at Marondera, Zimbabwe, dominated by relatively small-sized individuals of Brachystegia spiciformis and Julbernardia globiflora, were examined. Results show that the regular dispersion pattern is uncommon; that there are few significant positive correlations between size of individual and distance to nearest neighbour; and that growth rate is not consistently correlated with size and distance of nearest neighbour. Results of a study of regeneration relative to canopy cover suggest a possible mechanism for these findings: unlike semi-arid savannas, young plants often grow in under-canopy environments so that early spacing of young trees does not occur. Significant positive correlations between the size of a tree and the distance to its nearest neighbour were found in a stand of larger, presumably older, trees, suggesting that such a relationship only develops in mesic miombo woodland through a thinning process as the trees mature. Familial clumping, which is common in the study area, may mask spatial patterns.Abbreviations RBAI Relative basal area increment     

A metric for phylogenetic trees based on matching

Comparing two or more phylogenetic trees is a fundamental task in computational biology. The simplest outcome of such a comparison is a pairwise measure of similarity, dissimilarity, or distance. A large number of such measures have been proposed, but so far all suffer from problems varying from computational cost to lack of robustness; many can be shown to behave unexpectedly under certain plausible inputs. For instance, the widely used Robinson-Foulds distance is poorly distributed and thus affords little discrimination, while also lacking robustness in the face of very small changes--reattaching a single leaf elsewhere in a tree of any size can instantly maximize the distance. In this paper, we introduce a new pairwise distance measure, based on matching, for phylogenetic trees. We prove that our measure induces a metric on the space of trees, show how to compute it in low polynomial time, verify through statistical testing that it is robust, and finally note that it does not exhibit unexpected behavior under the same inputs that cause problems with other measures. We also illustrate its usefulness in clustering trees, demonstrating significant improvements in the quality of hierarchical clustering as compared to the same collections of trees clustered using the Robinson-Foulds distance.     

从空间分布特征认识珍稀植物领春木的种群动态

领春木(Euptelea pleiosperrnum)系第三纪孑遗植物和东亚特有种,目前已被列为国家Ⅲ级重点保护植物.基于空间定位数据以最近邻体距离统计研究了神农架地区领春木的空间分布特征,比较幼苗(DBH≤2.5cm)、幼树(2.5～7.5cm)和成树(＞7.5cm)各径级(代表各生活史阶段)形成的时间序列上的空间格局差异,进而探讨空间格局与立苗、补员、种内竞争等种群动态过程的相互关系.结果显示,在邻域尺度上,领春木的空间格局呈聚集态;幼苗(或幼树)的大小与其距离最近幼树(或成树)的远近没有相关性,幼树(或成树)周围一定距离以内出现同等大小个体的概率约等于幼苗(或幼树)出现的概率,且幼树与最近幼苗(或成树与最近幼树)的平均距离与幼树之间(或成树之间)的平均最近邻体距离没有显著差异;任意个体的大小、任意个体与相应最近邻体的大小之和与相应的最近邻体距离均为显著的正相关关系,但幼树间的最近邻体距离并不大于幼苗随机死亡产生的最近邻体距离,成树间最近邻体距离也不大于幼苗+幼树随机死亡产生的最近邻体距离.这些结果表明,领春木的聚集分布可能与种子散布、生境异质性对立苗格局的作用有关;已定植的大个体可能不限制其邻域内小个体的布局与生长,但是长期的补员过程与邻体间的相互作用不无关系;邻体间存在一定程度的竞争作用,但是竞争强度并未充分激化至发生距离依赖的死亡.     

湖北九宫山成熟常绿落叶阔叶混交林3种优势种的邻域效应研究

以最近邻株距离统计研究了湖北九宫山成熟常绿落叶阔叶混交林3种优势种青冈栎(Cyclobalanopsis glauca)、甜槠(Castanopsis eyrei)和短柄枹栎(Quercus serrata var.brevipetiolata)的邻域效应,进而探讨了局域尺度上的竞争/帮促关系与物种共存格局.结果显示,青冈栎、甜槠和短柄枹栎的最近邻株距离不存在下限;青冈栎的胸径大小与其种内最近邻株距离存在正相关(p=0.029),甜槠的胸径大小与种内、种间最近邻株距离均无相关性(p≥0.360),而短柄枹栎的胸径大小与种间最近邻株距离为负相关(p=0.040);3树种中任意一个的种内与种间最近邻株距离都没有显著差异(p≥0.122).这些结果表明,九宫山成熟常绿落叶阔叶混交林内邻域尺度上的竞争排斥并未充分激化,但是青冈栎的种内竞争仍然在起作用,而甜槠的竞争效应不明显,短柄枹栎则依赖种间帮促甚于相互竞争.同种和异种之间的排斥效果没有差异表明局域尺度的物种共存格局可能出于随机过程而非负密度制约过程.     

Seeds and seedlings of oaks suffer from mammals and molluscs close to phylogenetically isolated,old adults

Background and AimsMammals and molluscs (MaM) are abundant herbivores of tree seeds and seedlings, but how the trees and their environment affect MaM herbivory has been little studied. MaM tend to move much larger distances during the feeding stage than the more frequently studied insect herbivores. We hypothesize that MaM (1) select and stay within the patches that promise to be relatively the richest in seeds and seedlings, i.e. patches around adult trees that are old and within a distantly related, less productive neighborhood; and (2) try to remain sheltered from predators while foraging, i.e. mammals remain close to adult trees or to cover by herbs while foraging, and might force their mollusc prey to show the opposite distribution.MethodsWe exposed oak acorns and seedlings in a temperate forest along transects from adult conspecifics in different neighbourhoods. We followed acorn removal and leaf herbivory. We used exclusion experiments to separate acorn removal by ungulates vs. rodents and leaf herbivory by insects vs. molluscs. We measured the size of the closest conspecific adult tree, its phylogenetic isolation from the neighbourhood and the herbaceous ground cover.Key ResultsConsistent with our hypothesis, rodents removed seeds around adult trees surrounded by phylogenetically distant trees and by a dense herb cover. Molluscs grazed seedlings surrounding large conspecific adults and where herb cover is scarce. Contrary to our hypothesis, the impact of MaM did not change from 1 to 5 m distance from adult trees.ConclusionsWe suggest that foraging decisions of MaM repulse seedlings from old adults, and mediate the negative effects of herbaceous vegetation on tree recruitment. Also, an increase in mammalian seed predation might prevent trees from establishing in the niches of phylogenetically distantly related species, contrary to what is known from insect enemies.     

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.     

\sqrt 2 Rule for Controlling the Tree Pattern in Forest Cut

A forest’s productivity can be optimized by the application of rules derived from monopolized circles. A monopolized circle is defined as a circle whose center is a tree and whose radius is half of the distance between the tree itself and its nearest neighbor. Three characteristics of monopolized circle are proved. (1) Monopolized circles do not overlay each other, the nearest relationship being tangent. (2) “Full uniform pattern” means that the grid of trees (a×b=N) covers the whole plot, so that the distance between each tree in a row is the same as the row spacing. The total monopolized circle area with a full uniform pattern is independent on the number of trees and $\frac{\pi }{4}$ times the plot area. (3) If a tree is removed, the area of some trees’ monopolized circle will increase without decreasing the monopolized circles of the other trees. According to the above three characteristics, “uniform index” is defined as the total area of monopolized circles in a plot divided by the total area of the monopolized circles, arranged in a uniform pattern in the same shaped plot. According to the definition of monopolized circle, the distribution of uniform index $(L) = \frac{{\chi ^2 (2n)}}{{2\pi n}}$ for a random pattern and $E(L) = \frac{1}{\pi }$ the variance of L is $D(L) = \frac{1}{{n\pi ^2 }}$ . It is evident that E(L) is independent on N and the plot area; hence, L is a relative index. L can be used to compare the uniformity among plots with different areas and the numbers of trees. In a random pattern, where L is equivalent to the tree density of the plot in which the number of trees is 1 and the area is π, the influence of tree number and plot area to L is eliminated. When n→∞, D(L)→0 and $L \to \frac{1}{\pi } = 0.318$ it indicates that the greater the number of tree is in the plots, the smaller the difference between the uniform indices will be. There are three types of patterns for describing tree distribution (aggregated, random, and uniform patterns). Since the distribution of L in the random pattern is accurately derived, L can be used to test the pattern types. The research on Moarshan showed that the whole plot has an aggregated pattern; the first, third, and sixth parts have an aggregated pattern; and the second, fourth, and fifth parts have a random pattern. None of the uniform indices is more than 0.318 (1/∏), which indicates that uniform patterns are rare in natural forests. The rules of uniform index can be applied to forest thinning. If you want to increase the value of uniform index, you must increase the total area of monopolized circles, which can be done by removing select trees. “Increasing area trees” are the removed trees and can increase the value of the uniform index. A tree is an increasing area tree if the distance between the tree and its second nearest neighbor is $\sqrt 2 $ times longer than that between the tree itself and its first nearest neighbor, which is called the $\sqrt 2 $ rule. It was very interesting to find that when six plots were randomly separated from the original plot, the proportion of increasing area trees in each plot was always about 0.5 without exception. In random pattern, the expected proportion of increasing area trees is about 0.35–0.44, which is different from the sampling value of 0.5. The reason is very difficult to explain, and further study is needed. Two criteria can be used to identify which trees should be removed to increase the uniform index during forest thinning. Those trees should be (1) trees whose monopolized circle areas are on the small side and (2) increasing area trees, which are found via the $\sqrt 2 $ rule.     

湖北九宫山成熟常绿落叶阔叶混交林 3种优势种的邻域效应研究

以最近邻株距离统计研究了湖北九宫山成熟常绿落叶阔叶混交林3种优势种青冈栎(Cyclobalanopsis glauca)、甜槠(Castanopsis eyrei)和短柄枹栎(Quercus serrata var.brevipetiolata)的邻域效应,进而探讨了局域尺度上的竞争/帮促关系与物种共存格局。结果显示,青冈栎、甜槠和短柄枹栎的最近邻株距离不存在下限;青冈栎的胸径大小与其种内最近邻株距离存在正相关(p= 0.029),甜槠的胸径大小与种内、种间最近邻株距离均无相关性(p≥ 0.360),而短柄枹栎的胸径大小与种间最近邻株距离为负相关(p= 0.040);3树种中任意一个的种内与种间最近邻株距离都没有显著差异(p≥ 0.122)。这些结果表明,九宫山成熟常绿落叶阔叶混交林内邻域尺度上的竞争排斥并未充分激化,但是青冈栎的种内竞争仍然在起作用,而甜槠的竞争效应不明显,短柄枹栎则依赖种间帮促甚于相互竞争。同种和异种之间的排斥效果没有差异表明局域尺度的物种共存格局可能出于随机过程而非负密度制约过程。     

Social Aggregation in Pea Aphids: Experiment and Random Walk Modeling

From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid''s nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.     

基于相邻木排列关系的混交度研究

混交度是反映森林群落中树种相互隔离状况的一个重要指标,目前已提出多种混交度指数.Mg考虑了对象木与最近相邻木的树种异同,Mv和Ms进一步考虑了最近相邻木(空间结构单元)树种数,但仍不能准确描述树种隔离程度.基于相邻木排列关系的混交度Mp,利用“1+4”结构的17个不同空间结构单元和天目山常绿阔叶林数据对Mg、Mv、Ms和Mp4个混交度进行了比较分析.结果表明:Mp的区分能力最强,Mv和Ms次之,Mg最差.Mp最适用于分析混交结构复杂的林分.在天目山常绿阔叶林分析中,混交度水平为中度,4个最近邻体中有2个相同种顺序排列的空间结构单元个数明显多于交错排列的个数.基于相邻木排列关系的混交度Mp能准确区分树种隔离程度,提高了混交度的区分度,可反映森林实际混交状况.     

Severe limitations of the FEve metric of functional evenness and some alternative metrics

The metric of functional evenness FEve is an example of how approaches to conceptualizing and measuring functional variability may go astray. This index has several critical conceptual and practical drawbacks:

1. Different values of the FEve index for the same community can be obtained if the species have unequal species abundances; this result is highly likely if most of the traits are categorical.
2. Very minor differences in even one pairwise distance can result in very different values of FEve.
3. FEve uses only a fraction of the information contained in the matrix of species distances. Counterintuitively, this can cause very similar FEve scores for communities with substantially different patterns of species dispersal in trait space.
4. FEve is a valid metric only if all species have exactly the same abundances. However, the meaning of FEve in such an instance is unclear as the purpose of the metric is to measure the variability of abundances in trait space.

We recommend not using the FEve metric in studies of functional variability. Given the wide usage of FEve index over the last decade, the validity of the conclusions based on those estimates is in question. Instead, we suggest three alternative metrics that combine variability in species distances in trait space with abundance in various ways. More broadly, we recommend that researchers think about which community properties (e.g., trait distances of a focus species to the nearest neighbor or all other species, variability of pairwise interactions between species) they want to measure and pick from among the appropriate metrics.     

Efficient mitigation of founder effects during the establishment of a leading-edge oak population

Numerous plant species are shifting their range polewards in response to ongoing climate change. Range shifts typically involve the repeated establishment and growth of leading-edge populations well ahead of the main species range. How these populations recover from founder events and associated diversity loss remains poorly understood. To help fill this gap, we exhaustively investigated a newly established population of holm oak (Quercus ilex) growing more than 30 km ahead of the nearest larger stands. Pedigree reconstructions showed that plants belong to two non-overlapping generations and that the whole population originates from only two founder trees. The four first-generation trees that have reached maturity showed disparate mating patterns despite being full-sibs. Long-distance pollen immigration was notable despite the strong isolation of the stand: 6 per cent gene flow events in acorns collected on the trees (n = 255), and as much as 27 per cent among their established offspring (n = 33). Our results show that isolated leading-edge populations of wind-pollinated forest trees can rapidly restore their genetic diversity through the interacting effects of efficient long-distance pollen flow and purging of inbred individuals during recruitment. They imply that range expansions of these species are primarily constrained by initial propagule arrival rather than by subsequent gene flow.     

Tree dispersion in oak-dominated forests along an environmental gradient

Summary Spatial pattern was analyzed in seventeen stands of oak-dominated forest to address the hypothesis that species tended to be aggregated under favorable conditions and widely spaced in xeric, nutrient poor conditions. Trees were sampled at 80–100 points in each stand with the distance-to-nearest neighbor method. Soil samples were collected in each stand for analysis of total nitrogen, total phosphorus, total potassium, soil pH, soil texture, and soil organic matter. Growing season precipitation was also recorded from climate stations near each stand. Quercus stellata (Wang.) dominated 10 stands, Q. marilandica (Muenchh.) dominated three stands and these species were codominant in four stands. Principal components analysis identified a soil texture/fertility gradient across the study area. Quercus stellata and all species combined were aggregated in most stands, whereas Q. marilandica was mostly randomly distributed within a stand. Small trees of all species combined tended to be aggregated and large trees were randomly dispersed in all but two stands, suggesting competition. Mean distance between large-large pairs was always greater than mean distance between small-small pairs in all stands, but this difference was only significant in one stand. Correlations between nearest neighbor distance and combined size of nearest neighbors were significant and positive in 12 of 17 stands. In all cases, however, slopes were shallow suggesting that competition is weak in these communities and has a limited effect on spacing of neighboring trees. Contrary to our hypothesis, trees were more aggregated on coarse-textured soils with low organic matter content. For all species combined, degree of aggregation was unrelated to growing season precipitation. Aggregation appears to be common in these forests because environmental stress in many stands reduces growth rates. Trees have not yet reached a size at which competition or other interactions can greatly increase interplant distances and reduce the degree of aggregation. A simple graphical model is developed to describe the relationship between patterns, stress and competition in plant communities.     

Spatial Distribution and Exploitation of Trees Gouged by Common Marmosets (Callithrix jacchus)

Resource distribution shapes many aspects of primate behavioral ecology. Though the spatial patterning of fruits, leaves, and insects has been explored among primate foods, comparatively less is known about exudate distributions. Tree exudates are a renewable resource, provide long-term evidence of exploitation, and may be selectively exploited to manipulate spatial distribution. We assessed the spatial patterning of trees gouged by common marmosets (Callithrix jacchus) to determine if they exhibit a uniform, random, or clumped distribution. We also asked whether marmosets selectively gouge trees in home range centers, which may afford them exclusive access to exudates. We explored whether spatial or physical characteristics of trees predict how intensely gouged trees were exploited. The mean nearest neighbor distance of gouged trees was significantly closer than expected for a random distribution and Ripley’s K-function showed that gouged trees were clumped across all spatial scales in our study area. Clumping may enable marmosets to reduce day and home ranges and facilitate repeated gouging of trees. Gouged trees were not closer to marmosets’ home range centers than peripheries, nor were centrally located trees more intensely gouged. Increased gouging intensity was associated with larger tree circumferences, although this effect was primarily driven by interspecific differences in circumference. Although marmosets may benefit from exploiting clumped exudates, they do not concentrate gouging in areas where they are more likely to gain exclusive access. Species-specific tree characteristics such as exudate quality and/or bark properties may play a larger role in determining gouging patterns than intergroup feeding competition.     

Consistency of Topological Moves Based on the Balanced Minimum Evolution Principle of Phylogenetic Inference

Many phylogenetic algorithms search the space of possible trees using topological rearrangements and some optimality criterion. FastME is such an approach that uses the {em balanced minimum evolution (BME)} principle, which computer studies have demonstrated to have high accuracy. FastME includes two variants: {em balanced subtree prune and regraft (BSPR)} and {em balanced nearest neighbor interchange (BNNI)}. These algorithms take as input a distance matrix and a putative phylogenetic tree. The tree is modified using SPR or NNI operations, respectively, to reduce the BME length relative to the distance matrix, until a tree with (locally) shortest BME length is found. Following computer simulations, it has been conjectured that BSPR and BNNI are consistent, i.e. for an input distance that is a tree-metric, they converge to the corresponding tree. We prove that the BSPR algorithm is consistent. Moreover, even if the input contains small errors relative to a tree-metric, we show that the BSPR algorithm still returns the corresponding tree. Whether BNNI is consistent remains open.     

Understanding 3D structural complexity of individual Scots pine trees with different management history

Tree functional traits together with processes such as forest regeneration, growth, and mortality affect forest and tree structure. Forest management inherently impacts these processes. Moreover, forest structure, biodiversity, resilience, and carbon uptake can be sustained and enhanced with forest management activities. To assess structural complexity of individual trees, comprehensive and quantitative measures are needed, and they are often lacking for current forest management practices. Here, we utilized 3D information from individual Scots pine (Pinus sylvestris L.) trees obtained with terrestrial laser scanning to, first, assess effects of forest management on structural complexity of individual trees and, second, understand relationship between several tree attributes and structural complexity. We studied structural complexity of individual trees represented by a single scale‐independent metric called “box dimension.” This study aimed at identifying drivers affecting structural complexity of individual Scots pine trees in boreal forest conditions. The results showed that thinning increased structural complexity of individual Scots pine trees. Furthermore, we found a relationship between structural complexity and stem and crown size and shape as well as tree growth. Thus, it can be concluded that forest management affected structural complexity of individual Scots pine trees in managed boreal forests, and stem, crown, and growth attributes were identified as drivers of it.