Power laws for family sizes in a duplication model

Published

Journal Article

Qian, Luscombe and Gerstein [J. Molecular Biol. 313 (2001) 673-681] introduced a model of the diversification of protein folds in a genome that we may formulate as follows. Consider a multitype Yule process starting with one individual in which there are no deaths and each individual gives birth to a new individual at rate 1. When a new individual is born, it has the same type as its parent with probability 1 - r and is a new type, different from all previously observed types, with probability r. We refer to individuals with the same type as families and provide an approximation to the joint distribution of family sizes when the population size reaches N. We also show that if 1 ≪ S ≪ N 1-r, then the number of families of size at least 5 is approximately CNS -1/(1-r), while if N 1-r ≪ S the distribution decays more rapidly than any power. © Institute of Mathematical Statistics, 2005.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Schweinsberg, J

Published Date

  • November 1, 2005

Published In

Volume / Issue

  • 33 / 6

Start / End Page

  • 2094 - 2126

International Standard Serial Number (ISSN)

  • 0091-1798

Digital Object Identifier (DOI)

  • 10.1214/009117905000000369

Citation Source

  • Scopus