Chris Heyde on Branching Processes and Population Genetics

  • Eugene Seneta
Part of the Selected Works in Probability and Statistics book series (SWPS)


When Chris Heyde returned to Australia in September 1968 to take up aposition as Reader in Ted Hannan’s teaching Department of Statistics in the-thenSchool of General Studies at the Australian National University, there was still astrong trend of research into population genetics emanating from Pat Moran’spurely research department in the Institute of Advanced Studies, a directionsynthesized in Moran (1962). There was also strong activity in both departmentsin the theory of branching processes. With its common focus with populationgenetics on reproduction and extinction, it was the primary interest at thetime of the author of this commentary. A strong impetus to branchingprocess theory had occurred with the appearance of the book of Harris(1963).


Central Limit Theorem Iterate Logarithm Selective Neutrality Offspring Distribution Asymptotic Relative Efficiency 
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  1. 1.
    Brown, B.M. (1971) Martingale central limit theorems. Ann. Math. Statist, 42,59–66.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Buckley, M.J. and Seneta, E. (1983) The genetic balance between varying population size and selective neutrality. J. Mathematical Biology, 17, 217–222.MATHCrossRefGoogle Scholar
  3. 3.
    Donnelly, P. (1986) A genealogical approach to variable-population-size models in population genetics. J. Appl. Prob., 23, 283–296.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Harris, T.E. (1963) The Theory of Branching Processes. Springer, Berlin.MATHGoogle Scholar
  5. 5.
    Ku, S. and Seneta, E. (1998) Practical estimation from the sum of AR(1) processes. Commun. Statist. — Simula., 27, 981–998.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Moran, P.A.P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.MATHGoogle Scholar
  7. 7.
    Prince, T. and Weber, N. (2007) Fixation in conditional branching process models in population genetics. J. Appl. Prob., 44, 1103–1110.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Qi, Y. (2007) On asymptotic normality of sequential estimators for branching processes with immigration. Journal of Statistical Planning and Inference, 137, 2892–2902.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Seneta, E. (1968) On recent theorems concerning the supercritical Galton-Watson process. Ann. Math. Statist.,39, 2098–2102.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Seneta, E. (1970) On the supercritical Galton-Watson process with immigration. Math. Biosciences, 7, 9–14.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Seneta, E. (1974) A note on the balance between random sampling and population size. (On the 30th anniversary of G. Malécot’s paper.) Genetics, 77, 607–610.MathSciNetGoogle Scholar

Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, FO7University of SydneySydneyAustralia

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