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The determination of the age of a clone from characteristics of its geographical distribution

Published online by Cambridge University Press:  14 July 2016

Aid An Sudbury*
Affiliation:
Monash University
Peter Clifford*
Affiliation:
University of Oxford
*
Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
∗∗Postal address: Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB, U.K.

Abstract

Each point with integer coordinates in d dimensions is occupied by one individual. These individuals produce offspring at a Poisson rate 1, and these offspring migrate and displace other individuals. With probability u (the mutation rate) an offspring is of an entirely new type. A number of points N0 will be occupied by the same type as the individual at the origin. It is shown that the distribution of N0 arising from an ancient mutation does not differ greatly from the distribution of N0 when the mutation is recent. However, the geographical spread is shown to be important, and a central limit theorem is proved for the age of the mutant clone given that a representative is present at a large distance from the origin.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 

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References

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