Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-31T15:23:00.251Z Has data issue: false hasContentIssue false
  • English
  • Français

A relaxation view of a genetic problem

Published online by Cambridge University Press:  01 July 2016

E. Seneta
E. Seneta*
Affiliation:
The Australian National University, Canberra
Get access Rights & Permissions [Opens in a new window]

Extract

Suppose where S is a compact set (of say). Let Φ (mapping S into S) and Ψ be continuous on S and such that Ψ(xk ) is monotone (non-decreasing, say) as k increases, and xk+1 = Φ(xk ). Put Ψ∗ = lim (k → ∞)Ψ(xk ); if {x k(i)}∞ i=0 is a convergent subsequence of {xk }, with a limit-point α, then Ψ∗ = Ψ(α), and and

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 716 - 720
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Edwards, A. W. F. (1977) Foundations of Mathematical Genetics. Cambridge University Press.Google Scholar
[2] Hughes, P. J. and Seneta, E. (1975) Selection equilibria in a multiallele single-locus setting. Heredity 35, 185–194.CrossRefGoogle Scholar
[3] Kingman, J. F. C. (1961) On an inequality in partial averages. Quart. J. Math. Oxford (2) 12, 78–80.Google Scholar
[4] Li, C. C. (1967) Fundamental theorem of natural selection. Nature (London) 214, 505–506.Google Scholar
[5] Ljubič, Ju. I., Maistrovskii, G. D. and Olhovskii, Ju. G. (1976) Convergence to equilibrium under the action of selection in a single locus population (in Russian). Dokl. Akad. Nauk SSSR 226, 58–60. English translation in Soviet Math. Doklady 17, 55–58.Google Scholar
[6] Moran, P. A. P. (1962) Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford. Russian annotated translation (1973), with appendix, ed. LinnikJu. V. and LjubičJu. I., Nauka, Moscow.Google Scholar
[7] Moran, P. A. P. (1967) Unsolved problems in evolutionary theory. Proc. 5th Berkeley Symp. Math. Stat. Prob. 4, 457–480.Google Scholar
[8] Mulholland, H. P. and Smith, C. A. B. (1959) An inequality arising in genetical theory. Amer. Math. Monthly 66, 673–683.CrossRefGoogle Scholar
[9] Olhovskii, Ju. G. (1973) On the application of an inequality of Lojasiewicz to the theory of relaxation processes (in Russian). Sibirsk. Mat. Ž. 14, 1134–1138. English translation in Siberian Math. J. 14, 492.Google Scholar
[10] Seneta, E. (1973) On a genetic inequality. Biometrics 29, 810–814.CrossRefGoogle Scholar
[11] Thompson, E. A. (1973) The increase in fitness inequality. Mimeographed note, 9 February 1973.Google Scholar