{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:39:37Z","timestamp":1762079977360,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,18]],"date-time":"2022-12-18T00:00:00Z","timestamp":1671321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF Division of Mathematical Sciences: Statistics Program","doi-asserted-by":"publisher","award":["DMS 1916037"],"award-info":[{"award-number":["DMS 1916037"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a15120483","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T07:59:21Z","timestamp":1671436761000},"page":"483","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic Safety Radius on UPGMA"],"prefix":"10.3390","volume":"15","author":[{"given":"Ruriko","family":"Yoshida","sequence":"first","affiliation":[{"name":"Naval Postgraduate School, 1411 Cunningham Road, Monterey, CA 93943-5219, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4051-2540","authenticated-orcid":false,"given":"Lillian","family":"Paul","sequence":"additional","affiliation":[{"name":"Naval Postgraduate School, 1411 Cunningham Road, Monterey, CA 93943-5219, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Nesbitt","sequence":"additional","affiliation":[{"name":"Naval Postgraduate School, 1411 Cunningham Road, Monterey, CA 93943-5219, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Semple, C., and Steel, M. (2003). Phylogenetics, Oxford University Press. Number 22 in Mathematics and Its Applications Series.","DOI":"10.1093\/oso\/9780198509424.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1007\/s00453-015-0005-y","article-title":"A \u2018Stochastic Safety Radius\u2019 for Distance-Based Tree Reconstruction","volume":"74","author":"Gascuel","year":"2016","journal-title":"Algorithmica"},{"key":"ref_3","unstructured":"Xi, J., Xie, J., Yoshida, R., and Forcey, S. (2015). Stochastic safety radius on Neighbor-Joining method and Balanced Minimal Evolution on small trees. arXiv."},{"key":"ref_4","first-page":"72","article-title":"Mesquite: A Modular System for Evolutionary Analysis","volume":"2","author":"Maddison","year":"2009","journal-title":"Evolution"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1007\/s11538-018-0493-4","article-title":"Tropical Principal Component Analysis and its Application to Phylogenetics","volume":"81","author":"Yoshida","year":"2019","journal-title":"Bull. Math. Biol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.neunet.2022.10.002","article-title":"Tropical Support Vector Machines: Evaluations and Extension to Function Spaces","volume":"157","author":"Yoshida","year":"2023","journal-title":"Neural Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1137\/16M1079841","article-title":"Convexity in Tree Spaces","volume":"3","author":"Lin","year":"2017","journal-title":"SIAM Discret. Math"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4590","DOI":"10.1093\/bioinformatics\/btaa564","article-title":"Tropical principal component analysis on the space of phylogenetic trees","volume":"36","author":"Page","year":"2020","journal-title":"Bioinformatics"},{"key":"ref_9","unstructured":"Yoshida, R., Miura, K., Barnhill, D., and Howe, D. (2022). Tropical Density Estimation of Phylogenetic Trees. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s10013-021-00526-3","article-title":"Tree Topologies along a Tropical Line Segment","volume":"50","author":"Yoshida","year":"2022","journal-title":"Vietnam. J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1007\/s00454-022-00410-y","article-title":"Tropical Geometric Variation of Tree Shapes","volume":"68","author":"Monod","year":"2022","journal-title":"Discret. Comput. Geom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.aam.2012.10.002","article-title":"Polyhedral combinatorics of UPGMA cones","volume":"50","author":"Davidson","year":"2013","journal-title":"Adv. Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013). An Introduction to Statistical Learning: With Applications in R, Springer.","DOI":"10.1007\/978-1-4614-7138-7"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/0095-8956(74)90047-1","article-title":"A note on the metric properties of trees","volume":"17","author":"Buneman","year":"1974","journal-title":"J. Comb. Theory Ser. B."},{"key":"ref_15","first-page":"1409","article-title":"A statistical method for evaluating systematic relationships","volume":"38","author":"Sokal","year":"1958","journal-title":"Univ. Kans. Sci. Bull."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1137\/16M1101027","article-title":"L-Infinity Optimization to Linear Spaces and Phylogenetic Trees","volume":"31","author":"Bernstein","year":"2017","journal-title":"SIAM J. Discret. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1093\/bioinformatics\/bty633","article-title":"ape 5.0: An environment for modern phylogenetics and evolutionary analyses in R","volume":"35","author":"Paradis","year":"2019","journal-title":"Bioinformatics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1093\/bioinformatics\/btq706","article-title":"Phangorn: Phylogenetic analysis in R","volume":"27","author":"Schliep","year":"2011","journal-title":"Bioinformatics"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1111\/2041-210X.12760","article-title":"Intertwining phylogenetic trees and networks","volume":"8","author":"Schliep","year":"2017","journal-title":"Methods Ecol. Evol."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/12\/483\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:43:33Z","timestamp":1760147013000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/12\/483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,18]]},"references-count":19,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["a15120483"],"URL":"https:\/\/doi.org\/10.3390\/a15120483","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,12,18]]}}}