Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T15:13:45.243Z Has data issue: false hasContentIssue false
  • English
  • Français

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  and
Peter Clifford
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.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

SPATIALINVASIONMUTATIONSTEPPING STONEPOPULATION GENETICS
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 725 - 731
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Feller, W. An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, New York.Google Scholar
Sawyer, S. (1977) Rates of consolidation of a selectively neutral migration model. Ann. Prob. 5, 486–493.CrossRefGoogle Scholar
Sawyer, S. (1979) A limit theorem for patch sizes in a selectively neutral migration model. J. Appl. Prob. 16, 482–495.CrossRefGoogle Scholar