Journal of the Australian Mathematical Society (Series A)

Research Article

An infinite alleles version of the Markov branching process

Anthony G. Pakesa1

a1 Department of Mathematics University of Western Australia Nedlands, W. A. 6009, Australia

Abstract

Individuals in a population which grows according to the rules defining the Markov branching process can mutate into novel allelic forms. We obtain some results about the time of the last mutation and the limiting frequency spectrum. In the present context these results refine certain results obtained in the discrete time case and they answer some conjectures still unresolved for the discrete time case.

(Received April 16 1987)

1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision)

  • 60 J 80;
  • 92 A 10

Keywords and phrases

  • Markov branching process;
  • infinite alleles mode.