Type of Document Master's Thesis Author De Ramos, Mariano Bauyon URN etd-08012012-040111 Title The evolution of a sex-linked genetic factor Degree Master of Science Department Statistics Advisory Committee

Advisor Name Title Watterson, Geoffrey A. Committee Chair David, Herbert A. Committee Member Keywords

- Evolution
Date of Defense 1961-08-15 Availability restricted AbstractThe genetical theory of evolution is bestunderstood by a knowledge of the distribution of

gene frequencies The sequence of changes in genes,

primarily due to effects of mutation, selection,

migration, and many other environmental influences,

would also gradually change gene frequencies after

a long period of time. The distribution of gene

frequencies is determined by application of theories

of probability and mathemetics. In particular,

Wright's diffusion theory (14) and early works of

Fisher (6,7) and Kolmegorov (9) play a central role.

The aim of this thesis is to discover the

evolutionary significance of mutation, selection,

and random mating in the case of sex-linked factors

when the generation structure of the population is

overlapping. To facilitate the application of

mathematical theory, we assume the population size

at any time is large and constant denoted by N.

Instead of discussing the individual genotype

frequencies, we introduce a properly defined random

variable U, approximetely the proportion of "a" genes

in the population. The first and second moments of

the change in U during the birth-death event are

obtained. For the diffueion process to work out,

we let the time be a function of N, and by moment

generating functions the diffusion equation (or

Fokker-Planck equation) is justified when N tends

to infinity. Following methods of solution given

by Barucha-Reid (2), Kimura (8), Li (10), Moran (11,12),

Watterson (13), and Wright (14), the density function

for the "a" gene frequency is obtained.

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