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Volume 8 - June 1976

Contents

Page 5 of 8

Front Matter

Conference on Patterns and Processes in the Plane: Swansea, 25–27 September 1975

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Back Matter

Conference on Patterns and Processes in the Plane: Swansea, 25–27 September 1975

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Conference on Patterns and Processes in the Plane: Swansea, 25–27 September 1975

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Conference on Patterns and Processes in the Plane: Swansea, 25–27 September 1975

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Conference on Patterns and Processes in the Plane: Swansea, 25–27 September 1975

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Conference on Patterns and Processes in the Plane: Swansea, 25–27 September 1975

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Research Article

  • Branching diffusion processes in population genetics

  • Stanley Sawyer
  • Published online by Cambridge University Press:
    01 July 2016, pp. 659-689

  • A branching random field is considered as a model of either of two situations in genetics in which migration or dispersion plays a role. Specifically we consider the expected number of individuals NA in a (geographical) set A at time t, the covariance of NA and NB for two sets A, B, and the probability I(x, y, u) that two individuals found at locations x, y at time t are of the same genetic type if the population is subject to a selectively neutral mutation rate u. The last also leads to limit laws for the average degree of relationship of individuals in various types of branching random fields. We also find the equations that the mean and bivariate densities satisfy, and explicit formulas when the underlying migration process is Brownian motion.

II. Contributed Papers

Fifth Conference on Stochastic Processes and their Applications

Page 5 of 8