Page 18 - Applied Probability

1
Basic Principles of Population
Genetics

1.1 Introduction

In this chapter we briefly review some elementary results from population
genetics discussed in more detail in the references [2, 3, 4, 6, 7, 10, 13].
Various genetic definitions are recalled merely to provide a context for this
and more advanced mathematical theory. Readers with a limited knowledge
of modern genetics are urged to learn molecular genetics by formal course
work or informal self-study. Appendix A summarizes a few of the major
currents in molecular genetics. In Chapter 15, we resume our study of pop-
ulation genetics from a stochastic perspective by exploiting the machinery
of diffusion processes.

1.2 Genetics Background

The classical genetic definitions of interest to us predate the modern molec-
ular era. First, genes occur at definite sites, or loci, along a chromosome.
Each locus can be occupied by one of several variant genes called alleles.
Most human cells contain 46 chromosomes. Two of these are sex chromo-
somes — two paired X’s for a female and an X and a Y for a male. The
remaining 22 homologous pairs of chromosomes are termed autosomes.
One member of each chromosome pair is maternally derived via an egg;
the other member is paternally derived via a sperm. Except for the sex
chromosomes, it follows that there are two genes at every locus. These con-
stitute a person’s genotype at that locus. If the two alleles are identical,
then the person is a homozygote; otherwise, he is a heterozygote. Typ-
ically, one denotes a genotype by two allele symbols separated by a slash
/. Genotypes may not be observable. By definition, what is observable is a
person’s phenotype.
A simple example will serve to illustrate these definitions. The ABO
locus resides on the long arm of chromosome 9 at band q34. This locus
determines detectable antigens on the surface of red blood cells. There
are three alleles, A, B, and O, which determine an A antigen, a B antigen,
and the absence of either antigen, respectively. Phenotypes are recorded by
reacting antibodies for A and B against a blood sample. The four observable
phenotypes are A (antigen A alone detected), B (antigen B alone detected),