{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:10:04Z","timestamp":1760202604960},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advs. Complex Syst."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p>Although much progress has been made in recent years in describing the dynamics of genetic systems, both in population genetics and evolutionary computation, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article, we propose and study perturbation theory and the renormalization group as potential tools to fill this gap. We concentrate mainly on selection\u2013mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus, however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory.<\/jats:p>","DOI":"10.1142\/s0219525909002350","type":"journal-article","created":{"date-parts":[[2009,12,28]],"date-time":"2009-12-28T09:13:38Z","timestamp":1261991618000},"page":"583-618","source":"Crossref","is-referenced-by-count":2,"title":["SYSTEMATIC APPROXIMATIONS FOR GENETIC DYNAMICS"],"prefix":"10.1142","volume":"12","author":[{"given":"CHRISTOPHER R.","family":"STEPHENS","sequence":"first","affiliation":[{"name":"Instituto de Ciencias Nucleares, Universidad Nacional Aut\u00f3noma de M\u00e9xico, A. Postal 70-543, M\u00e9xico 04510 D.F., Mexico"},{"name":"Centro de Ciencias de la Complejidad, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Torre de Ingenier\u00ed a, M\u00e9xico 04510 D.F., Mexico"}]},{"given":"ADOLFO","family":"ZAMORA","sequence":"additional","affiliation":[{"name":"Centro de Ciencias de la Complejidad, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Torre de Ingenier\u00ed a, M\u00e9xico 04510 D.F., Mexico"},{"name":"Departamento de Matem\u00e1ticas Aplicadas y Sistemas, Universidad Aut\u00f3noma Metropolitana \u2013 Cuajimalpa, M\u00e9xico 01120 D.F., Mexico"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Perturbation Techniques in Mathematics, Engineering and Physics","author":"Bellman R.","year":"2003"},{"key":"rf2","volume-title":"Matrix Analysis","author":"Bhatia R.","year":"1996"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1038\/35076523"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1093\/genetics\/109.4.799","volume":"109","author":"Hastings A.","journal-title":"Genetics"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1093\/genetics\/112.1.157","volume":"112","author":"Hastings A.","journal-title":"Genetics"},{"key":"rf7","volume-title":"Topics in Ordinary Differential Equations","author":"Lakin W. 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