Inheritance In Populations

Hardy-Weinberg

$p$ + $q$ = 1

instance of:
p (dominant) + q (recessive) = 1 (total population)

$p^2$ + $q^2$ + $2pq$ = 1

instance of:
$p^2$ (homozygous dominant)
$q^2$ (homozygous recessive)
$2pq$ (heterozygous)
equaling 1 (the total population)

This is an expansion of the same principal. When the recessive gene is rare enough, you can estimate carrier frequency by making p = 1 (almost everyone homozygous for the dominant gene).

PROBLEM
A disease has an incidence of 1 in 40,000 in a population. What is the carrier frequency?

SOLUTION
$q^2$ =1/40,000
$q$ = 1/200
2pq = 2 x (1) x 1/200
= 1/100 (of heterozygous individuals)