{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:33:59Z","timestamp":1787236439173,"version":"build-2736575974"},"reference-count":63,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>The grand challenges in biology today are being shaped by powerful high\u2010throughput technologies that have revealed the genomes of many organisms, global expression patterns of genes, and detailed information about variation within populations. We are therefore able to ask, for the first time, fundamental questions about the evolution of genomes, the structure of genes and their regulation, and the connections between genotypes and phenotypes of individuals. The answers to these questions are all predicated on progress in a variety of computational, statistical, and mathematical fields. The rapid growth in the characterization of genomes has led to the advancement of a new discipline called phylogenomics. This discipline results from the combination of two major fields in the life sciences: genomics, i.e., the study of the function and structure of genes and genomes; and molecular phylogenetics, i.e., the study of the hierarchical evolutionary relationships among organisms and their genomes. The objective of this article is to offer mathematicians a first introduction to this emerging field, and to discuss specific mathematical problems and developments arising from phylogenomics.<\/jats:p>","DOI":"10.1137\/050632634","type":"journal-article","created":{"date-parts":[[2007,4,23]],"date-time":"2007-04-23T14:28:15Z","timestamp":1177338495000},"page":"3-31","source":"Crossref","is-referenced-by-count":27,"title":["The Mathematics of Phylogenomics"],"prefix":"10.1137","volume":"49","author":[{"given":"Lior","family":"Pachter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernd","family":"Sturmfels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,1,30]]},"reference":[{"key":"R1","unstructured":"D. N. Adams,\n                      The Hitchhiker\u2019s Guide to the Galaxy\n                      , Pan Books, London, 1979."},{"key":"R2","unstructured":"M. Alexandersson, N. Bray, and L. Pachter,\n                      Pair hidden Markov models\n                      , in Encyclopedia of Genetics, Genomics, Proteomics and Bioinformatics, L. B. Jorde, P. Little, M. Dunn, and S. Subramaniam, eds., Wiley\u2010Interscience, New York, 2005; available online through Wiley Interscience."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1101\/gr.424203"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2003.08.004"},{"key":"R5","unstructured":"E. Allman and J. Rhodes,\n                      Phylogenetic Ideals and Varieties for the General Markov Model\n                      , preprint, http:\/\/www.citebase.org\/abstract?id=oai:arXiv.org:math\/0410604, 2004."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.genom.4.070802.110300"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1126\/science.1098119"},{"key":"R8","unstructured":"P. Bickel and K. Doksum,\n                      Mathematical Statistics: Basic Ideas and Selected Topics\n                      , Holden\u2010Day, San Francisco, CA, 1976."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2001.0759"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1101\/gr.1960404"},{"key":"R11","unstructured":"P. Bucher and K. Hofmann,\n                      A sequence similarity search algorithm based on a probabilistic interpretation of an alignment scoring system\n                      , in Proceedings of the Fourth International Conference on Intelligent Systems for Molecular Biology (ISMB \u201996), AAAI Press, Menlo Park, CA, 1996, pp. 44\u201351."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1006\/jmbi.1997.0951"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.96.16.9184"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"S. Chatterji and L. 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