Tree Reconstruction Methods Research Articles

Realistic reconstruction of trees from sparse images in volumetric space

The realistic reconstruction of real-world trees is a challenging task in the community of computer graphics because natural trees have complex structures of branches and leaves. Existing terrestrial laser scanning (TLS) system is able to capture dense and precise tree point clouds, yet the TLS system is expensive and not easy to carry around. An alternative low-cost and portable way is the reconstruction of tree point cloud from multiple view images. However, it is usually difficult to reconstruct a complete tree point cloud because of the texture similarity of branches and leaves as well as the lack of a sufficient number of images. Thus, we propose a new approach for reconstructing tree point clouds and geometries from sparse images. We first infer the camera parameters of each image, and then calculate the bounding volume of a tree from the camera parameters. Next, we set the mask of each image and the resolution of voxel, and then project each voxel in 3D space to all the mask images to determine the validity of the voxel. To alleviate the miss deletion of valid voxel, we utilize a boundary threshold and adjust mask resolution for robust point cloud reconstruction. Finally, an efficient tree reconstruction method is proposed to generate plausible tree geometries. We tested 6 different tree species that contain deciduous and evergreen trees, and the results showed that our approach is able to generate complete tree point cloud and realistic tree models even from a few number of images.

Scuphr: A probabilistic framework for cell lineage tree reconstruction.

Cell lineage tree reconstruction methods are developed for various tasks, such as investigating the development, differentiation, and cancer progression. Single-cell sequencing technologies enable more thorough analysis with higher resolution. We present Scuphr, a distance-based cell lineage tree reconstruction method using bulk and single-cell DNA sequencing data from healthy tissues. Common challenges of single-cell DNA sequencing, such as allelic dropouts and amplification errors, are included in Scuphr. Scuphr computes the distance between cell pairs and reconstructs the lineage tree using the neighbor-joining algorithm. With its embarrassingly parallel design, Scuphr can do faster analysis than the state-of-the-art methods while obtaining better accuracy. The method's robustness is investigated using various synthetic datasets and a biological dataset of 18 cells.

Evaluating the Point Cloud of Individual Trees Generated from Images Based on Neural Radiance Fields (NeRF) Method

Three-dimensional (3D) reconstruction of trees has always been a key task in precision forestry management and research. Due to the complex branch morphological structure of trees themselves and the occlusions from tree stems, branches and foliage, it is difficult to recreate a complete three-dimensional tree model from a two-dimensional image by conventional photogrammetric methods. In this study, based on tree images collected by various cameras in different ways, the Neural Radiance Fields (NeRF) method was used for individual tree dense reconstruction and the exported point cloud models are compared with point clouds derived from photogrammetric reconstruction and laser scanning methods. The results show that the NeRF method performs well in individual tree 3D reconstruction, as it has a higher successful reconstruction rate, better reconstruction in the canopy area and requires less images as input. Compared with the photogrammetric dense reconstruction method, NeRF has significant advantages in reconstruction efficiency and is adaptable to complex scenes, but the generated point cloud tend to be noisy and of low resolution. The accuracy of tree structural parameters (tree height and diameter at breast height) extracted from the photogrammetric point cloud is still higher than those derived from the NeRF point cloud. The results of this study illustrate the great potential of the NeRF method for individual tree reconstruction, and it provides new ideas and research directions for 3D reconstruction and visualization of complex forest scenes.

Designing Weights for Quartet-Based Methods When Data are Heterogeneous Across Lineages

Homogeneity across lineages is a general assumption in phylogenetics according to which nucleotide substitution rates are common to all lineages. Many phylogenetic methods relax this hypothesis but keep a simple enough model to make the process of sequence evolution more tractable. On the other hand, dealing successfully with the general case (heterogeneity of rates across lineages) is one of the key features of phylogenetic reconstruction methods based on algebraic tools. The goal of this paper is twofold. First, we present a new weighting system for quartets (ASAQ) based on algebraic and semi-algebraic tools, thus especially indicated to deal with data evolving under heterogeneous rates. This method combines the weights of two previous methods by means of a test based on the positivity of the branch lengths estimated with the paralinear distance. ASAQ is statistically consistent when applied to data generated under the general Markov model, considers rate and base composition heterogeneity among lineages and does not assume stationarity nor time-reversibility. Second, we test and compare the performance of several quartet-based methods for phylogenetic tree reconstruction (namely QFM, wQFM, quartet puzzling, weight optimization and Willson’s method) in combination with several systems of weights, including ASAQ weights and other weights based on algebraic and semi-algebraic methods or on the paralinear distance. These tests are applied to both simulated and real data and support weight optimization with ASAQ weights as a reliable and successful reconstruction method that improves upon the accuracy of global methods (such as neighbor-joining or maximum likelihood) in the presence of long branches or on mixtures of distributions on trees.

Tree Reconstruction Using Topology Optimisation

Generating accurate digital tree models from scanned environments is invaluable for forestry, agriculture, and other outdoor industries in tasks such as identifying fall hazards, estimating trees’ biomass and calculating traversability. Existing methods for tree reconstruction rely on sparse feature identification to segment a forest into individual trees and generate a branch structure graph, limiting their application to easily separable trees and uniform forests. However, the natural world is a messy place in which trees present with significant heterogeneity and are frequently encroached upon by the surrounding environment. We present a general method for extracting the branch structure of trees from point cloud data, which estimates the structure of trees by adapting the methods of structural topology optimisation to find the optimal material distribution to interpolate the input data. We present the results of this optimisation over a wide variety of scans, and discuss the benefits and drawbacks of this novel approach to tree structure reconstruction. Our method generates detailed and accurate tree structures, with a mean Surface Error (SE) of 15 cm over 13 diverse tree datasets.

Stochastic Safety Radius on UPGMA

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.

A scalable model for simulating multi-round antibody evolution and benchmarking of clonal tree reconstruction methods.

Affinity maturation (AM) of B cells through somatic hypermutations (SHMs) enables the immune system to evolve to recognize diverse pathogens. The accumulation of SHMs leads to the formation of clonal lineages of antibody-secreting b cells that have evolved from a common naïve B cell. Advances in high-throughput sequencing have enabled deep scans of B cell receptor repertoires, paving the way for reconstructing clonal trees. However, it is not clear if clonal trees, which capture microevolutionary time scales, can be reconstructed using traditional phylogenetic reconstruction methods with adequate accuracy. In fact, several clonal tree reconstruction methods have been developed to fix supposed shortcomings of phylogenetic methods. Nevertheless, no consensus has been reached regarding the relative accuracy of these methods, partially because evaluation is challenging. Benchmarking the performance of existing methods and developing better methods would both benefit from realistic models of clonal lineage evolution specifically designed for emulating B cell evolution. In this paper, we propose a model for modeling B cell clonal lineage evolution and use this model to benchmark several existing clonal tree reconstruction methods. Our model, designed to be extensible, has several features: by evolving the clonal tree and sequences simultaneously, it allows modeling selective pressure due to changes in affinity binding; it enables scalable simulations of large numbers of cells; it enables several rounds of infection by an evolving pathogen; and, it models building of memory. In addition, we also suggest a set of metrics for comparing clonal trees and measuring their properties. Our results show that while maximum likelihood phylogenetic reconstruction methods can fail to capture key features of clonal tree expansion if applied naively, a simple post-processing of their results, where short branches are contracted, leads to inferences that are better than alternative methods.

DNA barcode data confirm the placement of subterranean Noemacheilus (Troglocobitis) starostini Parin 1983 in the genus Paracobitis (Teleostei, Nemacheilidae)

DNA barcodes (COI) of Troglocobitis starostini, endemic to a single site in Turkmenistan, were analysed and put into the taxonomic context of the large group of nemacheilid loaches known from Western and Central Asia. All applied phylogenetic tree-based analyses place the species into the genus Paracobitis. This finding supports previous morphological studies. While the exact position of Troglocobitis starostini within Paracobitis was not resolved unambiguously, it was constantly recovered within Paracobitis, irrespective of the tree reconstruction method applied. With a minimum interspecific K2P distance of 7.19% P. persa was the closest hit in our dataset, which comprised a total of ten species of Paracobitis, which showed an average interspecific K2P distance of 5.43% (range 2.78-9.44%).

Insertions and deletions as phylogenetic signal in an alignment-free context.

Most methods for phylogenetic tree reconstruction are based on sequence alignments; they infer phylogenies from substitutions that may have occurred at the aligned sequence positions. Gaps in alignments are usually not employed as phylogenetic signal. In this paper, we explore an alignment-free approach that uses insertions and deletions (indels) as an additional source of information for phylogeny inference. For a set of four or more input sequences, we generate so-called quartet blocks of four putative homologous segments each. For pairs of such quartet blocks involving the same four sequences, we compare the distances between the two blocks in these sequences, to obtain hints about indels that may have happened between the blocks since the respective four sequences have evolved from their last common ancestor. A prototype implementation that we call Gap-SpaM is presented to infer phylogenetic trees from these data, using a quartet-tree approach or, alternatively, under the maximum-parsimony paradigm. This approach should not be regarded as an alternative to established methods, but rather as a complementary source of phylogenetic information. Interestingly, however, our software is able to produce phylogenetic trees from putative indels alone that are comparable to trees obtained with existing alignment-free methods.

Interpreting phylogenetic conflict: Hybridization in the most speciose genus of lichen-forming fungi

While advances in sequencing technologies have been invaluable for understanding evolutionary relationships, increasingly large genomic data sets may result in conflicting evolutionary signals that are often caused by biological processes, including hybridization. Hybridization has been detected in a variety of organisms, influencing evolutionary processes such as generating reproductive barriers and mixing standing genetic variation. Here, we investigate the potential role of hybridization in the diversification of the most speciose genus of lichen-forming fungi, Xanthoparmelia. As Xanthoparmelia is projected to have gone through recent, rapid diversification, this genus is particularly suitable for investigating and interpreting the origins of phylogenomic conflict. Focusing on a clade of Xanthoparmelia largely restricted to the Holarctic region, we used a genome skimming approach to generate 962 single-copy gene regions representing over 2 Mbp of the mycobiont genome. From this genome-scale dataset, we inferred evolutionary relationships using both concatenation and coalescent-based species tree approaches. We also used three independent tests for hybridization. Although different species tree reconstruction methods recovered largely consistent and well-supported trees, there was widespread incongruence among individual gene trees. Despite challenges in differentiating hybridization from ILS in situations of recent rapid radiations, our genome-wide analyses detected multiple potential hybridization events in the Holarctic clade, suggesting one possible source of trait variability in this hyperdiverse genus. This study highlights the value in using a pluralistic approach for characterizing genome-scale conflict, even in groups with well-resolved phylogenies, while highlighting current challenges in detecting the specific impacts of hybridization.

Local and 2-Local Derivations of Locally Simple Lie Algebras

In this paper, we study a two-state Hard-Core (HC) model with activity λ0{\lambda >0} on a Cayley tree of order k ≥2{k \ge 2}. It is known that there are λcr{\lambda_{cr}}, λcr0{\lambda_{cr}^0} and λcr'{\lambda_{cr}^'} such that
 
 for λ≤λcr{\lambda \le \lambda_{cr}} this model has a unique Gibbs measure λ0{\lambda >0}, which is translation invariant. The measure λ0{\lambda >0} is extreme for λλcr0{\lambda < \lambda_{cr}^0} and not extreme for λλcr'{\lambda > \lambda_{cr}^'};
 for λλcr{\lambda > \lambda_{cr}} there exist exactly three 2-periodic Gibbs measures, one of which is μ*{\mu^*}, the other two are not translation-invariant and are always extreme.
 
 The extremity of these periodic measures was proved using the maximality and minimality of the corresponding solutions of some equation, which ensures the consistency of these measures. In this paper, we give a brief overview of the known Gibbs measures for the HC-model and an alternative proof of the extremity of 2-periodic measures for k=2,3{k = 2 , 3}. Our proof is based on the tree reconstruction method.

A stochastic Farris transform for genetic data under the multispecies coalescent with applications to data requirements.

Species tree estimation faces many significant hurdles. Chief among them is that the trees describing the ancestral lineages of each individual gene-the gene trees-often differ from the species tree. The multispecies coalescent is commonly used to model this gene tree discordance, at least when it is believed to arise from incomplete lineage sorting, a population-genetic effect. Another significant challenge in this area is that molecular sequences associated to each gene typically provide limited information about the gene trees themselves. While the modeling of sequence evolution by single-site substitutions is well-studied, few species tree reconstruction methods with theoretical guarantees actually address this latter issue. Instead, a standard-but unsatisfactory-assumption is that gene trees are perfectly reconstructed before being fed into a so-called summary method. Hence much remains to be done in the development of inference methodologies that rigorously account for gene tree estimation error-or completely avoid gene tree estimation in the first place. In previous work, a data requirement trade-off was derived between the number of loci m needed for an accurate reconstruction and the length of the locus sequences k. It was shown that to reconstruct an internal branch of length f, one needs m to be of the order of [Formula: see text]. That previous result was obtained under the restrictive assumption that mutation rates as well as population sizes are constant across the species phylogeny. Here we further generalize this result beyond this assumption. Our main contribution is a novel reduction to the molecular clock case under the multispecies coalescent, which we refer to as a stochastic Farris transform. As a corollary, we also obtain a new identifiability result of independent interest: for any species tree with [Formula: see text] species, the rooted topology of the species tree can be identified from the distribution of its unrooted weighted gene trees even in the absence of a molecular clock.

How to date a crocodile: estimation of neosuchian clade ages and a comparison of four time‐scaling methods

AbstractClade ages within the crocodylomorph clade Neosuchia have long been debated. Molecular and morphological studies have yielded remarkably divergent results. Despite recent advances, there has been no comprehensive relative comparison of the major time calibration methods available to estimate clade ages based on morphological data. We used four methods (cal3, extended Hedman, smoothed ghost lineage analysis (sGLA) and the fossilized birth–death model (FBD)) to date clade ages derived from a published crocodylomorph supertree and a new neosuchian phylogeny. All time‐scaling methods applied here agree on the origination of Neosuchia during the Late Triassic or Early Jurassic, and the presence of the major extant eusuchian groups (Crocodyloidea, Gavialoidea, Alligatoroidea and Caimaininae) by the end of the Late Cretaceous. The number of distinct lineages present before the K/Pg boundary is less certain, with support for two competing scenarios in which Crocodylinae, Tomistominae and Diplocynodontinae either: (1) diverged from other eusuchian lineages before the K/Pg boundary; or (2) evolved during a ‘burst’ of diversification after the K/Pg event. Cal3 and FBD proved to be the most suitable methods for time‐scaling phylogenetic trees dominated by fossil taxa. Extended Hedman estimates are substantially older than the others, with larger standard deviations and a strong sensitivity to taxon sampling and topological changes; sGLA has similar problems. We conclude that a detailed understanding of phylogenetic relationships, tree reconstruction methods, and good taxonomic coverage (in particular the inclusion of the oldest taxon in each clade) is essential when evaluating the results of such dating analyses.

An Information-Entropy Position-Weighted K-Mer Relative Measure for Whole Genome Phylogeny Reconstruction.

Alignment methods have faced disadvantages in sequence comparison and phylogeny reconstruction due to their high computational costs in handling time and space complexity. On the other hand, alignment-free methods incur low computational costs and have recently gained popularity in the field of bioinformatics. Here we propose a new alignment-free method for phylogenetic tree reconstruction based on whole genome sequences. A key component is a measure called information-entropy position-weighted k-mer relative measure (IEPWRMkmer), which combines the position-weighted measure of k-mers proposed by our group and the information entropy of frequency of k-mers. The Manhattan distance is used to calculate the pairwise distance between species. Finally, we use the Neighbor-Joining method to construct the phylogenetic tree. To evaluate the performance of this method, we perform phylogenetic analysis on two datasets used by other researchers. The results demonstrate that the IEPWRMkmer method is efficient and reliable. The source codes of our method are provided at https://github.com/ wuyaoqun37/IEPWRMkmer.

Phylogenetic relationships among subclades within the Trinity bristle snail species complex, riverine barriers, and re-classification

The Trinity bristle snail (Monadenia setosa) is listed as a threatened species under the California Endangered Species Act (CESA). In northern California, populations of this endemic terrestrial gastropod occur in rare, isolated, and highly fragmented locations within the greater Trinity Basin. Since 1952 when it was originally described, the taxonomic status of the Trinity bristle snail has been questioned based on unpublished information limited in geographic scope and sample size, which resulted in the taxon being reduced from species status (M. setosa) to subspecific status (M. i. setosa) within the Redwood sideband (M. infumata) species complex. Primary objectives of the present study were to: 1) use DNA extraction and PCR sequencing to gain insight into patterns of genetic variation and phylogenetic relationships among a larger sample of endemic populations of the Trinity bristle snail; 2) re-evaluate the systematic and taxonomic status of the species using outgroup analysis and references samples from sympatric ecologically co-occurring taxa within the genus Monadenia; and 3) evaluate the potential biogeographic effects of major riverine systems on genetic differentiation among relic and disjunct populations within the Trinity Basin. Results of the DNA sequence analysis using several different tree reconstruction methods revealed that subspecies of the Redwood sideband (M. i. subcarinata), Yellow-based sideband (M. i. ochromphalus), and the Trinity bristle (M. i. setosa) exhibited a phylogenetic signal at > 95% species probability. Except for the Yellow-based sideband, molecular evidence detected the presence of several morphologically cryptic subclades within each species clade formerly undescribed by the scientific community. Syntopic1 ecological relationships between subclades of the Trinity bristle snail and the Redwood sideband occurred in several areas within the geographic range of the Trinity bristle snail, which indicated that these subclades were conservatively differentiated at the subspecific level. A Bayesian coalescent tree showed that genetic variation 1 Syntopy refers to the joint occurrence of two species in the same habitat at the same time, which may result in hybridization between closely related taxa or sister species. In contrast, sympatric species occur together in the same region, but do not necessarily share the same localities as syntopic species do (Futuma 2009). among allopatric subclades of the Trinity bristle snail and the Redwood sideband were congruent with hydrological discontinuities associated with site-specific riparian stream corridors and the primary river systems within the Trinity Basin. Correlation analysis revealed a pattern of area effects, wherein sparsely bristled Trinity bristle snails were generally found to the northwest and more abundantly bristled individuals to the southeast in relation to primary river corridors that bisect the central Trinity Basin. A similar but opposite trend was observed in the directional pattern of banding. Here the most conspicuously banded individuals were found in samples distributed to the northwest while individuals with less conspicuous banding patterns occurred in a more southeasterly direction in relation to primary riverine corridors. These geographic patterns of bristles and bands appeared to reflect shallow clines that were evident in samples of both the Trinity bristle snail and the Redwood sideband. Parsimony character state reconstructions revealed that the presence of bristles and conspicuousness of bands was widespread among genetic samples, but these attributes did not provide a definitive morphological character that could be used to distinguish among co-occurring taxa.

Reconstructing tumor evolutionary histories and clone trees in polynomial-time with SubMARine.

Tumors contain multiple subpopulations of genetically distinct cancer cells. Reconstructing their evolutionary history can improve our understanding of how cancers develop and respond to treatment. Subclonal reconstruction methods cluster mutations into groups that co-occur within the same subpopulations, estimate the frequency of cells belonging to each subpopulation, and infer the ancestral relationships among the subpopulations by constructing a clone tree. However, often multiple clone trees are consistent with the data and current methods do not efficiently capture this uncertainty; nor can these methods scale to clone trees with a large number of subclonal populations. Here, we formalize the notion of a partially-defined clone tree (partial clone tree for short) that defines a subset of the pairwise ancestral relationships in a clone tree, thereby implicitly representing the set of all clone trees that have these defined pairwise relationships. Also, we introduce a special partial clone tree, the Maximally-Constrained Ancestral Reconstruction (MAR), which summarizes all clone trees fitting the input data equally well. Finally, we extend commonly used clone tree validity conditions to apply to partial clone trees and describe SubMARine, a polynomial-time algorithm producing the subMAR, which approximates the MAR and guarantees that its defined relationships are a subset of those present in the MAR. We also extend SubMARine to work with subclonal copy number aberrations and define equivalence constraints for this purpose. Further, we extend SubMARine to permit noise in the estimates of the subclonal frequencies while retaining its validity conditions and guarantees. In contrast to other clone tree reconstruction methods, SubMARine runs in time and space that scale polynomially in the number of subclones. We show through extensive noise-free simulation, a large lung cancer dataset and a prostate cancer dataset that the subMAR equals the MAR in all cases where only a single clone tree exists and that it is a perfect match to the MAR in most of the other cases. Notably, SubMARine runs in less than 70 seconds on a single thread with less than one Gb of memory on all datasets presented in this paper, including ones with 50 nodes in a clone tree. On the real-world data, SubMARine almost perfectly recovers the previously reported trees and identifies minor errors made in the expert-driven reconstructions of those trees. The freely-available open-source code implementing SubMARine can be downloaded at https://github.com/morrislab/submarine.

Evolutionary aspects of the Viridiplantae nitroreductases

BackgroundNitroreductases are a family of evolutionarily related proteins catalyzing the reduction of nitro-substituted compounds. Nitroreductases are widespread enzymes, but nearly all modern research and practical application have been concentrated on the bacterial proteins, mainly nitroreductases of Escherichia coli. The main aim of this study is to describe the phylogenic distribution of the nitroreductases in the photosynthetic eukaryotes (Viridiplantae) to highlight their structural similarity and areas for future research and application. ResultsThis study suggests that homologs of nitroreductase proteins are widely presented also in Viridiplantae. Maximum likelihood phylogenetic tree reconstruction method and comparison of the structural models suggest close evolutional relation between cyanobacterial and Viridiplantae nitroreductases. ConclusionsThis study provides the first attempt to understand the evolution of nitroreductase protein family in Viridiplantae. Our phylogeny estimation and preservation of the chloroplasts/mitochondrial localization indicate the evolutional origin of the plant nitroreductases from the cyanobacterial endosymbiont. A defined high level of the similarity on the structural level suggests conservancy also for the functions. Directions for the future research and industrial application of the Viridiplantae nitroreductases are discussed.

Alignment of Cell Lineage Trees Elucidates Genetic Programs for the Development and Evolution of Cell Types

SummaryA full understanding of the developmental process requires fine-scale characterization of cell divisions and cell types, which are naturally organized as the developmental cell lineage tree (CLT). Technological breakthroughs facilitated determination of more CLTs, but complete comprehension of the data remains difficult without quantitative comparison among CLTs. We hereby quantified phenotypic similarity between CLTs using a novel computational method that exhaustively searches for optimal correspondence between individual cells meanwhile retaining their topological relationships. The revealed CLT similarities allowed us to infer functional similarity at the transcriptome level, identify cell fate transformations, predict functional relationships between mutants, and find evolutionary correspondence between cell types of different species. By allowing quantitative comparison between CLTs, our work is expected to greatly enhance the interpretability of relevant data and help answer the myriad of questions surrounding the developmental process.

Radiation history of Asian Asarum (sect. Heterotropa, Aristolochiaceae) resolved using a phylogenomic approach based on double-digested RAD-seq data.

The genus Asarum sect. Heterotropa (Aristolochiaceae) probably experienced rapid diversification into 62 species centred on the Japanese Archipelago and Taiwan, providing an ideal model for studying island adaptive radiation. However, resolving the phylogeny of this plant group using Sanger sequencing-based approaches has been challenging. To uncover the radiation history of Heterotropa, we employed a phylogenomic approach using double-digested RAD-seq (ddRAD-seq) to yield a sufficient number of phylogenetic signals and compared its utility with that of the Sanger sequencing-based approach. We first compared the performance of phylogenetic analysis based on the plastid matK and trnL-F regions and nuclear ribosomal internal transcribed spacer (nrITS), and phylogenomic analysis based on ddRAD-seq using a reduced set of the plant materials (83 plant accessions consisting of 50 species, one subspecies and six varieties). We also conducted more thorough phylogenomic analyses including the reconstruction of biogeographic history using comprehensive samples of 135 plant accessions consisting of 54 species, one subspecies, nine varieties of Heterotropa and six outgroup species. Phylogenomic analyses of Heterotropa based on ddRAD-seq were superior to Sanger sequencing-based approaches and resulted in a fully resolved phylogenetic tree with strong support for 72.0-84.8 % (depending on the tree reconstruction methods) of the branches. We clarified the history of Heterotropa radiation and found that A. forbesii, the only deciduous Heterotropa species native to mainland China, is sister to the evergreen species (core Heterotropa) mostly distributed across the Japanese Archipelago and Taiwan. The core Heterotropa group was divided into nine subclades, each of which had a narrow geographic distribution. Moreover, most estimated dispersal events (22 out of 24) were between adjacent areas, indicating that the range expansion has been geographically restricted throughout the radiation history. The findings enhance our understanding of the remarkable diversification of plant lineages in the Japanese Archipelago and Taiwan.

Electrical tree reconstruction method for oil-impregnated pressboards based on the inverse problem for the electrostatic field

There is still a lack of effective means of observation for electrical trees in opaque materials, which hampers experimental and theoretical research on the growth of such trees in the oil-impregnated pressboards of power transformers. This presents a great obstacle to the accurate diagnosis and prediction of partial discharge (PD) defects. This paper describes a method to monitor the growth process of electrical trees in pressboards based on solution of the inverse problem for the electrostatic field. The three-dimensional structure of the carbonized branches is reconstructed from the positions of PDs. Each PD is located by the charge remaining in the material. This charge is calculated from the electric field intensity or potential at some points in the field using the mirror image method and solution of the inverse problem for the electrostatic field. The electric field intensity is measured using an array of metal strips near the zero-potential border while PDs are occurring. High-voltage PD experiments are performed on oil-impregnated pressboard strips to verify the feasibility of the method. From the results of these experiments, the accuracy of PD site location is found to be as good as 0.35 mm in the χ direction (the horizontal coordinate), which is sufficient to describe the general structure of electrical trees in oil-impregnated pressboard. The movement of the PD positions indicates the growth process of tree branches. The calculated positions and lengths of the branches are consistent with observations of carbonized tracks after the pressboard has been torn open. The results obtained here will be of benefit to establishing a real-time monitoring method for three-dimensional reconstruction of electrical trees to reveal their internal growth mechanism in opaque materials such as oil-impregnated pressboards.