Skip to main content Accessibility help

A simple model for the balance between selection and mutation

  • J. F. C. Kingman (a1)


A model for the variation in time of the fitness distribution in a large haploid population is shown to have simple limiting properties which can be elucidated in fairly explicit terms. The novel feature is that mutation is not assumed to cause a small perturbation in fitness but to bring down the evolutionary ‘house of cards’. A threshold phenomenon appears: if a certain inequality holds the limiting distribution is a skewed version of the mutant fitness distribution, but otherwise an atom of probability builds up at the upper limit of fitness.



Hide All
[1] Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theoret. Pop. Biol. 3, 87112.
[2] Kingman, J. F. C. (1976) Markov transition probabilities II: completely monotonic functions. Z. Wahrscheinlichkeitsth. 9, 19.
[3] Kingman, J. F. C. (1972) Regenerative Phenomena. Wiley, London.
[4] Kingman, J. F. C. (1972) Semi-p-functions. Trans. Amer. Math. Soc. 174, 257273.
[5] Kingman, J. F. C. (1977) The population structure associated with the Ewens sampling formula. Theoret. Pop. Biol. 11, 274283.
[6] Kingman, J. F. C. (1977) On the properties of bilinear models for the balance between genetic mutation and selection. Proc. Camb. Phil. Soc. 81, 443453.
[7] Moran, P. A. P. (1976) Global stability of genetic systems governed by mutation and selection. Proc. Camb. Phil. Soc. 80, 331336.
[8] Moran, P. A. P. (1976) A selective model for electrophoretic profiles in protein polymorphisms. Genet. Res. 28, 4754.
[9] Moran, P. A. P. (1977) Global stability of genetic systems governed by mutation and selection II. Proc. Camb. Phil. Soc. 81, 435441.
[10] Ohta, T. and Kimura, M. (1973) A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet. Res. 22, 201204.
[11] Reuter, G. E. H. (1956) Über eine Volterrasche Integralgleichung mit totalmonotonem Kern. Arch. Math. 7, 5966.
[12] Watterson, G. A. (1976) The stationary distribution of the infinitely-many neutral alleles diffusion model. J. Appl. Prob. 13, 639651.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed