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Journal of Biological Dynamics Volume 5, 2011 - Issue 3: Thomas L. Vincent Memorial Issue
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Original Articles

Darwinian dynamics and evolutionary game theory

Thomas L. Vincent Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85721, USA E-mail: [email protected]View further author information
,
Tania L.S. Vincent Alaska Pacific University, 4101 University Dr., Anchorage, AK, 99508, USACorrespondence[email protected]
&
Yosef Cohen Department of Fisheries, Wildlife and Conservation Biology, University of Minnesota, 1980 Folwell Avenue, St. Paul, MN, 55108, USA E-mail: [email protected]
Pages 215-226 | Received 09 Apr 2010, Accepted 08 Sep 2010, Published online: 29 Apr 2011

References

  • Brown , J. S. and Vincent , T. L. 1992 . Organization of predator-prey communities as an evolutionary game . Evolution , 46 : 1269 – 1283 .
  • Brown , J. S. , Cohen , Y. and Vincent , T. L. 2007 . Adaptive dynamics with vector-valued strategies . Evol. Ecol. Res. , 9 : 1 – 38 .
  • Cohen , Y. Darwinian evolutionary distributions with time-delays . Nonlinear Dyn. Syst. Theory , in press
  • Darwin , C. 1859 . The Origin of Species , London : Avenel Books .
  • Gatenby , R. A. and Vincent , T. L. 2003 . An evolutionary model of carcinogenesis . Cancer Res. , 63 : 6212 – 6220 .
  • Issacs , R. 1965 . Differential Games , New York : Wiley .
  • Maynard Smith , J. 1982 . Evolution and the Theory of Games , Cambridge : Cambridge University Press .
  • Maynard Smith , J. and Price , G. R. 1973 . The logic of animal conflict . Nature , 246 : 15 – 18 .
  • Nash , J. F. 1951 . Noncooperative games . Ann. Math , 54 : 286 – 295 .
  • Pareto , V. 1896 . Cours d'Economie Politique , Lausanne : Rouge .
  • Pontryagin , L. S. , Boltyanskii , V. G. , Gamkrelidze , R. V. and Mishchenko , E. F. 1962 . The Mathematical Theory of Optimal Processes , New York : Wiley .
  • Rael , R. C. , Constantino , R. F. , Cushing , J. M. and Vincent , T. L. 2009 . Using stage-structured evolutionary game theory to model the experimentally observed evolution of genetic polymorphism . Evol. Ecol. Res. , 11 : 141 – 151 .
  • Samuelson , L. 1997 . Evolutionary Games and Equilibrium Selection , Cambridge : MIT Press .
  • Scheel , D. and Vincent , T. L. 2009 . Life: Optimality, evolutionary, and intelligent design? . Evol. Ecol. Res. , 11 : 589 – 610 .
  • Von Neumann , J. and Morgenstern , O. 1944 . Theory of Games and Economic Behavior , New York : Wiley .
  • Vincent , T. L. and Brown , J. S. 1984 . Stability in an evolutionary game . Theor. Popul. Biol. , 26 : 408 – 427 .
  • Vincent , T. L. and Brown , J. S. 1988 . The evolution of ESS theory . Annu. Rev. Ecol. Syst. , 19 : 423 – 443 .
  • Vincent , T. L. and Brown , J. S. 2005 . Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics , Cambridge : Cambridge University Press .
  • Vincent , T. L. and Grantham , W. J. 1981 . Optimality in Parametric Systems , New York : Wiley .
  • Vincent , T. L. and Grantham , W. J. 1982 . Trajectory following methods in control system design . J. Global Optim. , 23 : 267 – 282 .
  • Vincent , T. L.S. and Vincent , T. L. 2009 . Predicting relative abundance using evolutionary game theory . Evol. Ecol. Res. , 11 : 265 – 294 .
  • Vincent , T. L. , Cohen , Y. and Brown , J. S. 1993 . Evolution via strategy dynamics . Theor. Popul. Biol. , 44 : 149 – 176 .
  • Weibull , J. W. 1997 . Evolutionary Game Theory , Cambridge : MIT Press .

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