Tree Decomposition Research Articles

Clique trees with a given zero forcing number maximizing the $$A_\alpha $$-spectral radius

Clique trees with a given zero forcing number maximizing the $$A_\alpha $$-spectral radius

Anti-factor is FPT Parameterized by Treewidth and List Size (but Counting is Hard)

AbstractIn the general AntiFactor problem, a graph G and, for every vertex v of G, a set $$X_v\subseteq {\mathbb {N}}$$ X v ⊆ N of forbidden degrees is given. The task is to find a set S of edges such that the degree of v in S is not in the set $$X_v$$ X v . Standard techniques (dynamic programming plus fast convolution) can be used to show that if M is the largest forbidden degree, then the problem can be solved in time $$(M+2)^{{{\text {tw}}}}\cdot n^{{\mathcal {O}}(1)}$$ ( M + 2 ) tw · n O ( 1 ) if a tree decomposition of width $${{\text {tw}}}$$ tw is given. However, significantly faster algorithms are possible if the sets $$X_v$$ X v are sparse: our main algorithmic result shows that if every vertex has at most $$x$$ x forbidden degrees (we call this special case AntiFactorx), then the problem can be solved in time $$(x+1)^{{\mathcal {O}}({{\text {tw}}})}\cdot n^{{\mathcal {O}}(1)}$$ ( x + 1 ) O ( tw ) · n O ( 1 ) . That is, AntiFactorx is fixed-parameter tractable parameterized by treewidth $${{\text {tw}}}$$ tw and the maximum number $$x$$ x of excluded degrees. Our algorithm uses the technique of representative sets, which can be generalized to the optimization version, but (as expected) not to the counting version of the problem. In fact, we show that #AntiFactor1 is already #$$[1]$$ [ 1 ] -hard parameterized by the width of the given decomposition. Moreover, we show that, unlike for the decision version, the standard dynamic programming algorithm is essentially optimal for the counting version. Formally, for a fixed nonempty set $$X$$ X , we denote by $$X$$ X -AntiFactor the special case where every vertex v has the same set $$X_v=X$$ X v = X of forbidden degrees. We show the following lower bound for every fixed set $$X$$ X : if there is an $$\epsilon >0$$ ϵ > 0 such that #$$X$$ X -AntiFactor can be solved in time $$(\max X+2-\epsilon )^{{{\text {tw}}}}\cdot n^{{\mathcal {O}}(1)}$$ ( max X + 2 - ϵ ) tw · n O ( 1 ) given a tree decomposition of width $${{\text {tw}}}$$ tw , then the counting strong exponential-time hypothesis (#SETH) fails.

Parallel Sampling of Decomposable Graphs Using Markov Chains on Junction Trees

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficulty in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a novel parallel nonreversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph. At every step, the parallel sampler executes simultaneously all edge perturbations within a partition. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current state-of-the-art methods in terms of accuracy and computational efficiency. The implementation of our work is available in the Python package parallelDG. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Short-term air quality prediction using point and interval deep learning systems coupled with multi-factor decomposition and data-driven tree compression

Clean air, as a symbol of high-quality air quality, is the most basic requirement for people to maintain health. Moreover, in keeping humans fit, accurate short-term air quality prediction is vital. The decomposition algorithm can better capture the local features and temporal changes of the data. However, it increases the computation time, resource consumption, and complexity of the model. On the other hand, existing forecasting systems overlook instability and uncertainty. To solve the above problems, a deterministic and uncertainty AOA-DBGRU-MDN deep learning systems is proposed, which combines arithmetic optimization algorithm (AOA), double-layer bi-directional GRUs (DBGRU), and mixture density network (MDN). The above systems consider meteorological factors and air pollutants comprehensively. It involves feature selection using maximum information coefficient (MIC), decomposition using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm, classification, and compression of decomposed components using entropy-Huffman tree compression. Firstly, the information measurement process reduces the number of components significantly. Following the incorporation of multi-factor data, the optimal DBGRU model is then obtained using AOA. Finally, the training errors are fitted using MDN to obtain interval prediction results. The experiments demonstrate that (1) Using the CEEMDAN algorithm can improve the prediction accuracy; (2) Classifying and reconstructing the data based on entropy-Huffman tree compression can not only decrease the model's training volume and improve training efficiency but also boost the model's prediction accuracy; (3) The AOA-DBGRU-MDN system performs probabilistic prediction to obtain an effective and intuitive prediction interval to improve the point prediction of air quality prediction.

High nitrate and sulfate leaching in response to wetter winters in temperate beech forests

Climate models project moderate to large increases in air temperature for most temperate ecosystems with an overall increase in winter precipitation and a shift from snow towards rain. We investigated the effects of increased winter rainfall on the ecosystem functioning of European beech forests at their north-eastern distribution range. In a large-scale field experiment we manipulated winter climate at nine forest sites by increasing the amount of rainfall and excluding snow. Nutrient availability in the topsoil and leaching in 50 cm depth as well as litter decomposition and radial growth of mature European beech trees were analysed. It was hypothesized that (1) wetter winters lead to increased nutrient deposition as well as leaching, with an overall increase in net nutrient availability, (2) decomposition decreases in response to water addition containing also additional nutrients and (3) primary production during the subsequent growing season increases as presumably not all additionally available nutrients would be leached. We found an increase in topsoil nitrate and sulfate availability during winter in response to rain addition, likely as a consequence of collecting more atmospheric deposition, and surprisingly high leaching rates of the additionally available nutrients. During the subsequent early growing season, no difference in nutrient availability could be observed anymore. Enhanced nutrient availability in the topsoil and leaching do not seem to have a strong short-term influence on forest ecosystem processes in ecosystems which are close to their critical load of N deposition. Decomposition rates during winter and early growing season as well as stem diameter growth during the following growing season were not influenced. This indicates that additional nutrients in the topsoil in response to wetter winters are not available for plant growth but pollute ground- and surface waters.

Reliability-centered availability collaborative optimization allocation approach for machine tools

The availability of computer numerical control (CNC) machine tools is a comprehensive reflection of reliability and maintainability. To ensure the availability requirements of products, it is necessary to allocate the availability indicators of the entire machine to all units. Traditional methods based on reliability allocation or maintainability allocation ignore the coupling relationships among them, which cannot comprehensively improve the availability level of machine tools. Therefore, in this paper, a availability collaborative optimization allocation model for CNC machine tools is proposed to maximize the availability under the optimal combination of failure rate and repair rate. Firstly, a two-stage reliability allocation model based on different allocation mechanisms is established by taking the Function-Motion-Action (FMA) decomposition tree as the allocation path. In the first stage, the allocation weights are determined based on global sensitivity analysis. In the second stage, the reliability optimization allocation model based on Copula function is established. Then, with reliability as the center, an availability collaborative optimization allocation model constrained by maintainability is constructed, and the non-dominated sorting genetic algorithm II (NSGA-II) algorithm is used to solve the model. Finally, a CNC gear milling machine is taken as an example to verify the rationality and effectiveness of the method on product availability requirements under collaborative allocation.

Genomic characterisation and diversity assessment of eight endangered Belgian sheep breeds

Assessing the genetic diversity of local breeds is essential for conserving these unique breeds, which may possess unique traits. This study provides the genomic characterisation of eight indigenous sheep breeds in Belgium based on pedigree and single nucleotide polymorphism (SNP) analysis. A total of 687 sheep were genotyped and were subjected to a rigorous quality control, resulting in a set of 45 978 autosomal SNPs. Pedigree analysis showed breed-average inbreeding estimates between 3.3% and 11.3%. The genomic analysis included an assessment of runs of homozygosity (ROH) to examine the genomic inbreeding coefficient, with breed-average inbreeding coefficients estimated between 4.1% and 8.5%. Runs of homozygosity islands were identified in six of the eight breeds studied, with some exhibiting an incidence of up to 58%. Interestingly, several ROH islands overlapped with other breeds included in this study, as well as with international sheep breeds. Pedigree-based effective population sizes were estimated below 100 for all breeds, whereas genomic-based effective population sizes were below 24, indicating that these eight local sheep breeds are endangered. Principal component analysis, admixture analyses, and Fst computations were used to study the population structure and genetic differences. A neighbour−joining tree using 95 international sheep breeds positioned the eight local breeds in the group of milksheep, Texel sheep and the Scandinavian breeds. Additionally, the investigation of paternal oY1 genotypes revealed diverse lineage origins within the Belgian sheep population. This study refines and deepens our knowledge about the local sheep breeds in Belgium, thereby improving their management and conservation. Moreover, as these breeds are linked to other international breeds, these insights are significant for the global scientific community.

The Complexity of Finding and Enumerating Optimal Subgraphs to Represent Spatial Correlation

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee et al. (Stat Comput 31(4):51, 2021. https://doi.org/10.1007/s11222-021-10025-7) recently demonstrated that improved inference for areal unit count data can be achieved by carrying out modifications to a graph representing spatial correlations; specifically, they delete edges of the planar graph derived from border-sharing between geographic regions in order to maximise a specific objective function. In this paper, we address the computational complexity of the associated graph optimisation problem. We demonstrate that this optimisation problem is NP-hard; we further show intractability for two simpler variants of the problem. We follow these results with two parameterised algorithms that exactly solve the problem. The first is parameterised by both treewidth and maximum degree, while the second is parameterised by the maximum number of edges that can be removed and is also restricted to settings where the input graph has maximum degree three. Both of these algorithms solve not only the decision problem, but also enumerate all solutions with polynomial time precalculation, delay, and postcalculation time in respective restricted settings. For this problem, efficient enumeration allows the uncertainty in the spatial correlation to be utilised in the modelling. The first enumeration algorithm utilises dynamic programming on a tree decomposition of the input graph, and has polynomial time precalculation and linear delay if both the treewidth and maximum degree are bounded. The second algorithm is restricted to problem instances with maximum degree three, as may arise from triangulations of planar surfaces, but can output all solutions with FPT precalculation time and linear delay when the maximum number of edges that can be removed is taken as the parameter.

Game Comonads & Generalised Quantifiers

Game comonads, introduced by Abramsky, Dawar and Wang and developed by Abramsky and Shah, give an interesting categorical semantics to some Spoiler-Duplicator games that are common in finite model theory. In particular they expose connections between one-sided and two-sided games, and parameters such as treewidth and treedepth and corresponding notions of decomposition. In the present paper, we expand the realm of game comonads to logics with generalised quantifiers. In particular, we introduce a comonad graded by two parameters $n \leq k$ such that isomorphisms in the resulting Kleisli category are exactly Duplicator winning strategies in Hella's $n$-bijection game with $k$ pebbles. We define a one-sided version of this game which allows us to provide a categorical semantics for a number of logics with generalised quantifiers. We also give a novel notion of tree decomposition that emerges from the construction.

First Report of Xanthomonas euvesicatoria pv. sesami Causing Leaf Spot on Sesame (Sesamum indicum L.) in South Carolina, USA.

Sesame (Sesamum indicum L.) is an annual plant known as one of the first domesticated oilseed crops. It is cultivated worldwide, mostly in Asia, Africa, and the Americas (Singh, 2006). In August 2022 and September 2023, dark angular necrotic spots on leaves and stems (100% incidence), blights, and severe defoliation were observed in a 4-acre rainfed sesame field located in the Colleton County of South Carolina, USA (Fig. S1). Bacterial streaming from cut leaf lesions was observed from diseased plants in both years. Two plants were collected for pathogen isolation in 2023. Symptomatic leaves were surface sterilized with 70% ethanol for 1 min and dried in a laminar flow hood. For each isolate, four sterile toothpicks were used to poke lesion margins and stirred in 300 µl of sterile distilled water in a 2-ml sterile microcentrifuge tube and soaked at room temperature (c. 21 °C) for 10 min. Each bacterial suspension (10 µl) was streaked on nutrient agar (NA) in a Petri dish. Convex and mucoid yellow colonies formed after a 48-h incubation at 28°C in the dark. Two isolates (S813 and S814), one from each plant, were obtained by transferring single colonies to new NA plates. Both isolates were preliminarily identified as Xanthomonas [S813: X. campestris (P = 0.53); S814: X. campestris (P = 0.77)] using a Biolog Microbial Identification System (GEN III Microplate; Identification Database v.2.8.0.15G). PCR amplification of the atpD and dnaK genes was performed for both isolates using the conditions described in Félix-Gastélum et al. (2019). The sequences of both amplicons are 100% identical for each gene between the two isolates. PCR and sequencing of the gyrB gene was also done for S813 with the primers from Young et al. (2008). The atpD (S813/S814), dnaK (S813/S814), and gyrB (S813) sequences (GenBank accessions: PP507118 to PP507120) showed the best match with 100% identity to the corresponding gene sequences [GenBank accessions: KJ491167 (100% coverage), KJ491257 (99% coverage), EU285201 (100% coverage)] of the X. euvesicatoria pv. sesami (=X. campestris pv. sesami) type strain LMG865 (Constantin et al. 2015, Parkinson et al. 2009). A neighbor joining tree with the concatenated sequences of these three genes (2,210 nt) showed that S813 and LMG 865 had the closet relationship with X. euvesicatoria pv. alfalfae (CFBP3836, Fig. S2). To fulfill Koch's postulates, three healthy sesame plants (cultivar Shirogoma) were spray inoculated separately with each suspension of S813 and S814 in sterile tap water until runoff (approx. 5×108 CFU/ml). Two sesame plants were sprayed with sterile tap water and served as negative control. All plants were maintained in a greenhouse at approximately 28/20°C (day/night) with natural photoperiod. Dark leaf spots and leaf yellowing were observed on inoculated plants 7 to 14 days after inoculation. No disease symptom was observed on the control plants. Bacteria were reisolated from leaf spots of the inoculated plants and confirmed to be X. euvesicatoria pv. sesami based on atpD and dnaK sequences. The disease was first reported in Sudan (Sabet and Dowson, 1960), after which it was reported in USA (Isakeit et al., 2012) and Mexico (Félix-Gastélum et al. 2019). To the best of our knowledge, this is the first report of this disease in South Carolina, USA. Since the interest of sesame to the farmers is increasing in the southeastern USA, it is necessary to perform further research to examine the disease distribution and its economic impact.

Insights into the genomic homogeneity of Moroccan indigenous sheep breeds though the lens of runs of homozygosity

Numerous studies have indicated that Morocco’s indigenous sheep breeds are genetically homogenous, posing a risk to their survival in the challenging harsh climate conditions where they predominantly inhabit. To understand the genetic behind genetic homogeneity through the lens of runs of homozygosity (ROH), we analyzed the whole genome sequences of five indigenous sheep breeds (Beni Guil, Ouled Djellal, D’man, Sardi, Timahdite and Admixed).The results from principal component, admixture, Fst, and neighbour joining tree analyses consistently showed a homogenous genetic structure. This structure was characterized by an average length of 1.83 Mb for runs of homozygosity (ROH) segments, with a limited number of long ROH segments (24–48 Mb and > 48 Mb). The most common ROH segments were those ranging from 1–6 Mb. The most significant regions of homozygosity (ROH Islands) were mostly observed in two chromosomes, namely Chr1 and Chr5. Specifically, ROH Islands were exclusively discovered in the Ouled Djellal breed on Chr1, whereas Chr5 exhibited ROH Islands in all breeds. The analysis of ROH Island and iHS technique was employed to detect signatures of selection on Chr1 and Chr5. The results indicate that Chr5 had a high level of homogeneity, with the same genes being discovered across all breeds. In contrast, Chr1 displays some genetic variances between breeds. Genes identified on Chr5 included SLC39A1, IL23A, CAST, IL5, IL13, and IL4 which are responsible for immune response while genes identified on Chr1 include SOD1, SLAMF9, RTP4, CLDN1, and PRKAA2. ROH segment profile and effective population sizes patterns suggests that the genetic uniformity of studied breeds is the outcome of events that transpired between 250 and 300 generations ago. This research not only contributes to the understanding of ROH distribution across breeds but helps design and implement native sheep breeding and conservation strategies in Morocco. Future research, incorporating a broader sample size and utilizing the pangenome for reference, is recommended to further elucidate these breeds’ genomic landscapes and adaptive mechanisms.

A Deep Learning Image Corrosion Classification Method for Marine Vessels Using an Eigen Tree Hierarchy Module

This paper involves the automation of a visual characterisation technique for corrosion in marine vessels, as it appears in the hull preventive coatings of marine vessels and their surfaces. We propose a module that maximizes the utilisation of features learned by a deep convolutional neural network to identify areas of corrosion and segment pixels in regions of inspection interest for corrosion detection. Our segmentation module is based on Eigen tree decomposition and information-based decision criteria in order to produce specific corroded spots—regions of interest. To assess performance and compare it with our method, we utilize several state-of-the-art deep learning architectures.The results indicate that our method achieves higher accuracy and precision while maintaining the significance score across the entire dataset. To the best of our knowledge, this is the first Eigen tree-based module in the literature in the context of trained neural network predictors for classifying corrosion in marine vessel images.

DNA barcoding for identification of forensically important synanthropic flesh flies (Diptera: Sarcophagidae) from Eastern India

ABSTRACT Sarcophagidae is a significant Diptera family because several of its species are among the first to visit a corpse, and it helps in minPMI estimation. Sarcophagidae species identification for a layman is difficult due to identical morphological appearance and if the fly is a female. Also, fly specimens get damaged due to improper storage of forensic specimens collected from crime scenes. Thus, in this study, we aimed to check the efficiency of cytochrome oxidase 1 (COI) for identifying eleven sarcophagid flies species. Flesh flies were collected from various biogeographic regions of West Bengal. COI barcodes successfully differentiated between species with a very significant K2P interspecific genetic divergence, which ranged between 3.12% and 20.11%, and intraspecific genetic divergences ranged from 0% to 1%. The subgenera Uroxanthisca and Sinonipponia are used in the phylogenetic analysis for the first time in the oriental context. Phylogenetic analysis was performed using a Neighbour Joining (NJ) tree constructed using Kimura two-parameter (K2P) in MEGA X software. Thus, COI barcodes proved to be quite effective as an alternate method of identifying flesh fly species, and future studies should include additional markers for further phylogenetic investigations of the Sarcophagidae family.

Using Earley Parser for Verification of Totally Ordered Hierarchical Plans

Hierarchical planning extends classical planning by capturing the hierarchical structure of tasks via decomposition of tasks to subtasks. Hierarchical plan verification is the problem of determining whether a given plan is valid according to that structure. As decomposition trees in totally ordered hierarchical planning domains resemble parsing trees of context-free grammars, one may exploit the techniques for context-free grammars also for hierarchical plans. In this paper, we study how the Earley parser, proposed for checking whether a given word belongs to a language defined by context-free grammar, can be extended to verification of totally ordered hierarchical plans.

Voronoi-based splinegon decomposition and shortest-path tree computation

In motion planning, two-dimensional (2D) splinegons are typically used to represent the contours of 2D objects. In general, a 2D splinegon must be pre-decomposed to support rapid queries of the shortest paths or visibility. Herein, we propose a new region decomposition strategy, known as the Voronoi-based decomposition (VBD), based on the Voronoi diagram of curved boundary-segment generators (either convex or concave). The number of regions in the VBD is O(n+c1). Compared with the well-established horizontal visibility decomposition (HVD), whose complexity is O(n+c2), the VBD decomposition generally contains less regions because c1≤c2, where n is the number of the vertices of the input splinegon, and c1 and c2 are the number of inserted vertices at the boundary. We systematically discuss the usage of VBD. Based on the VBD, the shortest path tree (SPT) can be computed in linear time. Statistics show that the VBD performs faster than HVD in SPT computations. Additionally, based on the SPT, we design algorithms that can rapidly compute the visibility between two points, the visible area of a point/line-segment, and the shortest path between two points.

Reduced Clique Graphs: A Correction to “Chordal Graphs and Their Clique Graphs”

Galinier, Habib, and Paul introduced the reduced clique graph of a chordal graph G. The nodes of the reduced clique graph are the maximal cliques of G, and two nodes are joined by an edge if and only if they form a non-disjoint separating pair of cliques in G. In this case the weight of the edge is the size of the intersection of the two cliques. A clique tree of G is a tree with the maximal cliques of G as its nodes, where for any v∈V(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v\\in V(G)$$\\end{document}, the subgraph induced by the nodes containing v is connected. Galinier et al. prove that a spanning tree of the reduced clique graph is a clique tree if and only if it has maximum weight, but their proof contains an error. We explain and correct this error. In addition, we initiate a study of the structure of reduced clique graphs by proving that they cannot contain any induced cycle of length five (although they may contain induced cycles of length three or any even integer greater than two). We show that no cycle of length four or more is isomorphic to a reduced clique graph. We prove that the class of clique graphs of chordal graphs is not comparable to the class of reduced clique graphs of chordal graphs by providing examples that are in each of these classes without being in the other.

Contraction Decomposition in Unit Disk Graphs and Algorithmic Applications in Parameterized Complexity

We give a new decomposition theorem in unit disk graphs (UDGs) and demonstrate its applicability in the fields of Structural Graph Theory and Parameterized Complexity. First, our new decomposition theorem shows that the class of UDGs admits an “almost” Contraction Decomposition Theorem. Prior studies on this topic exhibited that the classes of planar graphs [Klein, SICOMP, 2008], graphs of bounded genus [Demaine, Hajiaghayi and Mohar, Combinatorica 2010], and H -minor free graphs [Demaine, Hajiaghayi and Kawarabayashi, STOC 2011] admit a Contraction Decomposition Theorem. Even bounded-degree UDGs can contain arbitrarily large cliques as minors, and therefore our result is a significant advance in the study of contraction decompositions. Additionally, this result answers an open question posed by Hajiaghayi ( www.youtube.com/watch?v=2Bq2gy1N01w ) regarding the existence of contraction decompositions for classes of graphs beyond H -minor free graphs though under a relaxation of the original formulation. Second, we present a “parameteric version” of our new decomposition theorem. We prove that there is an algorithm that, given a UDG G and a positive integer k , runs in polynomial time and outputs a collection of \(\mathcal {O}(k)\) tree decompositions of G with the following properties. Each bag in any of these tree decompositions can be partitioned into \(\mathcal {O}(k)\) connected pieces (we call this measure the chunkiness of the tree decomposition). Moreover, for any subset S of at most k edges in G , there is a tree decomposition in the collection such that S is well preserved in the decomposition in the following sense. For any bag in the tree decomposition and any edge in S with both endpoints in the bag, either its endpoints lie in different pieces or they lie in a piece that is a clique. Having this decomposition at hand, we show that the design of parameterized algorithms for some cut problems becomes elementary. In particular, our algorithmic applications include single-exponential (or slightly super-exponential) algorithms for well-studied problems such as Min Bisection , Steiner Cut , s -Way Cut , and Edge Multiway Cut-Uncut on UDGs; these algorithms are substantially faster than the best-known algorithms for these problems on general graphs.

Induced Subgraphs and Tree Decompositions VIII: Excluding a Forest in (Theta, Prism)-Free Graphs

Induced Subgraphs and Tree Decompositions VIII: Excluding a Forest in (Theta, Prism)-Free Graphs

The Graft Transformation and Their Application on the Spectral Radius of Block Graphs

Let [Formula: see text] be a connected graph and [Formula: see text] be the adjacency matrix of [Formula: see text]. Suppose that [Formula: see text] are the eigenvalues of [Formula: see text]. In this paper, we first give a graft transformation on the spectral radius of graphs and then as their application, we determine the extremal graphs with maximum and minimum spectral radii among all clique trees. Furthermore, we also determine the unique graph with maximum spectral radius among all block graphs by using different methods.

Genetic diversity, population structure and marker-trait associations in Indian kale (Brassica oleracea L. gp. acephala) using cross-species microsatellite markers

Kale is known for its exceptional nourishing and functional benefits to human body. However, it is an understudied species from genomic as well as agronomic aspects. It is important to characterize niche kale germplasms around the world to systematically conserve and utilize its genetic variability, especially for commercial traits in the interest of growers, consumers and industry. With this view, genomic and phenotypic characterizations of 62 Kashmiri kale accessions including popular landraces were done to estimate and partition genetic diversity, understand trait relationships, develop population structure and divulge marker-trait associations of economic significance. Sixty-six cross species microsatellite (SSR) markers within Brassica genus amplified 269 alleles in the germplasm. Their polymorphic information content (PIC) ranged from 0.00078 to 0.953 with an average of 0.407. The population structure analysis and neighbour joining tree clustering categorized the germplasm into three sub-populations. AMOVA revealed more within-population variance (67.73 %) than among-populations (32.27 %) variance. The principal component analysis (PCA) involving 24 agronomical traits revealed seven PCs (PC1 to PC7) having Eigen values more than 1, which explained a cumulative variation of 69.21 %. Association mapping with respect to these 24 agronomical traits using mixed linear model and general linear model revealed six overlapping significant marker-trait relationships with five being significant at probability value of 0.001/0.0001. The highly significant associations of two SSRs with economically important traits (siliqua length and seed weight) significantly correlated/related with leaf yield and seed yield were revealed for their possible utilization in marker assisted breeding for higher leaf and seed yields.