This document introduces the Hardy-Weinberg principle of genetic equilibrium and provides examples of how to use Hardy-Weinberg equations to calculate expected genotype and allele frequencies in a population. It explains that the Hardy-Weinberg model provides a baseline to measure if evolutionary forces are impacting a population's genetic makeup over time, though natural populations rarely remain perfectly in equilibrium. Examples are given to demonstrate calculating genotype frequencies based on known allele frequencies using the Hardy-Weinberg equations.

2. In a non-evolving population allele
frequencies are preserved (they are said
to be in Hardy-Weinberg equilibrium), but:
natural populations are rarely in Hardy-
Weinberg equilibrium
However it provides a useful model to
measure if evolutionary forces are
acting on a population

3. G.H. Hardy
mathematician
W. Weinberg
physician

4. Hardy-Weinberg theory
Counting Alleles
assume 2 alleles = B, b
frequency of dominant allele (B) = p
frequency of recessive allele (b) = q
frequencies must add up to 1 (100%), so:
p + q = 1
bbBbBB

5. Hardy-Weinberg theory
Counting Genotypes
frequency of homozygous dominant: p x p = p2
frequency of homozygous recessive: q x q = q2
frequency of heterozygotes: (p x q) + (q x p) = 2pq
frequencies of all individuals must add to 1 (100%),
so:
p2 + 2pq + q2 = 1
BB Bb bb

6. H-W formulas
• Alleles: p + q = 1
• Genotypes p2 + 2pq + q2 = 1
B b
BB Bb bb

7. • population:
100 cats
• 84 black, 16
white
• How many of
each genotype?
• p2 + 2pq + q2
= 1
• q2 (bb): 16/100 = .16
• q (b): √.16 = 0.4
• p (B): 1 - 0.4 = 0.6
• Now work out
genotype
frequencies
p2=0.36
2pq=0.48
q2=0.16
Using Hardy-Weinberg equation
BB Bb bb

8. Hardy Weinberg problems
Now have a go at sorting out some:
Allele frequencies
Genotype frequencies
Phenotype frequencies
And use the frequencies to make
deductions about data