Journal articles: 'Tree distance'

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LYAUDET, LAURENT, PAULIN MELATAGIA YONTA, MAURICE TCHUENTE, and RENÉ NDOUNDAM. "DISTANCE PRESERVING SUBTREES IN MINIMUM AVERAGE DISTANCE SPANNING TREES." Discrete Mathematics, Algorithms and Applications 05, no. 03 (September 2013): 1350010. http://dx.doi.org/10.1142/s1793830913500109.

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Given an undirected graph G = (V, E) with n vertices and a positive length w(e) on each edge e ∈ E, we consider Minimum Average Distance (MAD) spanning trees i.e., trees that minimize the path length summed over all pairs of vertices. One of the first results on this problem is due to Wong who showed in 1980 that a Distance Preserving (DP) spanning tree rooted at the median of G is a 2-approximate solution. On the other hand, Dankelmann has exhibited in 2000 a class of graphs where no MAD spanning tree is distance preserving from a vertex. We establish here a new relation between MAD and DP trees in the particular case where the lengths are integers. We show that in a MAD spanning tree of G, each subtree H′ = (V′, E′) consisting of a vertex [Formula: see text] and the union of branches of [Formula: see text] that are each of size less than or equal to [Formula: see text], where w+ is the maximum edge-length in G, is a distance preserving spanning tree of the subgraph of G induced by V′.

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Adams, Richard H., and Todd A. Castoe. "Probabilistic Species Tree Distances: Implementing the Multispecies Coalescent to Compare Species Trees Within the Same Model-Based Framework Used to Estimate Them." Systematic Biology 69, no. 1 (May 14, 2019): 194–207. http://dx.doi.org/10.1093/sysbio/syz031.

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Abstract Despite the ubiquitous use of statistical models for phylogenomic and population genomic inferences, this model-based rigor is rarely applied to post hoc comparison of trees. In a recent study, Garba et al. derived new methods for measuring the distance between two gene trees computed as the difference in their site pattern probability distributions. Unlike traditional metrics that compare trees solely in terms of geometry, these measures consider gene trees and associated parameters as probabilistic models that can be compared using standard information theoretic approaches. Consequently, probabilistic measures of phylogenetic tree distance can be far more informative than simply comparisons of topology and/or branch lengths alone. However, in their current form, these distance measures are not suitable for the comparison of species tree models in the presence of gene tree heterogeneity. Here, we demonstrate an approach for how the theory of Garba et al. (2018), which is based on gene tree distances, can be extended naturally to the comparison of species tree models. Multispecies coalescent (MSC) models parameterize the discrete probability distribution of gene trees conditioned upon a species tree with a particular topology and set of divergence times (in coalescent units), and thus provide a framework for measuring distances between species tree models in terms of their corresponding gene tree topology probabilities. We describe the computation of probabilistic species tree distances in the context of standard MSC models, which assume complete genetic isolation postspeciation, as well as recent theoretical extensions to the MSC in the form of network-based MSC models that relax this assumption and permit hybridization among taxa. We demonstrate these metrics using simulations and empirical species tree estimates and discuss both the benefits and limitations of these approaches. We make our species tree distance approach available as an R package called pSTDistanceR, for open use by the community.

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Xia, Xuhua. "Imputing missing distances in molecular phylogenetics." PeerJ 6 (July 24, 2018): e5321. http://dx.doi.org/10.7717/peerj.5321.

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Missing data are frequently encountered in molecular phylogenetics, but there has been no accurate distance imputation method available for distance-based phylogenetic reconstruction. The general framework for distance imputation is to explore tree space and distance values to find an optimal combination of output tree and imputed distances. Here I develop a least-square method coupled with multivariate optimization to impute multiple missing distance in a distance matrix or from a set of aligned sequences with missing genes so that some sequences share no homologous sites (whose distances therefore need to be imputed). I show that phylogenetic trees can be inferred from distance matrices with about 10% of distances missing, and the accuracy of the resulting phylogenetic tree is almost as good as the tree from full information. The new method has the advantage over a recently published one in that it does not assume a molecular clock and is more accurate (comparable to maximum likelihood method based on simulated sequences). I have implemented the function in DAMBE software, which is freely available athttp://dambe.bio.uottawa.ca.

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Juan, Justie Su-Tzu, Yi-Ching Chen, Chen-Hui Lin, and Shu-Chuan Chen. "Efficient Approaches to the Mixture Distance Problem." Algorithms 13, no. 12 (November 28, 2020): 314. http://dx.doi.org/10.3390/a13120314.

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The ancestral mixture model, an important model building a hierarchical tree from high dimensional binary sequences, was proposed by Chen and Lindsay in 2006. As a phylogenetic tree (or evolutionary tree), a mixture tree created from ancestral mixture models, involves the inferred evolutionary relationships among various biological species. Moreover, it contains the information of time when the species mutates. The tree comparison metric, an essential issue in bioinformatics, is used to measure the similarity between trees. To our knowledge, however, the approach to the comparison between two mixture trees is still unknown. In this paper, we propose a new metric named the mixture distance metric, to measure the similarity of two mixture trees. It uniquely considers the factor of evolutionary times between trees. If we convert the mixture tree that contains the information of mutation time of each internal node into a weighted tree, the mixture distance metric is very close to the weighted path difference distance metric. Since the converted mixture tree forms a special weighted tree, we were able to design a more efficient algorithm to calculate this new metric. Therefore, we developed two algorithms to compute the mixture distance between two mixture trees. One requires O(n2) and the other requires O(nh1h2) computational time with O(n) preprocessing time, where n denotes the number of leaves in the two mixture trees, and h1 and h2 denote the heights of these two trees.

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Mlinaric, Danijel, Boris Milasinovic, and Vedran Mornar. "Tree Inheritance Distance." IEEE Access 8 (2020): 52489–504. http://dx.doi.org/10.1109/access.2020.2981260.

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Ledermann, Thomas. "Evaluating the performance of semi-distance-independent competition indices in predicting the basal area growth of individual trees." Canadian Journal of Forest Research 40, no. 4 (April 2010): 796–805. http://dx.doi.org/10.1139/x10-026.

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Recent individual-tree growth models use either distance-dependent or distance-independent competition measures to predict tree increment. However, both measures have deficiencies: the latter because the effects of local variation in spacing are not represented, and the former because they cannot be calculated from normal inventory data for lack of spatial information. To overcome these shortcomings, the new class of semi-distance-independent competition indices was proposed. A semi-distance-independent competition index is a distance-independent competition measure that uses only the trees of a single small sample plot that includes the subject tree. Moreover, a semi-distance-independent competition index can be calculated in an analogous way to a distance-dependent competition index by using sample plot size, tree attributes, and intertree distances. However, many semi-distance-independent competition measures are based on simple tree attributes. Therefore, the objective of this study was to analyze if the semi-distance-independent competition indices explain the variation in measurements of tree increment more or less effectively than a set of classical distance-dependent competition indices. The results show that some of the semi-distance-independent competition indices explain at least as much variation in measurements of tree increment as any of the distance-dependent competition indices.

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Dill, Lawrence M., and Robert Houtman. "The influence of distance to refuge on flight initiation distance in the gray squirrel (Sciurus carolinensis)." Canadian Journal of Zoology 67, no. 1 (January 1, 1989): 233–35. http://dx.doi.org/10.1139/z89-033.

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Gray squirrels (Sciurus carolinensis) typically run to the nearest tree to escape from predators they encounter while foraging on the ground. As the risk of capture increases with distance from the refuge tree, squirrels feeding far from trees should have greater flight initiation distances than those feeding closer by. This prediction was confirmed: flight initiation distance in response to a motorized model predator (a cat) increased as distance to refuge increased. This could not be attributed to any effect of distance to refuge on vigilance.

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Khan, Md Nasir Uddin, and Mohammad Kamrul Hasan. "Performance of bitter gourd in association with Karanja (Pongamia pinnata L.) tree." Research in Agriculture Livestock and Fisheries 2, no. 1 (April 27, 2015): 63–73. http://dx.doi.org/10.3329/ralf.v2i1.23030.

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The study was conducted at the Char Kalibari which is situated along the bank of Old Brahmaputra River under Sadar Upazila of Mymensingh district during November 2013 to March 2014 to observe the performance of bitter gourd (Momordica charantia) as arable crop with karanja (Pongamia pinnata L.) trees in an agroforestry system. The experiment was laid out in a Randomized Complete Block Design (RCBD) with three replications having four treatments viz., T0 (open field condition referred as control), T1 (< 50 cm distance from the tree base), T2 (50-100 cm distance from the tree base) and T3 (>100 cm distance from the tree base). The result showed that all the growth parameters and yield of bitter gourd were significantly influenced by the associated tree component at different distances from the karanja tree base. The highest (1.92 tha-1) fresh yield of bitter gourd was obtained in open field condition compare to any other treatments but no significant different was found from the treatment T3 (distance >100 cm from the tree) while the lowest (0.8 tha-1) in < 50 cm distance from the tree base. It was found that on an average 58.33%, 29.17% and 14.58% yield of bitter gourd were decreased in <50 cm, 50-100 cm and >100 cm distances from karanja tree base compare to open field condition. On the other hand, the growth performance of karanja trees i.e. both height and girth increment was better in sole tree condition compare to tree with bitter gourd condition. Therefore, it can be concluded that tree-crop combination i.e. >100 cm distance from the tree base would be possible although there was some yield loss (14.58%) which was less significant compare to alone bitter gourd. Through this combination we can get diversified product. So, we can follow this agroforestry system to improve char based farming system of Bangladesh during the early establishment period of trees.Res. Agric., Livest. Fish.2(1): 63-73, April 2015

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Kim, Jaehee, Noah A. Rosenberg, and Julia A. Palacios. "Distance metrics for ranked evolutionary trees." Proceedings of the National Academy of Sciences 117, no. 46 (November 2, 2020): 28876–86. http://dx.doi.org/10.1073/pnas.1922851117.

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Genealogical tree modeling is essential for estimating evolutionary parameters in population genetics and phylogenetics. Recent mathematical results concerning ranked genealogies without leaf labels unlock opportunities in the analysis of evolutionary trees. In particular, comparisons between ranked genealogies facilitate the study of evolutionary processes of different organisms sampled at multiple time periods. We propose metrics on ranked tree shapes and ranked genealogies for lineages isochronously and heterochronously sampled. Our proposed tree metrics make it possible to conduct statistical analyses of ranked tree shapes and timed ranked tree shapes or ranked genealogies. Such analyses allow us to assess differences in tree distributions, quantify estimation uncertainty, and summarize tree distributions. We show the utility of our metrics via simulations and an application in infectious diseases.

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Jiang, Yueyu, Puoya Tabaghi, and Siavash Mirarab. "Learning Hyperbolic Embedding for Phylogenetic Tree Placement and Updates." Biology 11, no. 9 (August 24, 2022): 1256. http://dx.doi.org/10.3390/biology11091256.

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Phylogenetic placement, used widely in ecological analyses, seeks to add a new species to an existing tree. A deep learning approach was previously proposed to estimate the distance between query and backbone species by building a map from gene sequences to a high-dimensional space that preserves species tree distances. They then use a distance-based placement method to place the queries on that species tree. In this paper, we examine the appropriate geometry for faithfully representing tree distances while embedding gene sequences. Theory predicts that hyperbolic spaces should provide a drastic reduction in distance distortion compared to the conventional Euclidean space. Nevertheless, hyperbolic embedding imposes its own unique challenges related to arithmetic operations, exponentially-growing functions, and limited bit precision, and we address these challenges. Our results confirm that hyperbolic embeddings have substantially lower distance errors than Euclidean space. However, these better-estimated distances do not always lead to better phylogenetic placement. We then show that the deep learning framework can be used not just to place on a backbone tree but to update it to obtain a fully resolved tree. With our hyperbolic embedding framework, species trees can be updated remarkably accurately with only a handful of genes.

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NATH, MILAN, and SOMNATH PAUL. "GRAPH TRANSFORMATION AND DISTANCE SPECTRAL RADIUS." Discrete Mathematics, Algorithms and Applications 05, no. 03 (September 2013): 1350014. http://dx.doi.org/10.1142/s1793830913500146.

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Trees are very common in the theory and applications of combinatorics. In this paper, we consider graphs whose underlying structure is a tree and study the behavior of the distance spectral radius under a graph transformation. As an application, we find the corona tree that maximizes the distance spectral radius among all corona trees with a fixed maximum degree. We also find the graph with minimal (maximal) distance spectral radius among all corona trees. Finally, we determine the graph with minimal distance spectral radius in a special class of corona trees.

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Amenta, Nina, Matthew Godwin, Nicolay Postarnakevich, and Katherine St. John. "Approximating geodesic tree distance." Information Processing Letters 103, no. 2 (July 2007): 61–65. http://dx.doi.org/10.1016/j.ipl.2007.02.008.

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Hansen, Poul, Hans Chr Jacobsen, and J. Vittrup Christensen. "Row Distance and Tree Heights in Apple Trees." Acta Agriculturae Scandinavica, Section B - Soil & Plant Science 43, no. 3 (September 1993): 181–84. http://dx.doi.org/10.1080/09064719309411239.

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Kleinn, Christoph, and Frantiek Vilčko. "Design-unbiased estimation for point-to-tree distance sampling." Canadian Journal of Forest Research 36, no. 6 (June 1, 2006): 1407–14. http://dx.doi.org/10.1139/x06-038.

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Point-to-tree distance sampling designs, sometimes also referred to as k-tree sampling or fixed-count sampling, are practical response design options for field sampling in forest inventories and ecological surveys. While practitioners accept and use several approaches to estimate stem density and other stand attributes, a major concern from a statistical point of view is the lack of a general unbiased estimator for this class of sampling strategies. In this paper we analyse point-to-tree distance sampling in the framework of design-based probabilistic sampling and present an unbiased estimator valid for estimation of any stand attribute. This estimator draws upon the idea of defining an inclusion zone around each tree. A tree is taken as a sample tree if a selected sample point falls into its inclusion zone. The size of the inclusion zone is therefore a measure of the individual tree's inclusion probability when sampling is done with random sample points. Once the inclusion probabilities are known for all sampled trees, the Horwitz-Thompson estimator can be used as an unbiased estimator for any stand variable. In point-to-tree distance sampling, the inclusion zone of a particular tree depends exclusively on the spatial arrangement of the neighbouring trees. Such inclusion zones are determined by k-order Voronoi polygons, where k is the number of trees being sampled per sample point. The approach, however, requires the positions of the k sample trees and a number of surrounding trees to be mapped. Field application is therefore difficult, but a comparison of plot designs by simulation studies in fully mapped stands can now also be done with an unbiased estimator for k-tree sampling.

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Aratsu, Taku, Kouichi Hirata, and Tetsuji Kuboyama. "Approximating Tree Edit Distance through String Edit Distance for Binary Tree Codes." Fundamenta Informaticae 101, no. 3 (2010): 157–71. http://dx.doi.org/10.3233/fi-2010-282.

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Gonçalves, CS, and MA Batalha. "Towards testing the "honeycomb rippling model" in cerrado." Brazilian Journal of Biology 71, no. 2 (May 2011): 401–8. http://dx.doi.org/10.1590/s1519-69842011000300009.

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Savannas are tropical formations in which trees and grasses coexist. According to the "honeycomb rippling model", inter-tree competition leads to an effect of trees growing and dying due to competition, which, at fine spatial scale, would resemble honeycomb rippling. The model predicts that the taller the trees, the higher the inter-tree distances and the evenness of inter-tree distances. The model had been corroborated in arid savannas, in what appears to be caused by uneven distribution of rains, but had not yet been tested in seasonal savannas, such as the cerrado, which could be caused by the irregular occurrence of fire.A basic assumption of the model is that strong inter-tree competition affects growth (estimated by height) and mortality (estimated by inter-tree distances). As a first step towards testing this model in the cerrado, we tested this assumption in a single cerrado patch in southeastern Brazil. We placed 80 quadrats, each one with 25 m², in which we sampled all shrubs and trees. For each individual, we measured its height and the distance to its nearest neighbour - the inter-tree distance. We did not find correlations between tree height and both inter-tree distances and evenness of inter-tree distances, refuting the honeycomb rippling model. Inter-tree distances were spatially autocorrelated, but height was not. According to our results, the basic assumption of the model does not apply to seasonal savannas. If, in arid savannas, rainfall events are rare and unpredictable, in seasonal savannas, the rainy season is well-defined and rainfall is considerable. We found horizontal structuring in the community, which may be due to soil nutrient heterogeneity. The absence of vertical structuring suggests that competition for light among adult trees is not as important as competition for nutrients in the soil. We tested the basic assumption of the model in a single patch and at a single moment. To test the model effectively, we suggest this assumption to be tested in many patches over time.

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DiNardo, Zach, Kiran Tomlinson, Anna Ritz, and Layla Oesper. "Distance measures for tumor evolutionary trees." Bioinformatics 36, no. 7 (November 21, 2019): 2090–97. http://dx.doi.org/10.1093/bioinformatics/btz869.

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Abstract Motivation There has been recent increased interest in using algorithmic methods to infer the evolutionary tree underlying the developmental history of a tumor. Quantitative measures that compare such trees are vital to a number of different applications including benchmarking tree inference methods and evaluating common inheritance patterns across patients. However, few appropriate distance measures exist, and those that do have low resolution for differentiating trees or do not fully account for the complex relationship between tree topology and the inheritance of the mutations labeling that topology. Results Here, we present two novel distance measures, Common Ancestor Set distance (CASet) and Distinctly Inherited Set Comparison distance (DISC), that are specifically designed to account for the subclonal mutation inheritance patterns characteristic of tumor evolutionary trees. We apply CASet and DISC to multiple simulated datasets and two breast cancer datasets and show that our distance measures allow for more nuanced and accurate delineation between tumor evolutionary trees than existing distance measures. Availability and implementation Implementations of CASet and DISC are freely available at: https://bitbucket.org/oesperlab/stereodist. Supplementary information Supplementary data are available at Bioinformatics online.

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Pukkala, Timo, and Jari Miina. "Tree-selection algorithms for optimizing thinning using a distance-dependent growth model." Canadian Journal of Forest Research 28, no. 5 (May 1, 1998): 693–702. http://dx.doi.org/10.1139/x98-038.

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When a distance-dependent yield model is used in growth simulation and optimization, the stand is described by a plot on which the trees are described by species, DBH, height, age, coordinates, and other characteristics. Optimizing a distance-dependent model requires that the trees to be removed in a thinning treatment be specified individually and that a special algorithm be developed for this selection. This algorithm affects the formulation of the optimization problem. In this study, we compared four different problem formulations for optimizing a distance-dependent yield model: (1) Harvest percentages in different diameter classes were utilized together with a tree-selection algorithm proposed earlier; this algorithm removed trees on the basis of competitive status. The algorithm was fixed, i.e., it was not amenable to numerical optimization. (2) Minimum distances between remaining trees were used as decision variables. (3) Minimum distances were used with harvest percentages and the existing tree-selection algorithm. (4) The tree-selection algorithm was made dependent on two parameters, which were optimized together with harvest percentages in different diameter classes. Based on case optimizations in pure and mixed conifer stands, the fourth formulation was considered to be the best one from the standpoint of simplicity of optimization and in terms of the objective function value.

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Kenning, Robert S., Mark J. Ducey, John C. Brissette, and Jeffrey H. Gove. "Field efficiency and bias of snag inventory methods." Canadian Journal of Forest Research 35, no. 12 (December 1, 2005): 2900–2910. http://dx.doi.org/10.1139/x05-207.

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Snags and cavity trees are important components of forests, but can be difficult to inventory precisely and are not always included in inventories because of limited resources. We tested the application of N-tree distance sampling as a time-saving snag sampling method and compared N-tree distance sampling to fixed-area sampling and modified horizontal line sampling in mixed pine-hardwood forests of southern Maine and New Hampshire. We also present a novel modification of N-tree distance sampling that limits the distance from plot center that an observer must search to find tally trees. A field test shows N-tree to be quick, but generally biased and characterized by high variability. Distance-limited N-tree sampling mitigates these problems, but not completely. We give recommendations for operational snag inventory in similar forest types.

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Kalaghatgi, Prabhav, Nico Pfeifer, and Thomas Lengauer. "Family-Joining: A Fast Distance-Based Method for Constructing Generally Labeled Trees." Molecular Biology and Evolution 33, no. 10 (July 19, 2016): 2720–34. http://dx.doi.org/10.1093/molbev/msw123.

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Abstract The widely used model for evolutionary relationships is a bifurcating tree with all taxa/observations placed at the leaves. This is not appropriate if the taxa have been densely sampled across evolutionary time and may be in a direct ancestral relationship, or if there is not enough information to fully resolve all the branching points in the evolutionary tree. In this article, we present a fast distance-based agglomeration method called family-joining (FJ) for constructing so-called generally labeled trees in which taxa may be placed at internal vertices and the tree may contain polytomies. FJ constructs such trees on the basis of pairwise distances and a distance threshold. We tested three methods for threshold selection, FJ-AIC, FJ-BIC, and FJ-CV, which minimize Akaike information criterion, Bayesian information criterion, and cross-validation error, respectively. When compared with related methods on simulated data, FJ-BIC was among the best at reconstructing the correct tree across a wide range of simulation scenarios. FJ-BIC was applied to HIV sequences sampled from individuals involved in a known transmission chain. The FJ-BIC tree was found to be compatible with almost all transmission events. On average, internal branches in the FJ-BIC tree have higher bootstrap support than branches in the leaf-labeled bifurcating tree constructed using RAxML. 36% and 25% of the internal branches in the FJ-BIC tree and RAxML tree, respectively, have bootstrap support greater than 70%. To the best of our knowledge the method presented here is the first attempt at modeling evolutionary relationships using generally labeled trees.

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JIA, Nan, Xiao-dong FU, Yuan HUANG, Xiao-yan LIU, and Zhi-hua DAI. "Workflow distance metric based on tree edit distance." Journal of Computer Applications 32, no. 12 (May 29, 2013): 3529–33. http://dx.doi.org/10.3724/sp.j.1087.2012.03529.

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Akutsu, Tatsuya, Daiji Fukagawa, and Atsuhiro Takasu. "Approximating Tree Edit Distance through String Edit Distance." Algorithmica 57, no. 2 (July 30, 2008): 325–48. http://dx.doi.org/10.1007/s00453-008-9213-z.

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Vololazskiy, Yevgen V. "A Modification of the Frechet Distance for Nonisomorphic Trees." Control Systems and Computers, no. 2-3 (292-293) (July 2021): 20–27. http://dx.doi.org/10.15407/csc.2021.02.020.

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The paper presents a modification of the Frechet distance for nonisomorphic trees. While the classical Frechet distance between nonisomorphic trees is undefined, a new measure called similarity of a tree to a reference tree is given that is defined for a wider class of trees. A polynomial-time algorithm is given to determine whether one tree’s similarity to another is less than a given number.

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Smith, Michael W., William D. Goff, and M. Lenny Wells. "Pecan Orchard Renewal: Influence of Established Trees and Remaining Stumps on Transplant Growth and Crown Gall Infection." HortScience 48, no. 6 (June 2013): 720–23. http://dx.doi.org/10.21273/hortsci.48.6.720.

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The productive life of a pecan [Carya illinoinensis (Wangenh.) K. Koch] orchard frequently spans two or more generations, but eventually orchards require renewal. Weather events damage tree canopies, pests affect tree health and productivity, and new cultivars offer greater yield potential or better nut quality. A popular method of orchard renewal is selective tree removal combined with interplanting new trees. Many old pecan orchards in the southeastern United States are infected with crown gall [Agrobacterium tumefaciens (Smith and Townsend) Conn.], potentially a problem for interplanted trees. Two tree types, nursery-grafted trees and seedling trees that were grafted 3 years after transplanting, were evaluated 6 years after transplanting. Transplanted trees varied in distances from established 80-year-old trees or residual stumps after tree removal. Ten trees near the study site, located 3.6 m from crown gall-infected stumps, were excavated to determine disease incidence. No crown gall was observed on any of the 87 trees in the study or the excavated trees. Trunk diameters of interplanted trees increased as distance from the nearest stump decreased and distance from the nearest established tree increased. Leaf elemental concentrations of the 6-year-old transplants were not related to observed growth differences. Conclusions include 1) stumps promoted rapid transplant growth; 2) crown gall infections of transplanted trees were unlikely even when crown gall symptoms were obvious on adjacent trees and stumps; and 3) transplant growth was suppressed by established trees.

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TANAKA, EIICHI, and KEIKO TANAKA. "THE TREE-TO-TREE EDITING PROBLEM." International Journal of Pattern Recognition and Artificial Intelligence 02, no. 02 (June 1988): 221–40. http://dx.doi.org/10.1142/s0218001488000157.

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This paper describes the computing alogrithms for the tree distance based on the structure preserving mapping. The distance is defined as the minimum sum of the weights of edit operations needed to transform tree Tα to tree Tβ under restriction of the structure preserving mapping. The edit operations allow substituting a vertex of a tree to another, deleting a vertex of a tree and inserting a vertex to a tree. Proposed algorithms determine the distance between Tα and Tβ in time O(NαNβLα) or O(NαNβLβ), and in space O(NαNβ), where Nα, Nβ, Lα and Lβ are the number of vertices of Tα, Tβ, the number of’ leaves of Tα and Tβ, respectively. The time complexity is close to the unapproachable lowest bound O(NαNβ). Improved algorithms are presented. This tree distance can be applied to any problems including pattern recognition, syntactic tree comparison and classification, and tree comparison whose structures are important in structure preserving mapping.

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Shi, Haijin, Lianjun Zhang, and Jianguo Liu. "A new spatial-attribute weighting function for geographically weighted regression." Canadian Journal of Forest Research 36, no. 4 (April 1, 2006): 996–1005. http://dx.doi.org/10.1139/x05-295.

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In recent years, geographically weighted regression (GWR) has become popular for modeling spatial heterogeneity in a regression context. However, the current weighting function used in GWR only considers the geographical distances of trees in a stand, while the attributes (e.g., tree diameter) of the neighboring trees are totally ignored. In this study, we proposed a new weighting function that combines the "geographical space" and "attribute space" between the subject tree and its neighbors, such that (1) neighbors with greater geographical distances from the subject tree are assigned smaller weights, and (2) at a given geographical distance, neighboring trees with sizes that are similar to that of the subject tree are assigned larger weights. The results indicate that the GWR model with the new spatial-attribute weighting function performs better than the one with the spatial weighting function in terms of model residuals and predictions for different spatial patterns of tree locations.

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Blamires, S. J. "Factors influencing the escape response of an arboreal agamid lizard of tropical Australia (Lophognathus temporalis) in an urban environment." Canadian Journal of Zoology 77, no. 12 (December 1, 1999): 1998–2003. http://dx.doi.org/10.1139/z99-166.

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The escape response of the agamid lizard Lophognathus temporalis in an urban population was examined during the dry season. Two measurements of escape response were made: the distance an observer can approach before the lizard flees (approach distance) and the distance the lizard flees to refuge (flight distance). The relationship between approach distance and flight distance was examined, as was the relationship between air temperature and both approach distance and flight distance. The influence of time of day, the lizard's perch (in a tree or on the ground), and year (1996 or 1998) on the escape response was determined. Approach distance and flight distance had no relationship with each other. Air temperature had a positive relationship with approach distance, so variations in temperature between the two years might explain variations in approach distance between them. The lizard's perch had the greatest influence on flight distance. Lizards in trees fled shorter distances, usually to the opposite side of the tree trunk or branch to the observer. Lizards on the ground always fled to the nearest refuge.

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Gamage, Gihan, Nadeeshan Gimhana, Indika Perera, Shanaka Bandara, Thilina Pathirana, Anuradha Wickramarachchi, and Vijini Mallawaarachchi. "Phylogenetic Tree Construction Using K-Mer Forest- Based Distance Calculation." International Journal of Online and Biomedical Engineering (iJOE) 16, no. 07 (June 19, 2020): 4. http://dx.doi.org/10.3991/ijoe.v16i07.13807.

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Phylogenetics is one of the dominant data engineering research disciplines based on biological information. More particularly here, we consider raw DNA sequences and do comparative analysis in order to come up with important conclusions. When representing evolutionary relationships among different organisms in a concise manner, the phylogenetic tree helps significantly. When constructing phylogenetic trees, the elementary step is to calculate the genetic distance among species. Alignment-based sequencing and alignment-free sequencing are the two main distance computation methods that are used to find genetic relatedness of different species. In this paper we propose a novel alignment-free, pairwise, distance calculation method based on k-mers and a state of art machine learning-based phylogenetic tree construction mechanism. With the proposed approach we can convert longer DNA sequences into compendious k-mer forests which gear up the efficiency of comparison. Later we construct the phylogenetic tree based on calculated distances with the help of an algorithm build upon k-medoid clustering, which guaranteed significant efficiency and accuracy compared to traditional phylogenetic tree construction methods.

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Petroni, Filippo, and Maurizio Serva. "Language distance and tree reconstruction." Journal of Statistical Mechanics: Theory and Experiment 2008, no. 08 (August 22, 2008): P08012. http://dx.doi.org/10.1088/1742-5468/2008/08/p08012.

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Mäkinen, Erkki. "Left distance binary tree representations." BIT 27, no. 2 (June 1987): 163–69. http://dx.doi.org/10.1007/bf01934181.

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Edahiro, M. "Equispreading tree in Manhattan distance." Algorithmica 16, no. 3 (September 1996): 316–38. http://dx.doi.org/10.1007/bf01955680.

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Touzet, Hélène. "Tree edit distance with gaps." Information Processing Letters 85, no. 3 (February 2003): 123–29. http://dx.doi.org/10.1016/s0020-0190(02)00369-1.

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Edahiro, M. "Equispreading Tree in Manhattan Distance." Algorithmica 16, no. 3 (March 1, 1996): 316–38. http://dx.doi.org/10.1007/s004539900052.

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Winkler, Peter. "Mean distance in a tree." Discrete Applied Mathematics 27, no. 1-2 (May 1990): 179–85. http://dx.doi.org/10.1016/0166-218x(90)90137-2.

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GIL, MANUEL, CHRISTOPHE DESSIMOZ, and GASTON H. GONNET. "A DIMENSIONLESS FIT MEASURE FOR PHYLOGENETIC DISTANCE TREES." Journal of Bioinformatics and Computational Biology 03, no. 06 (December 2005): 1429–40. http://dx.doi.org/10.1142/s0219720005001636.

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We present a dimensionless fit index for phylogenetic trees that have been constructed from distance matrices. It is designed to measure the quality of the fit of the data to a tree in absolute terms, independent of linear transformations on the distance matrix. The index can be used as an absolute measure to evaluate how well a set of data fits to a tree, or as a relative measure to compare different methods that are expected to produce the same tree. The usefulness of the index is demonstrated in three examples.

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Cholewińska, Olga, Andrzej Keczyński, Barbara Kusińska, and Bogdan Jaroszewicz. "Species Identity of Large Trees Affects the Composition and the Spatial Structure of Adjacent Trees." Forests 12, no. 9 (August 27, 2021): 1162. http://dx.doi.org/10.3390/f12091162.

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Large trees are keystone structures for the functioning and maintenance of the biological diversity of wooded landscapes. Thus, we need a better understanding of large-tree–other-tree interactions and their effects on the diversity and spatial structure of the surrounding trees. We studied these interactions in the core of the Białowieża Primeval Forest—Europe’s best-preserved temperate forest ecosystem, characterized by high abundance of ancient trees. We measured diameter and bark thickness of the monumental trees of Acer platanoides L., Carpinus betulus L., Picea abies L. H. Karst, Quercus robur L., and Tilia cordata Mill., as well as the diameter and distance to the monumental tree of five nearest neighbor trees. The effects of the monumental tree on arrangements of the surrounding trees were studied with the help of linear models. We revealed that the species identity of a large tree had, in the case of C. betulus and T. cordata, a significant impact on the diversity of adjacent tree groupings, their distance to the central tree, and frequency of the neighboring trees. The distance between the neighbor and the large trees increased with the increasing diameter of the central tree. Our findings reinforce the call for the protection of large old trees, regardless of their species and where they grow from the geographical or ecosystem point of view.

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Bose, S. S., M. Nath, and D. Sarma. "Maximal distance spectral radius of trees." Discrete Mathematics, Algorithms and Applications 11, no. 02 (April 2019): 1950025. http://dx.doi.org/10.1142/s1793830919500253.

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Dick, Adam R., John A. Kershaw, and David A. MacLean. "Spatial Tree Mapping Using Photography." Northern Journal of Applied Forestry 27, no. 2 (June 1, 2010): 68–74. http://dx.doi.org/10.1093/njaf/27.2.68.

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Abstract Stem maps describing the spatial location of trees sampled in a forest inventory are used increasingly to model relationships between neighboring trees in distance-dependent growth and yield models, as well as in stand visualization software. Current techniques and equipment available to acquire tree spatial locations prohibit widespread application because they are time-consuming, costly, and prone to measurement error. In this report, we present a technique to derive stem maps from a series of digital photographs processed to form a seamless 360° panorama plot image. Processes are described to derive distance from plot center and azimuth to each plot tree. The technique was tested on 46 field plots (1,398 sample trees) under a range of forest conditions and compared with traditional methods. Average absolute distance error was 0.38 ± 0.44 m, and average absolute azimuth error was 2.3 ± 2.5°. Computed average horizontal accuracy was 0.40 ± 0.42 m, with 85% of measured trees being within 0.5 m of the field-measured tree location.

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Ko, Sang-Ki, Yo-Sub Han, and Kai Salomaa. "Top-down tree edit-distance of regular tree languages." International Journal of Advances in Engineering Sciences and Applied Mathematics 11, no. 1 (July 11, 2018): 2–10. http://dx.doi.org/10.1007/s12572-018-0221-1.

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TANAKA, EIICHI. "A NOTE ON A TREE-TO-TREE EDITING PROBLEM." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 01 (February 1995): 167–72. http://dx.doi.org/10.1142/s0218001495000092.

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In the previous paper on a tree-to-tree editing problem some errors were included. This letter describes the corrected definition of a structure preserving mapping between rooted and ordered trees and a computing method of the tree distance based on the mapping.

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Ge, Guang Zu, Bo Tang, Jian Xiong Zhu, Yin Huang, and Zi Hang Qu. "Development of Decision Support System for Protecting Distance between Power Lines and Trees." Applied Mechanics and Materials 380-384 (August 2013): 3425–28. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.3425.

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Resolving the contradiction between trees and power transmission lines in time is an important work to ensure the safety of transmission line operation. While it is difficult to decide the trees trimmed time during the transmission line operation and maintenance, the development of the management information system for protecting distance between transmission lines and trees, which is used to auxiliary predict the date of pruning, is a way to solve the problem. Collected attribute data of transmission lines and trees, the corresponding database is established. Therefore, Visual Basic 6.0 is adopted to develop the software system. Based on the spatial coordinates of line towers, conductors, and tree crown, the three-dimensional mathematical model is established to calculate the spatial distance between the conductor and tree crown. According to the mathematical model, the trees growth rate of year, month and day, respectively, and the protecting distance standard between conductor and tree crown, the system could calculate the actual spatial distance between conductor and tree crown, and auxiliary predict the pruning date.

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Greene, D. F., and E. A. Johnson. "Long-distance wind dispersal of tree seeds." Canadian Journal of Botany 73, no. 7 (July 1, 1995): 1036–45. http://dx.doi.org/10.1139/b95-113.

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Long-distance seed dispersal figures prominently in most plant conservation biology arguments, yet we possess little more than anecdotes concerning the relationship among deposition (seeds/m2), source strength (seeds/m2), and distance. In this paper we derive two simple models for long-distance deposition. The models are tested at the scale of 100–1600 m from the source and found to be within 5-fold of the observed deposition. There is no discernable decline in deposition for the range 300–1600 m. While we hesitate to extend model predictions to greater distances, both the models and the empirical results allow us to assert that rare wind-dispersed species in woodlots (dispersal distance around 1 km) are effectively isolated from one another at the temporal scale of 1000 years. Key words: plant conservation biology, wind dispersal of seeds, metapopulations.

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Yoshida, Ruriko, Lillian Paul, and Peter Nesbitt. "Stochastic Safety Radius on UPGMA." Algorithms 15, no. 12 (December 18, 2022): 483. http://dx.doi.org/10.3390/a15120483.

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Unweighted Pair Group Method with Arithmetic Mean (UPGMA) is one of the most popular distance-based methods to reconstruct an equidistant phylogenetic tree from a distance matrix computed from an alignment of sequences. Since we use equidistant trees as gene trees for phylogenomic analyses under the multi-species coalescent model and since an input distance matrix computed from an alignment of each gene in a genome is estimated via the maximum likelihood estimators, it is important to conduct a robust analysis on UPGMA. Stochastic safety radius, introduced by Steel and Gascuel, provides a lower bound for the probability that a phylogenetic tree reconstruction method returns the true tree topology from a given distance matrix. In this article, we compute the stochastic safety radius of UPGMA for a phylogenetic tree with n leaves. Computational experiments show an improved gap between empirical probabilities estimated from random samples and the true tree topology from UPGMA, increasing confidence in phylogenic results.

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BOUSQUET, NICOLAS, LOUIS ESPERET, ARARAT HARUTYUNYAN, and RÉMI DE JOANNIS DE VERCLOS. "Exact Distance Colouring in Trees." Combinatorics, Probability and Computing 28, no. 2 (July 24, 2018): 177–86. http://dx.doi.org/10.1017/s0963548318000378.

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For an integer q ⩾ 2 and an even integer d, consider the graph obtained from a large complete q-ary tree by connecting with an edge any two vertices at distance exactly d in the tree. This graph has clique number q + 1, and the purpose of this short note is to prove that its chromatic number is Θ((d log q)/log d). It was not known that the chromatic number of this graph grows with d. As a simple corollary of our result, we give a negative answer to a problem of van den Heuvel and Naserasr, asking whether there is a constant C such that for any odd integer d, any planar graph can be coloured with at most C colours such that any pair of vertices at distance exactly d have distinct colours. Finally, we study interval colouring of trees (where vertices at distance at least d and at most cd, for some real c > 1, must be assigned distinct colours), giving a sharp upper bound in the case of bounded degree trees.

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Caraballo-Ortiz, Marcos A., Eugenio Santiago-Valentín, and Tomás A. Carlo. "Flower number and distance to neighbours affect the fecundity of Goetzea elegans (Solanaceae)." Journal of Tropical Ecology 27, no. 5 (August 2, 2011): 521–28. http://dx.doi.org/10.1017/s0266467411000289.

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Abstract:Pollinator visits to flowers of self-incompatible tropical trees are critical for plant fecundity. However, few studies have examined how much of the variance in tropical tree fecundity is explained by individual attributes of trees (e.g. number of flowers), and how much is due to contextual variables such as distances to nearest flowering neighbours. Using multiple regressions we examined the relative contributions of these factors to the pollination and fecundity of Goetzea elegans, a mainly self-incompatible tree endemic to Puerto Rico. We studied the largest wild population of the species during the peak flowering and collected data on the frequency of pollinator visits (N = 25 trees), and the fecundity of the whole population (N = 105), including the visitation rate of two pollinators (the honey bee Apis mellifera and the bananaquit Coereba flaveola), the total number of flowers produced by each tree, and the total fruit set and seed viability per tree. We also recorded the distance to flowering conspecifics and heterospecifics, and the height for each tree. Flower number had a strong positive effect on pollinator visitation, but distance to nearest neighbours was equally or more important than flower number in influencing fecundity. Also, competition for limited pollinators between G. elegans and other species has a stronger effect than the facilitation that conspecifics may provide. Our results suggest that pollinator visits and aspects of fecundity of G. elegans depend both on the attributes of individual plants, and on those of the community of other nearby plants.

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Verboom, B., and K. Spoelstra. "Effects of food abundance and wind on the use of tree lines by an insectivorous bat, Pipistrellus pipistrellus." Canadian Journal of Zoology 77, no. 9 (November 15, 1999): 1393–401. http://dx.doi.org/10.1139/z99-116.

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We tested the hypotheses that the distance bats fly from tree lines depend on food abundance and protection from wind. We monitored the activity of pipistrelle bats (Pipistrellus pipistrellus) and measured insect abundance and wind speed and direction at fixed distances up to 50 m from tree lines. We compared bat behaviour in different situations: with and without wind and with low and high insect abundances in adjacent open areas. In all situations, pipistrelle bats' activity decreased with increasing distance from the tree line. Within nights, we found no effect of wind speed on bat activity (sound recorded per 5 min) on the leeward side of the tree lines. Between nights, however, bats concentrated their activities closer to the tree lines at high wind speeds or angles of incidence of wind from 45° to 90°. A significant relationship between bat and insect abundances was found only when the tree line was bordered by insect-rich grassland. Since wind and insect abundance only partly explained the distances bats flew from tree lines, two alternative explanations, namely predator avoidance and the use of tree lines as acoustic landmarks, are discussed. Pipistrelle bats using a double row of trees as a commuting route at dusk flew mainly between the tree lines, regardless of insect abundance or wind speed. It is argued that predator avoidance explains this behaviour, being a constraint on movements of bats at relatively high light levels. At high wind speeds and angles of incidence greater than 45°, the proportion of pipistrelle bats commuting on the leeward side of the tree lines increased.

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EPPSTEIN, DAVID. "TREE-WEIGHTED NEIGHBORS AND GEOMETRIC k SMALLEST SPANNING TREES." International Journal of Computational Geometry & Applications 04, no. 02 (June 1994): 229–38. http://dx.doi.org/10.1142/s0218195994000136.

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We compute the k smallest spanning trees of a point set in the planar Euclidean metric in time O(n log n log k + k min (k, n)1/2 log (k/n)), and in the rectilinear metric in time O(n log n + n log log n log k + k ( min {k, n})1/2 log (k/n)). In three or four dimensions our time bound is O(n4/3 + ∊ + k( min {k, n})1/2 log (k/n)), and in higher dimensions the bound is O(n2−2/(⌈d/2⌉+1)+∊ + kn1/2 log n). Our technique involves a method of computing nearest neighbors using a modified set of distances formed by subtracting tree path lengths from the Euclidean distance.

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Rogozin, Mikhail V. "Spatial analysis of competition and cooperation of trees in pine forest crops." Вестник Пермского университета. Серия «Биология»=Bulletin of Perm University. Biology, no. 4 (2021): 235–48. http://dx.doi.org/10.17072/1994-9952-2021-4-235-248.

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In forest cultures of scots pine 1 in bonita at the age of 55 years with a standing density of 940-1620 pcs./ha with a fullness of 0.84-1.02 on an area of 1.9 ha, places with low and medium density (5 sample areas, 433 trees) were selected to study the influence of microcenoses on the diameters of trees in their center. To do this, in the "ArcMap-ArcView" program, food polygons for the age of 30-40 years and 41-55 years were built around the trees. Five indicators were used in the spatial analysis of the data: 1 - simple pressure of neighbors: the diameters of the neighbors on the polygon were summed up; 2 - specific pressure of neighbors: indicator 1 was divided by the feeding area of the central tree; 3 - pressure of neighbors taking into account the distances to the central tree: the diameter of the neighbor was divided by the distance to the central tree and the data were summed; 4 - specific pressure of neighbors taking into account the distances: indicator 3 was divided by the feeding area of the central tree; 5 - cooperation of trees on the sides of the polygon: the diameter of the neighbor was multiplied by the contact distance with the central tree on the side of the polygon and the data were summed. It was not possible to choose the best indicator, since all five were weaker than the influence of a simple power supply area. When using the feeding area at the age of 30-40 years, and then at 41-55 years, the specific pressure of neighbors varied in strength from 5.8 to 8.9%, averaging 7.4%, and when taking into account the distances to neighbors, this pressure increased to an average of 8.5%. At an average density, the strength of the trees ' cooperation was equal to 11.6%, and at a low density of 7.5%, averaging 9.6%. Thus, the cooperation of trees in the microcenosis was generally 1.13 times stronger than the competitive pressure of neighboring trees

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Santos, Alisson Borges Miranda, Vinicius Andrade Maia, Cléber Rodrigo de Souza, Nathalle Cristine Alencar Fagundes, Fernanda Moreira Gianasi, Aurélio de Jesus Rodrigues Pais, Natália de Aguiar-Campos, et al. "Disentangling spatial, environmental and historical effects on tropical forest tree species turnover." Journal of Plant Ecology 14, no. 4 (March 26, 2021): 717–29. http://dx.doi.org/10.1093/jpe/rtab027.

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Abstract Aims We aimed at disentangling the effects of spatial distance, current and past environmental dissimilarity, and their combinations on tree community taxonomic and phylogenetic turnover by addressing the following questions: (i) Is tree community taxonomic and phylogenetic turnover related to the indirect effects of spatial distance via environmental dissimilarity? (ii) Does tree community taxonomic and phylogenetic turnover respond to paleoclimate (Last Glacial Maximum and Mid-Holocene)? Methods The study was carried out in 14 Atlantic rainforest sites in Brazil (20.4 ha sampled) containing 615 tree species from 83 plant families. We obtained plot-level geographic coordinates and soil variables and site-level bioclimatic variables in the current, Mid-Holocene and Last Glacial Maximum. We used structural equation models with a distance-based approach to (i) test the direct effects of spatial distance and environmental dissimilarity and (ii) test the indirect effects of spatial distance via environmental dissimilarity on taxonomic (Bray–Curtis distance) and phylogenetic turnover (Comdist and Comdistnt distances). Important Findings Our results suggest a weak indirect effect of spatial distance via environmental dissimilarity on taxonomic and phylogenetic turnover. Tree community turnover was driven by the direct effects of neutral, niche-based and historical processes. Thus, we inferred that the paleoclimate (historical processes) promoted the selection of the clades that gave rise to the current flora, while spatial distances (neutral processes) limited the dispersal range of species from the regional pool and environmental conditions (niche-based processes) locally selected the taxa that are able to persist.

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Vonhof, Maarten J., and Robert M. R. Barclay. "Roost-site selection and roosting ecology of forest-dwelling bats in southern British Columbia." Canadian Journal of Zoology 74, no. 10 (October 1, 1996): 1797–805. http://dx.doi.org/10.1139/z96-200.

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We used radiotelemetry to examine the roost-site preferences of four species of tree-roosting bats (Eptesicus fuscus, Lasionycteris noctivagans, Myotis evotis, and M. volans) in southern British Columbia, Canada, by radio-tracking bats to their day roosts. We found a total of 21 roost trees: 14 roosts were beneath loose bark, 5 were in cavities excavated by woodpeckers, and 2 were in natural cavities. Entrance height increased with tree height, but roost entrances tended to be situated below the level of the canopy. Of the 22 tree and site variables examined, only 3 significantly discriminated between roost trees and available trees: tree height, distance to the nearest available tree, and percent canopy closure. Bats preferred tall trees associated with low percent canopy closure and a short distance to the nearest available tree. Bats roosted in western white pine, and to a lesser extent ponderosa pine and western larch, in intermediate stages of decay more often than would be expected at random. Bats switched roosts frequently. The distance between subsequent roost trees was short, suggesting a degree of fidelity to a particular group of trees or area of forest. The number of days of rain during the roosting period significantly influenced the number of days spent in a particular roost, and thus ambient conditions may restrict the frequency with which bats can switch roosts.

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Journal articles on the topic 'Tree distance'

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