Biology & Philosophy

, Volume 29, Issue 2, pp 197–205 | Cite as

Grafen, the Price equations, fitness maximization, optimisation and the fundamental theorem of natural selection

  • Warren J. EwensEmail author


This paper is a commentary on the focal article by Grafen and on earlier papers of his on which many of the results of this focal paper depend. Thus it is in effect a commentary on the “formal Darwinian project”, the focus of this sequence of papers. Several problems with this sequence are raised and discussed. The first of these concerns fitness maximization. It is often claimed in these papers that natural selection leads to a maximization of fitness and that this view is claimed in Fisher’s “fundamental theorem of natural selection”. These claims are refuted, and various incorrect statements about the meaning and interpretation of the fundamental theorem of natural selection, in this sequence and in other papers by other authors, are discussed. Next, much of the work in this sequence rests on the first Price equation. In the deterministic (infinite population) case this equation is no more than the standard classical equation relating to changes in gene frequencies. In the stochastic case the equation gives the change in gene frequencies as the sum of two terms (the second of which vanishes in the deterministic case). These two terms are of essentially equal importance in the situation considered in the focal article, yet one of Grafen’s results ignores the second term in the stochastic analysis. This is associated with a wavering between deterministic and stochastic analyses and the use of the Price fitness concept and the classical fitness concept. These comments cast doubts on Grafen’s optimization theory.


Optimization Maximization Price equations Fitness Fundamental theorem of natural selection Gene frequencies 


  1. Ewens WJ (1976) Remarks on the evolutionary effects of natural selection. Genetics 83:601–607Google Scholar
  2. Ewens WJ (1979) Mathematical population genetics. Springer, New YorkGoogle Scholar
  3. Ewens WJ (1992) An optimizing principle of natural selection in evolutionary population genetics. Theor Popul Biol 42:333–346CrossRefGoogle Scholar
  4. EwensWJ (2004) Mathematical population genetics. I. Theoretical Introduction, (second revised edition). Springer, New YorkGoogle Scholar
  5. Ewens WJ (2011) What is the gene trying to do? Br J Philos Sci 62:155–176CrossRefGoogle Scholar
  6. Fisher RA (1930) The genetical theory of natural selection. Oxford University Press, OxfordGoogle Scholar
  7. Frank SA (1997) The Price equation, Fisher’s fundamental theorem, kin selection, and causal analysis. Evolution 51(6):1712–1729CrossRefGoogle Scholar
  8. Gardner A (2008) The Price equation. Curr Biol 18:R198–R202CrossRefGoogle Scholar
  9. Gardner A (2009) Adaptation as organism design. Biol Lett 5:861–864CrossRefGoogle Scholar
  10. Grafen A (2002) A first formal link between the Price equation and an optimization program. J Theor Biol 217:75–91CrossRefGoogle Scholar
  11. Grafen A (2008) The simplest formal argument for fitness optimization. J Genet 87:421–433CrossRefGoogle Scholar
  12. Grafen A (2014) The formal darwinism project in outline. Biol Philos (29)2. doi: 10.1007/s10539-013-9414-y
  13. Price GR (1970) Selection and covariance. Nature 227:520–521CrossRefGoogle Scholar
  14. Price GR (1972a) Extension of covariance selection mathematics. Ann Hum Genet 35:485–490CrossRefGoogle Scholar
  15. Price GR (1972b) Fisher’s “fundamental theorem” made clear. Ann Hum Genet 36:129–140CrossRefGoogle Scholar
  16. Rice (2004) Evolutionary theory. Sinauer, Massachusetts, USA Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of BiologyThe University of PennsylvaniaPhiladelphiaUSA

Personalised recommendations