{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:21:09Z","timestamp":1761488469686,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2010,6,28]],"date-time":"2010-06-28T00:00:00Z","timestamp":1277683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Dynamics of many complex systems can be described by replicator equations (RE). Here we present an effective method for solving a wide class of RE based on reduction theorems for models of inhomogeneous communities. The solutions of the RE minimize the discrimination information of the initial and current distributions at each point of the system trajectory, not only at the equilibrium, under time-dependent constraints. Applications to inhomogeneous versions of some conceptual models of mathematical biology (logistic and Ricker models of populations and Volterra\u2019 models of communities) are given.<\/jats:p>","DOI":"10.3390\/e12071673","type":"journal-article","created":{"date-parts":[[2010,6,29]],"date-time":"2010-06-29T11:27:26Z","timestamp":1277810846000},"page":"1673-1695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Principle of Minimum Discrimination Information and Replica Dynamics"],"prefix":"10.3390","volume":"12","author":[{"given":"Georgiy P.","family":"Karev","sequence":"first","affiliation":[{"name":"Lockheed Martin MSD, National Institutes of Health, Bldg. 38A, Rm. 5N511N, 8600 Rockville Pike, Bethesda, MD 20894, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2010,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/0022-5193(83)90445-9","article-title":"Replicator dynamics","volume":"100","author":"Schuster","year":"1983","journal-title":"J. Theor. Biol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"374","DOI":"10.4153\/CJM-1982-025-4","article-title":"Exponential Families and game dynamics","volume":"XXXIV","author":"Akin","year":"1982","journal-title":"Can. J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1090\/S0273-0979-03-00988-1","article-title":"Evolutionary game dynamics","volume":"40","author":"Hofbauer","year":"2003","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_4","unstructured":"Kullback, S. (1959). Information Theory and Statistics, John Wiley."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics I","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jaynes, E.T. (2003). Probability Theory: The Logic of Science, Cambridge University Press.","DOI":"10.1017\/CBO9780511790423"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s00285-009-0252-0","article-title":"On mathematical theory of selection: continuous time population dynamics","volume":"60","author":"Karev","year":"2010","journal-title":"J. Math. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Karev, G.P. (2010). Replicator equations and the principle of minimal production of information. Bull. Math. Biol.","DOI":"10.1007\/s11538-009-9484-9"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"931","DOI":"10.3390\/e11040931","article-title":"Maximum entropy production as an inference algorithm that translates physical assumptions into macroscopic predictions: don\u2019t shoot the messenger","volume":"11","author":"Dewar","year":"2009","journal-title":"Entropy"},{"key":"ref_10","unstructured":"Chentsov, N.N. (1982). Statistical Decision Rules and Optimal Inference, AMS."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/mmnp:2008024","article-title":"Selection theorem for systems with inheritance","volume":"2","author":"Gorban","year":"2007","journal-title":"Math. Model. Nat. Phenom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1142\/S0218202599000610","article-title":"Survival of the fittest in a generalized logistic model","volume":"9","author":"Ackleh","year":"1999","journal-title":"Math. Model. Meth. Appl. Sci."},{"key":"ref_13","first-page":"31","article-title":"Inhomogeneous maps and mathematical theory of selection","volume":"14","author":"Karev","year":"2008","journal-title":"JDEA"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bazykin, A.D. (1998). Nonlinear Dynamics of Interacting Populations, World Scientific.","DOI":"10.1142\/9789812798725"},{"key":"ref_15","first-page":"1","article-title":"Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics","volume":"3","author":"Karev","year":"2006","journal-title":"Biol. Dir."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"L371","DOI":"10.1088\/0305-4470\/38\/21\/L01","article-title":"Maximum entropy production and the fluctuation theorem","volume":"38","author":"Dewar","year":"2005","journal-title":"J. Phys. A: Math. Gen."},{"key":"ref_17","unstructured":"Klein, M.J., Kox, A.J., Renn, J., and Schulmann, R. (1993). The Collected Papers of Albert Einstein, Volume 3: The Swiss Years: Writings, 1909-1911, Princeton University Press."},{"key":"ref_18","first-page":"149","article-title":"The molecular quasi-species","volume":"75","author":"Eigen","year":"1989","journal-title":"Adv. Chem. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T. (1970). Convex Analysis, Princeton University Press.","DOI":"10.1515\/9781400873173"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/7\/1673\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:47Z","timestamp":1760220167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/7\/1673"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,28]]},"references-count":19,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2010,7]]}},"alternative-id":["e12071673"],"URL":"https:\/\/doi.org\/10.3390\/e12071673","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2010,6,28]]}}}