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1 results

  • Yule process approximation for the skeleton of a branching process

  • Part of
  • Neil O'Connell
  • Journal:
    Journal of Applied Probability / Volume 30 / Issue 3 / September 1993
    Published online by Cambridge University Press:
    14 July 2016, pp. 725-729
    Print publication:
    September 1993

  • The skeleton of a (super-) critical Galton-Watson process with offspring mean 1 + r, r ≧ 0, and finite offspring variance, is considered. When r = 0 it is trivial. If r > 0 is small and the time unit is taken as α /r generations (α > 0) then the skeleton can be approximated by a Yule (linear pure birth) process of rate α. This approximation can be used to study the evolution of genetic types over a long period of time in an exponentially growing population.