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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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The genomes of eukaryotes are punctuated by long stretches of sequence which do not code for proteins or RNAs. Although some of these regions do contain crucial regulatory sequences, the vast majority of this DNA serves no known function. Typically, these regions of the genome are the ones in which the fastest change, in evolutionary terms, is observed, because there is typically little to no selection pressure acting on these regions to preserve their sequences.
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Algebraic Invariants for Inferring 4-Leaf Semi-Directed Phylogenetic Networks.

Samuel Martin1,2, Niels Holtgrefe3, Vincent Moulton4

  • 1European Bioinformatics Institute (EMBL-EBI), Wellcome Genome Campus, Hinxton, Cambridge CB10 1SD, UK.

Systematic Biology
|October 15, 2025
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Summary
This summary is machine-generated.

This study presents an algebraic method for inferring semi-directed phylogenetic networks from nucleotide sequences. The method accurately identifies undirected networks with 10kbp sequences and semi-directed networks with 10Mbp sequences.

Keywords:
Phylogenetic invariantsphylogenetic networksemi-directed network

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Area of Science:

  • Evolutionary biology
  • Computational phylogenetics
  • Bioinformatics

Background:

  • Phylogenomics aims to reconstruct species evolutionary history using sequence data.
  • Phylogenetic networks model complex evolutionary events but are challenging to infer.
  • Semi-directed phylogenetic networks are of growing interest, often built by combining smaller networks.

Purpose of the Study:

  • To investigate an algebraic method for inferring semi-directed phylogenetic networks.
  • To analyze leaf-pattern probabilities for phylogenetic network inference.
  • To assess the method's accuracy with varying sequence lengths.

Main Methods:

  • Utilized an algebraic approach analyzing leaf-pattern probabilities.
  • Applied the method to infer 4-leaf semi-directed phylogenetic networks from nucleotide sequences.
  • Tested the method on simulated data and a real dataset from Xiphophorus species.

Main Results:

  • Accurate identification of undirected phylogenetic networks with sequences >= 10kbp.
  • Accurate identification of semi-directed phylogenetic networks requires sequences approaching 10Mbp.
  • Successfully identified tree-like evolution and underlying trees, and applied to Xiphophorus data.

Conclusions:

  • The algebraic method is effective for inferring phylogenetic networks, particularly undirected ones.
  • Inferring semi-directed networks is more data-intensive, requiring significantly longer sequences.
  • The approach is valuable for both simulated and real-world phylogenetic analyses.