BSCI 160 - Hardy-Weinberg Principle: a null model for population genetics

How can you tell if evolutionary forces are acting on a population?

If the Hardy-Weinberg Principle is not true

What is the Hardy-Weinberg Principle (1908)

a null model: what happens to allele and genotype frequencies when none of the evolutionary mechanisms are operating and mating is random

What does the Hardy-Weinberg Principle (HWP) allow us to do? (2 things)

• identify when evolutionary agents are acting (and/or mating is non-random)

• predict allele or genotypic frequencies IF assume no evolutionary agents are acting (and mating is random)

What are the five assumptions of the HWP?

• no mutation

• no migration (no gene flow)

• no natural selection

• no genetic drift

• random mating

The HWP:

• models __________ across whole __________

• gametes go into ____ ____, paired at random
  

matings, population, gene pool

What is the gene pool?

all individuals alleles in a population for given locus (or loci) of interest

What is allele frequency?

proportion of total alleles composed of a particular allele

If 2 alleles are at a locus, A and a, how do we calculate

• p = f(A) = ?

• q = f(a) = ?
  

p = f(A) = (#A)/(#A+#a)

q = f(a) = (#a)/(#A+#a)

If genotype is AA, __ A added to the population

If genotype is aa, ___ a added to the population

If genotype is Aa, __ A and __ a added to the population

two, two, one, one

What is p + q?

1

Allele frequencies will ALWAYS sum to

1

What is genotype frequency?

proportion of total number of individuals composed of a particular genotype

f(AA) = ?

f(Aa) = ?

f(aa) = ?

f(AA) = (#AA)/(#total indivs)

f(Aa) = (#Aa)/(#total indivs)

f(aa) = (#aa)/(#total indivs)

Practice Problem:

• N = 1000

  • #AA = 700, #Aa = 200, #aa = 100

• What are the genotype and allele frequencies?

f(AA) = 0.7, f(Aa) = 0.2, f(aa) = 0.1

f(A) = 0.8, f(a) = 0.2

Genotype frequencies will ALWAYS sum to

1

What does it mean if p + q does not equal 1

you made a math error

What can you predict if you know allele frequencies?

the genotype frequencies

Given allele frequencies in parental generation:
Allele A1 = p = 0.7

Allele A2 = q = 0.3
Provide the possible genotypes.

A1A1, A1A2, A2A1, A2A2

What is the chance of getting each gamete pair combination?

A1A1 = (0.7)(0.7) = 0.49

A1A2 = (0.7)(0.3) = 0.21

A2A1 = (0.3)(0.7) = 0.21

A2A2 = (0.3)(0.3) = 0.09

Predicted genotype frequences must equal ___

What is the formula?

one, p²+2pq+q²

The HWE can be extended to more than 2 alleles: true or false?

true

What does it mean if p2+2pq+q2 does not equal 1

math error

Hardy-Weinberg Principle Key Points (2)

1. the frequencies of genotypes A1A1, A1A2, A2A2 will be p², 2pq, and q² for generation after generation if the population is in “Hardy-Weinberg equilibrium

2. allele frequencies do not change over time unless one of the HWE is violated

(note: non-random mating alone can change genotype frequencies but not allele frequencies)

Why is HWE useful?

• helps determine if evolutionary agents are acting - must know actual genotype frequencies

  • agents are acting if the actual genotypic frequencies are not as expected

  • can compare observed to expected genotype frequencies

  • If f(AA) does not equal p² and/or f(Aa) does not equal 2pq and/or f(aa) does not equal q², then one or more evolutionary agents are acting (and/or non-random mating)

  • Given known allele frequencies, HWE tells us what genotype frequencies we should see if none of the assumptions are violated

• helps determine what p and q are and what the genotype frequencies are assuming the population isin HW equilibrium

  • assuming HW equilibrium: population is not evolving and genotype frequencies are p2, 2pq, and q2

• Can determine why there may be excess homozygotes given allele frequencies

Example Problem:

• PKU, due to a recessive allele (a)

• expressed in 1/10,000, so f(aa) = 1/10000

• assuming HWE: what is f(a) = ?

q² = 1/10,000

q = 0.01

p = 1-q

p = 0.99

Can solve for genotypic frequencies with this information

Summary:

• Hardy-Weinberg provides a ______________ _____ ______ to test for agents of ___________/____-_________ __________

  • HWE assumes that none of the ______ evolutionary agents are acting and mating is ________

• HWE is useful in two distinct ways -

  • determine if evolutionary agents are acting (and/or mating is ___-_______), if you know __ and __ and observed __________ _____________

  • HWE predicts f(AA) = p², f(Aa) = 2pq, f(aa) = q²

• calculate __ and __ (and ____________ ______________), if assume HWE
  

mathematical null model, evolution, non random mating, four, random, non random, p, q, genotype frequencies, p, q, genotypic frequencies