Search PubMed⌕ Search
Home/Archive/PubMed

PubMed · 10942605

A rapid heuristic algorithm for finding minimum evolution trees.

A Rodin·W H Li
View original source ↗Export metadata ↓

Abstract

The minimum sum of branch lengths (S), or the minimum evolution (ME) principle, has been shown to be a good optimization criterion in phylogenetic inference. Unfortunately, the number of topologies to be analyzed is computationally prohibitive when a large number of taxa are involved. Therefore, simplified, heuristic methods, such as the neighbor-joining (NJ) method, are usually employed instead. The NJ method analyzes only a small number of trees (compared with the size of the entire search space); so, the tree obtained may not be the ME tree (for which the S value is minimum over the entire search space). Different compromises between very restrictive and exhaustive search spaces have been proposed recently. In particular, the "stepwise algorithm" (SA) utilizes what is known in computer science as the "beam search," whereas the NJ method employs a "greedy search." SA is virtually guaranteed to find the ME trees while being much faster than exhaustive search algorithms. In this study we propose an even faster method for finding the ME tree. The new algorithm adjusts its search exhaustiveness (from greedy to complete) according to the statistical reliability of the tree node being reconstructed. It is also virtually guaranteed to find the ME tree. The performances and computational efficiencies of ME, SA, NJ, and our new method were compared in extensive simulation studies. The new algorithm was found to perform practically as well as the SA (and, therefore, ME) methods and slightly better than the NJ method. For searching for the globally optimal ME tree, the new algorithm is significantly faster than existing ones, thus making it relatively practical for obtaining all trees with an S value equal to or smaller than that of the NJ tree, even when a large number of taxa is involved.

Explore related subjects

AlgorithmsBiological EvolutionModels, StatisticalModels, TheoreticalPhylogenySoftwareJournal ArticleResearch Support, U.S. Gov't, P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A Rodin, W H Li. 2000. A rapid heuristic algorithm for finding minimum evolution trees.. https://doi.org/10.1006/mpev.1999.0728

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2026

A note on a generalized single step theory for any number of hierarchical genomic matrices.

BACKGROUND: The Single Step algorithm allows combining information from genotyped and un-genotyped individuals, provided they are connected by a pedigree. However, current single step theory is limited to a single list of markers. RESULTS: We present a generalized single step (GSS) method that can accommodate any number of hierarchical molecular datasets (e.g. sequence, high and low density arrays) and pedigree, avoiding imputation. We prove that a similar efficient inversion algorithm exists. The method is recursive, starting with the highest marker density scenario. We illustrate the method with simulation and show that GSS can increase predictive accuracy compared to standard single step. R code is provided so that custom scenarios can be easily compared, either with simulated or real data. CONCLUSION: The method developed generalizes extant single step theory to any number of hierarchical molecular relationship matrices, broadening the scenarios where single step can be applied. A topic of particular interest can be ecology field data or human populations where pedigree is not available, but where samples sequenced and genotyped at different densities can exist. GSS can also be a useful tool to optimize allocation of genotyping and / or sequencing resources.

Algorithms↗
PubMed2026

cgDist: Nucleotide-level distance calculation from cgMLST allelic profiles.

Bacterial genomic surveillance requires balancing computational efficiency with genetic resolution for effective cluster investigation. cgMLST distance calculations treat all allelic differences as equivalent units, obscuring nucleotide-level variation. Furthermore, single nucleotide polymorphism-based pipelines provide finer resolution at substantially higher computational cost, which limits their routine deployment in surveillance laboratories. We present cgDist, an algorithm that calculates nucleotide-level distances directly from cgMLST allelic profiles, providing finer resolution than allele-count distances by leveraging within-allele nucleotide variation. The cache architecture stores alignment statistics, enabling distance calculation modes without computation and supporting both dataset-specific and schema-complete cache generation. This design enables incremental surveillance analysis, with performance benefits as laboratories accumulate alignment data. cgDist functions as a precision 'zoom lens' for the investigation of clusters identified through initial cgMLST screening. Rather than restructuring population relationships, this targeted approach concentrates enhanced resolution where it is most informative. The algorithm ensures that cgDist distances are greater than or equal to corresponding cgMLST distances, preserving epidemiological interpretability while adding genetic discrimination. By increasing resolution within identified clusters, cgDist may also support outbreak investigation, a potential application that remains to be evaluated on outbreak-derived data.

Algorithms↗
PubMed2026

Theseus: fast and optimal affine-gap sequence-to-graph alignment.

MOTIVATION: Sequence-to-graph alignment is a central problem in bioinformatics, with applications in multiple sequence alignment (MSA) and pangenome analysis, among others. However, current algorithms for optimal affine-gap alignment impose high memory and computational requirements, limiting their scalability to aligning long sequences to complex graphs. Practical solutions partially address this problem using heuristic strategies that ultimately trade off optimality for speed. RESULTS: This work presents Theseus, a novel, fast, and optimal affine-gap sequence-to-graph alignment algorithm. Theseus leverages similarities between genomic sequences to accelerate the alignment computation and reduces the overall memory requirements without compromising optimality. To that end, Theseus processes only a subset of the dynamic programming cells, using a sparse-data strategy that enables efficient sequence-to-graph alignment. Moreover, our algorithm supports optimal affine-gap alignment on arbitrary directed graphs, including those with cycles. We evaluate Theseus on two key problems: MSA and pangenome read mapping. For MSA, we compare it against SPOA, abPOA, and POASTA. Theseus is 1.6× to 17.6× faster than POASTA, and 7.3× faster, on average, than SPOA, both optimal aligners. Compared with abPOA, Theseus ensures optimality and scales to the largest problems. For pangenome read mapping, we benchmark Theseus against the alignment stage of the mapping tool vg map, along with the alignment kernels of SPOA, abPOA, and POASTA. Theseus outperforms the other methods, showing a 1.9× to 16.9× speedup on short reads. Moreover, Theseus is 1.5× to 36.3× faster than vg when aligning against synthetic cyclic graphs. AVAILABILITY AND IMPLEMENTATION: Theseus code and documentation are publicly available at https://github.com/albertjimenezbl/theseus-lib.

Algorithms↗