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
Date of Defense 1961-08-15 Availability restricted AbstractThe genetical theory of evolution is best
understood 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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