Accession Number:

AD0744126

Title:

A Diffusion Model for Random Drift with Variable Population Size,

Descriptive Note:

Corporate Author:

NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

• Smith,Woollcott
• Hsieh,J. J.

Report Date:

1972-04-01

Pagination or Media Count:

16.0

Abstract:

A diffusion model for random genetic drift with a variable population size is developed. The model is based on Karlins Markov chain model for genetic drift in a haploid population. The variable size diffusion model is shown to be equivalent to Wrights constant size diffusion model with a random time change. Conditions are given for the population growth that will assure a positive probability that the two types of individuals remain in the population indefinitely. The mean time to fixation or loss in the variable size model is found under certain conditions to be the same as the mean time to fixation or loss in Wrights constant size diffusion model. A diffusion approximation to a branching process is used to construct an example of a variable size population model with the same mean time to fixation or loss as the constant size diffusion model. Author

Descriptors:

• (*STOCHASTIC PROCESSES
• MATHEMATICAL MODELS)
• (*GENETICS
• STOCHASTIC PROCESSES)
• MUTATIONS
• DIFFUSION
• RANDOM VARIABLES
• THEOREMS

Subject Categories:

• Biology
• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE