Partition Complex Research Articles

An efficient supply management in water flow network using graph spectral techniques.

An efficient way of distributing water in urban cities is one of the major global challenges of our time. A Water Distribution Network (WDN) is a vital infrastructure, intended to provide fresh water to households within a city or designated boundary. Given the WDN's complexity, effective numerical techniques are required to aid in the development of an ideal monitoring system. Flow meters and gate valves should be placed in low-connected areas of the WDN with water flow reaching several regions of the network. This study proposes a general strategy for assisting water utilities in making decisions for effective water supply. The aim of the research is to use weighted spectral clustering algorithms to outline water districts while addressing hydraulic restrictions via weighted adjacency and Laplacian matrices of the weighted network. This work aims to identify influenced nodes in the network based on Eigen centrality and effectively distribute water across those nodes. This project also looks at how to measure the network's connection strength to avoid water leaks. The best clusters are found using Eigenvalues and Eigenvectors of weighted adjacency matrices and Laplacian matrices of the water network in the proposed graph spectral framework. In order to establish the optimum water network division approach, topological and graph metrics were used to compare multiple spectral clustering techniques. The proposed graph spectral approach is tested using a genuine water distribution network serving an urban area of Coimbatore city in India and offering a method for partitioning complex networks that employ the spectral graph partitioning algorithm.

A joint-ParB interface promotes Smc DNA recruitment.

SummaryChromosomes readily unlink and segregate to daughter cells during cell division, highlighting a remarkable ability of cells to organize long DNA molecules. SMC complexes promote DNA organization by loop extrusion. In most bacteria, chromosome folding initiates at dedicated start sites marked by the ParB/parS partition complexes. Whether SMC complexes recognize a specific DNA structure in the partition complex or a protein component is unclear. By replacing genes in Bacillus subtilis with orthologous sequences from Streptococcus pneumoniae, we show that the three subunits of the bacterial Smc complex together with the ParB protein form a functional module that can organize and segregate foreign chromosomes. Using chimeric proteins and chemical cross-linking, we find that ParB directly binds the Smc subunit. We map an interface to the Smc joint and the ParB CTP-binding domain. Structure prediction indicates how the ParB clamp presents DNA to the Smc complex, presumably to initiate DNA loop extrusion.

Stochastically multimerized ParB orchestrates DNA assembly as unveiled by single-molecule analysis

The tripartite ParABS system mediates chromosome segregation in a wide range of bacteria. Dimeric ParB was proposed to nucleate on parS sites and spread to neighboring DNA. However, how properly distributed ParB dimers further compact chromosomal DNA into a higher-order nucleoprotein complex for partitioning remains poorly understood. Here, using a single-molecule approach, we show that tens of Bacillus subtilis ParB (Spo0J) proteins can stochastically multimerize on and stably bind to nonspecific DNA. The introduction of CTP promotes the formation and diffusion of the multimeric ParB along DNA, offering an opportunity for ParB proteins to further forgather and cluster. Intriguingly, ParB multimers can recognize parS motifs and are more inclined to remain immobile on them. Importantly, the ParB multimer features distinct capabilities of not only bridging two independent DNA molecules but also mediating their transportation, both of which are enhanced by the presence of either CTP or parS in the DNA. These findings shed new light on ParB dynamics in self-multimerization and DNA organization and help to better comprehend the assembly of the ParB-DNA partition complex.

Research on an Intelligent Identification and Classification Method of Complex Holes in Triangle Meshes for 3D Printing.

In triangular mesh models, the repair of complex hole poses a difficult problem, which always causes serious repair defects. Therefore, it is needed to develop an intelligent identification and classification method of complex holes to reduce repair difficulties. First, the topological structure of the complex hole is studied and all the holes are divided into single holes and continuous holes depending on whether there are intersection points. Second, to tackle the nesting and connecting of complex continuous holes, a decomposition method of multiply connected domains based on intersection points is proposed to partition or reconstruct complex continuous holes into single holes. Based on the different geometric structures, single holes are classified into five common hole types and a corresponding identification method of single holes is presented. Finally, an experiment is carried out to verify the repair quality and efficiency of the proposed method. Compared with Geomagic software, the proposed method can automatically identify and partition complex holes with fewer defects and similar efficiency. It can reduce the difficulties of repairing complex holes and enable the repair of complex holes based on existing methods. It is shown that the method can be applied to complex hole repair of 3D printing models without the participation of technicians.

MUC1 and Polarity Markers INADL and SCRIB Identify Salivary Ductal Cells

Current treatments for xerostomia/dry mouth are palliative and largely ineffective. A permanent clinical resolution is being developed to correct hyposalivation using implanted hydrogel-encapsulated salivary human stem/progenitor cells (hS/PCs) to restore functional salivary components and increase salivary flow. Pluripotent epithelial cell populations derived from hS/PCs, representing a basal stem cell population in tissue, can differentiate along either secretory acinar or fluid-transporting ductal lineages. To develop tissue-engineered salivary gland replacement tissues, it is critical to reliably identify cells in tissue and as they enter these alternative lineages. The secreted protein α-amylase, the transcription factor MIST1, and aquaporin-5 are typical markers for acinar cells, and K19 is the classical ductal marker in salivary tissue. We found that early ductal progenitors derived from hS/PCs do not express K19, and thus earlier markers were needed to distinguish these cells from acinar progenitors. Salivary ductal cells express distinct polarity complex proteins that we hypothesized could serve as lineage biomarkers to distinguish ductal cells from acinar cells in differentiating hS/PC populations. Based on our studies of primary salivary tissue, both parotid and submandibular glands, and differentiating hS/PCs, we conclude that the apical marker MUC1 along with the polarity markers INADL/PATJ and SCRIB reliably can identify ductal cells in salivary glands and in ductal progenitor populations of hS/PCs being used for salivary tissue engineering. Other markers of epithelial maturation, including E-cadherin, ZO-1, and partition complex component PAR3, are present in both ductal and acinar cells, where they can serve as general markers of differentiation but not lineage markers.

Firefly Algorithm with Mini Batch K-Means Entropy Measure for Clustering Heterogeneous Categorical Timber Data

Clustering analysis is the process of identifying similar patterns in various types of data. Heterogeneous categorical data consists of data on ordinal, nominal, binary, and Likert scales. The clustering solution for heterogeneous data clustering remains difficult due to partitioning complex and dissimilarity features. It is necessary to find a solution to high-quality clustering techniques to efficiently determine the significant features of the data. This paper emphasizes using the firefly algorithm to reduce the distance gap between features and improve clustering performance. To obtain an optimal global solution for clustering, we proposed a hybrid of mini-batch k-means (MBK) clustering-based entropy distance measures (EM) with a firefly optimization algorithm (FA). This study compares the performance of hybrid K-Means, Agglomerative, DBSCAN, and Affinity clustering models with EM and FA. The evaluation uses a variety of data from the timber perception survey dataset. In terms of performance, the proposed MBK+EM+FA has superior and most effective clustering. It achieves a higher accuracy of 96.3 percent, a 97 percent F-measure, a 98 percent precision, and a 97 percent recall. Other external assessments revealed that the Homogeneity (HOMO) is 79.14 percent, the Fowlkes-Mallows Index (FMI) is 93.07 percent, the Completeness (COMP) is 78.04 percent, and the V-Measure (VM) is 78.58 percent. Both proposed MBK+EM+FA and MBK+EM took about 0.45s and 0.35s to compute, respectively. The excellent quality of the clustering results does not justify such time constraints. Surprisingly, the proposed model reduced the distance measure of all heterogeneous features. The future model could put heterogeneous categorical data from a different domain to the test.

CTP-controlled liquid–liquid phase separation of ParB

The ParABS system is supposed to be responsible for plasmid partitioning and chromosome segregation in bacteria. ParABS ensures a high degree of fidelity in inheritance by dividing the genetic material equally between daughter cells during cell division. However, the molecular mechanisms underlying the assembly of the partition complex, representing the core of the ParABS system, are still far from being understood. Here we demonstrate that the partition complex is formed via liquid–liquid phase separation. Assembly of the partition complex is initiated by the formation of oligomeric ParB species, which in turn are regulated by CTP-binding. Phase diagrams and in vivo analysis show how the partition complex can further be spatially regulated by parS. By investigating the phylogenetic variation in phase separation and its regulation by CTP, we find a high degree of evolutionary conservation among distantly related prokaryotes. These results advance the understanding of partition complex formation and regulation in general, by confirming and extending recently proposed models.

The CTPase activity of ParB determines the size and dynamics of prokaryotic DNA partition complexes

ParB-like CTPases mediate the segregation of bacterial chromosomes and low-copy number plasmids. They act as DNA-sliding clamps that are loaded at parS motifs in the centromere of target DNA molecules and spread laterally to form large nucleoprotein complexes serving as docking points for the DNA segregation machinery. Here, we solve crystal structures of ParB in the pre- and post-hydrolysis state and illuminate the catalytic mechanism of nucleotide hydrolysis. Moreover, we identify conformational changes that underlie the CTP- and parS-dependent closure of ParB clamps. The study of CTPase-deficient ParB variants reveals that CTP hydrolysis serves to limit the sliding time of ParB clamps and thus drives the establishment of a well-defined ParB diffusion gradient across the centromere whose dynamics are critical for DNA segregation. These findings clarify the role of the ParB CTPase cycle in partition complex assembly and function and thus advance our understanding of this prototypic CTP-dependent molecular switch.

Theory of Active Intracellular Transport by DNA Relaying.

The spatiotemporal organization of bacterial cells is crucial for the active segregation of replicating chromosomes. In several species, including Caulobacter crescentus, the ATPase ParA binds to DNA and forms a gradient along the long cell axis. The ParB partition complex on the newly replicated chromosome translocates up this ParA gradient, thereby contributing to chromosome segregation. A DNA-relay mechanism-deriving from the elasticity of the fluctuating chromosome-has been proposed as the driving force for this cargo translocation, but a mechanistic theoretical description remains elusive. Here, we propose a minimal model to describe force generation by the DNA-relay mechanism over a broad range of operational conditions. Conceptually, we identify four distinct force-generation regimes characterized by their dependence on chromosome fluctuations. These relay force regimes arise from an interplay of the imposed ParA gradient, chromosome fluctuations, and an emergent friction force due to chromosome-cargo interactions.

CTP and parS coordinate ParB partition complex dynamics and ParA-ATPase activation for ParABS-mediated DNA partitioning

ParABS partition systems, comprising the centromere-like DNA sequence parS, the parS-binding ParB-CTPase, and the nucleoid-binding ParA-ATPase, ensure faithful segregation of bacterial chromosomes and low-copy-number plasmids. F-plasmid partition complexes containing ParBF and parSF move by generating and following a local concentration gradient of nucleoid-bound ParAF. However, the process through which ParBF activates ParAF-ATPase has not been defined. We studied CTP- and parSF-modulated ParAF-ParBF complex assembly, in which DNA-bound ParAF-ATP dimers are activated for ATP hydrolysis by interacting with two ParBF N-terminal domains. CTP or parSF enhances the ATPase rate without significantly accelerating ParAF-ParBF complex assembly. Together, parSF and CTP accelerate ParAF-ParBF assembly without further significant increase in ATPase rate. Magnetic-tweezers experiments showed that CTP promotes multiple ParBF loading onto parSF-containing DNA, generating condensed partition complex-like assemblies. We propose that ParBF in the partition complex adopts a conformation that enhances ParBF-ParBF and ParAF-ParBF interactions promoting efficient partitioning.

Supercoiled DNA and non-equilibrium formation of protein complexes: A quantitative model of the nucleoprotein ParBS partition complex.

ParABS, the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS-anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParBS complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS. In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional “leaky” boundaries.

The action of Young subgroups on the partition complex

We study the restrictions, the strict fixed points, and the strict quotients of the partition complex |Pi_{n}|, which is the Sigma_{n}-space attached to the poset of proper nontrivial partitions of the set {1,ldots,n}.We express the space of fixed points |Pi_{n}|^{G} in terms of subgroup posets for general Gsubset Sigma_{n} and prove a formula for the restriction of |Pi_{n}| to Young subgroups Sigma_{n_{1}}times cdotstimes Sigma_{n_{k}}. Both results follow by applying a general method, proven with discrete Morse theory, for producing equivariant branching rules on lattices with group actions.We uncover surprising links between strict Young quotients of |Pi_{n}|, commutative monoid spaces, and the cotangent fibre in derived algebraic geometry. These connections allow us to construct a cofibre sequence relating various strict quotients |Pi_{n}|^{diamond} mathbin {operatorname* {wedge }_{Sigma_{n}}^{}} (S^{ell})^{wedge n} and give a combinatorial proof of a splitting in derived algebraic geometry.Combining all our results, we decompose strict Young quotients of |Pi_{n}| in terms of “atoms” |Pi_{d}|^{diamond} mathbin {operatorname* {wedge }_{Sigma_{d}}^{}} (S^{ell})^{wedge d} for ell odd and compute their homology. We thereby also generalise Goerss’ computation of the algebraic André-Quillen homology of trivial square-zero extensions from mathbf {F}_{2} to mathbf {F}_{p} for p an odd prime.

Prediction of the remaining useful life of cutting tool using the Hurst exponent and CNN-LSTM

To enhance production quality, productivity and energy consumption, it is paramount to predict the remaining useful life (RUL) of a cutting tool accurately and efficiently. Deep learning algorithm-driven approaches have been actively explored in the research field though there are still potential areas to further enhance the performance of the approaches. In this research, to improve accuracy and expedite computational efficiency for predicting the RUL of cutting tools, a novel systematic methodology is designed to integrate strategies of signal partition and deep learning for effectively processing and analysing multi-sourced sensor signals collected throughout the lifecycle of a cutting tool. In more detail, the methodology consists of two sub-systems: (i) a Hurst exponent–based method is developed to effectively partition complex and multi-sourced signals along the tool wear evolution, and (ii) a hybrid CNN-LSTM algorithm is designed to combine feature extraction, fusion and regression in a systematic means to facilitate the prediction based on segmented signals. The system was validated using a case study with a large set of databases with multiple cutting tools and multi-sourced signals. Comprehensive comparisons between the proposed methodology and some other mainstream algorithms, such as CNN, LSTM, DNN and PCA, were carried out under the conditions of partitioned and unpartitioned signals. Benchmarks showed that, based on the case study in this research, the prediction accuracy of the proposed methodology reached 87.3%, which is significantly better than those of the comparative algorithms.

Nonspecific DNA binding by P1 ParA determines the distribution of plasmid partition and repressor activities

The faithful segregation, or "partition," of many low-copy number bacterial plasmids is driven by plasmid-encoded ATPases that are represented by the P1 plasmid ParA protein. ParA binds to the bacterial nucleoid via an ATP-dependent nonspecific DNA (nsDNA)-binding activity, which is essential for partition. ParA also has a site-specific DNA-binding activity to the par operator (parOP), which requires either ATP or ADP, and which is essential for it to act as a transcriptional repressor but is dispensable for partition. Here we examine how DNA binding by ParA contributes to the relative distribution of its plasmid partition and repressor activities, using a ParA with an alanine substitution at Arg351, a residue previously predicted to participate in site-specific DNA binding. In vivo, the parAR351A allele is compromised for partition, but its repressor activity is dramatically improved so that it behaves as a "super-repressor." In vitro, ParAR351A binds and hydrolyzes ATP, and undergoes a specific conformational change required for nsDNA binding, but its nsDNA-binding activity is significantly damaged. This defect in turn significantly reduces the assembly and stability of partition complexes formed by the interaction of ParA with ParB, the centromere-binding protein, and DNA. In contrast, the R351A change shows only a mild defect in site-specific DNA binding. We conclude that the partition defect is due to altered nsDNA binding kinetics and affinity for the bacterial chromosome. Furthermore, the super-repressor phenotype is explained by an increased pool of non-nucleoid bound ParA that is competent to bind parOP and repress transcription.

Physical Modeling of a Sliding Clamp Mechanism for the Spreading of ParB at Short Genomic Distance from Bacterial Centromere Sites.

SummaryBacterial ParB partitioning proteins involved in chromosomes and low-copy-number plasmid segregation are cytosine triphosphate (CTP)-dependent molecular switches. CTP-binding converts ParB dimers to DNA clamps, allowing unidimensional diffusion along the DNA. This sliding property has been proposed to explain the ParB spreading over large distances from parS centromere sites where ParB is specifically loaded. We modeled such a “clamping and sliding” mechanism as a typical reaction-diffusion system, compared it to the F plasmid ParB DNA binding pattern, and found that it can account neither for the long range of ParB binding to DNA nor for the rapid assembly kinetics observed in vivo after parS duplication. Also, it predicts a strong effect on the F plasmid ParB binding pattern from the presence of a roadblock that is not observed in ChIP-sequencing (ChIP-seq). We conclude that although “clamping and sliding” can occur at short distances from parS, another mechanism must apply for ParB recruitment at larger genomic distances.

Parallelization of network motif discovery using star contraction

Network motifs are widely used to uncover structural design principles of complex networks. Current sequential network motif discovery algorithms become inefficient as motif size grows, thus parallelization methods have been proposed in the literature. In this study, we use star contraction algorithm to partition complex networks efficiently for parallel discovery of network motifs. We propose two new heuristics to make star contraction more suitable for partitioning of complex networks. The effectiveness of our partitioning strategies is verified using the ESU algorithm for subgraph counting. We also propose a ghost vertices detection algorithm to ensure that all the motifs located in multiple parts are exactly found. We implement our method using MPI libraries and tested on real-life complex networks of different domains. We compared speedups of star contraction algorithm with speedups of other graph partitioning algorithms. Our algorithm obtained better speedups than those of other partitioning algorithms for most cases. Our algorithm provides significant speedups when compared to sequential ESU algorithm allowing discovery of larger network motifs.

Multi-omics strategies and prospects to enhance seed quality and nutritional traits in pigeonpea

Food and nutritional security are an essential goals for the entire global population during climate change scenarios. These twin challenges can be addressed by expanding the global cropping system by promoting grain and legume crops, especially pulses in India. Legume seeds are known as “meat for vegetarian diets”. Ever-increasing pigeonpea consumption as a major source of protein necessitates the improvement of varieties for more efficient production. Pigeonpea is an important legume crop with high protein content and nutritional attributes for more than a billion people living in South Asia. This hardy legume has a considerable potential positive impact on the lives of poor farmers as compared to other legumes, due to better productivity under extreme environmental conditions such as heat, drought and low soil fertility. However, pigeonpea productivity is still low for decades because of sparse utilization of landraces and wild pigeonpea germplasm as genetic and genomic resources. Recent advances in next-generation sequencing, together with other “omics” technologies have significantly reinforced pigeonpea research. Despite the remarkable progress in these technologies, the analysis and mining of existing seed genomics data are still challenging due to the complexity of genetic inheritance, metabolic partitioning, and developmental regulations. The integration of “omics tools” is an effective strategy to discover critical regulators of various seed traits. To utilize its potential, a coordinated and comprehensive evaluation of germplasm is required. Identification of potential genes/alleles governing complex traits of seed quality and nutritional content such as seed weight, seed size, seed color, total protein content, amino acid, antioxidant, resistant starch and disease resistance are essential in genomic selection for quality trait improvement of pigeonpea. Therefore, we need to understand these complex genetic architectures of qualitative and quantitative traits in pigeonpea for the development of nutrient-dense varieties for value addition. It helps in reducing malnutrition, protein, energy, and amino acid deficiency in food and feed related problems that are common in the majority of the population and more specific to developing countries. In this review, a comprehensive discussion on recent advances in “omics” approaches, their use in pigeonpea seed quality, and nutritional trait investigations are presented along with the available databases and technological platforms and their applicability in the improvement of pigeonpea. This article highlights the catalog of important available resources to improve the knowledge base and its future utilization in pigeonpea crop improvement programs.

Разбиение сложных задач на подзадачи в процессе планирования целенаправленного поведения интегрального беспилотного летательного аппарата в пространстве состояний

Обозначены основные проблемы, связанные с разработкой интеллектуального решателя задач автоматической системы управления целенаправленным поведением интегрального беспилотного летательного аппарата в наземной проблемной среде. Рассмотрена конструкция типовых элементов представления знаний безотносительно к конкретной предметной области, позволяющих автономному беспилотному летальному аппарату, оснащенному манипулятором и системой технического зрения, решать сложные задачи в априори неописанных проблемных средах. Разработаны инструментальные средства разбиения сложных задач на подзадачи, обеспечивающие эффективный поиск их решения в пространстве состояний на основе типовых элементов представления знаний. Сформулированы основные методические положения, позволяющие синтезировать процедуры планирования целенаправленного поведения интегрального беспилотного летательного аппарата в сложных априори неописанных условиях функционирования. The main problems associated with the development of an intelligent problem solver of an automatic control system for the goal-seeking behavior of an integral unmanned aerial vehicle in a terrestrial problem environment are identified. The design of the typical elements of knowledge representation irrelative to the specific subject area is considered, allowing an autonomous unmanned aerial vehicle equipped with a manipulator and a vision system to solve complex problems in a priori undescribed problem environments. Tools are developed for partitioning complex tasks into sub-tasks, which provide an effective search for their solutions in the state space based on typical elements of knowledge representation. The main methodological provisions are formulated that allow synthesizing the planning procedures for the goal-seeking behavior of an integral unmanned aerial vehicle in a priori undescribed complex operating conditions.

Shadowed type 2 fuzzy-based Markov model to predict shortest path with optimized waiting time

Recently, the traffic network exhibits a very critical situation due to the speedy rise of urbanization and population growth. This paper suggests a better solution for such traffic issues via delay-optimized Shortest Path Prediction (SPP) method. Even though Shadowed Type 2 (ST2) fuzzy logic works well for delay optimization with uncertain data, it causes a rise in fuzzy partitioning complexity. This motivates to development Shadowed Type 2 Fuzzy Markov (ST2FM) scheme for accurate prediction of the shortest path. In ST2FM, waiting for time optimization performed at rush junction based on ST2 fuzzy rules. Optimized path detail is periodically updated in the Transition Probability Matrix of the Markov model for SPP. Thus, ST2FM helps a node to easily identify the shortest path to reach the destination without waiting at traffic junctions. The absence of fuzzy partitioning and the use of Markov prediction greatly reduce the computational complexity of ST2FM. Matlab 2016a working environment is utilized for research implementation and results are compared with ST2 fuzzy, Interval Type 2 fuzzy and Fuzzy-based Convolution Neural Network. From this analysis, the proposed work demonstrates 96% of prediction accuracy with less error than existing works.

Gene flow and species delimitation in fishes of Western North America: Flannelmouth (Catostomus latipinnis) and Bluehead sucker (C. Pantosteus discobolus).

The delimitation of species boundaries, particularly those obscured by reticulation, is a critical step in contemporary biodiversity assessment. It is especially relevant for conservation and management of indigenous fishes in western North America, represented herein by two species with dissimilar life histories codistributed in the highly modified Colorado River (i.e., flannelmouth sucker, Catostomus latipinnis; bluehead sucker, C. (Pantosteus) discobolus). To quantify phylogenomic patterns and examine proposed taxonomic revisions, we first employed double‐digest restriction site‐associated DNA sequencing (ddRAD), yielding 39,755 unlinked SNPs across 139 samples. These were subsequently evaluated with multiple analytical approaches and by contrasting life history data. Three phylogenetic methods and a Bayesian assignment test highlighted similar phylogenomic patterns in each, but with considerable difference in presumed times of divergence. Three lineages were detected in bluehead sucker, supporting elevation of C. (P.) virescens to species status and recognizing C. (P.) discobolus yarrowi (Zuni bluehead sucker) as a discrete entity. Admixture in the latter necessitated a reevaluation of its contemporary and historic distributions, underscoring how biodiversity identification can be confounded by complex evolutionary histories. In addition, we defined three separate flannelmouth sucker lineages as ESUs (evolutionarily significant units), given limited phenotypic and genetic differentiation, contemporary isolation, and lack of concordance (per the genealogical concordance component of the phylogenetic species concept). Introgression was diagnosed in both species, with the Little Colorado and Virgin rivers in particular. Our diagnostic methods, and the agreement of our SNPs with previous morphological, enzymatic, and mitochondrial work, allowed us to partition complex evolutionary histories into requisite components, such as isolation versus secondary contact.