HARDY-WEINBERG EQUILIBRIUM

What Darwin didn’t Get

Darwin couldn’t figure out why there was so much GENETIC VARIATION in natural populations.

Darwin thought that selection should ALWAYS favor the optimal form and eliminate vaiation…… hmmm…. But…….

The reality is, there is A LOT of variation in populations

So how could this be?

Hardy and Weinberg (1908)

Independently solved WHY this genetic variation exists

Hardy was a mathematician

Weinberg was a physician

They showed that the frequency of genotypes in a population will stay the same from one generation to the next.

That is if : SEVEN conditions are met

We call this HARDY-WEINBERG EQUILIBRIUM

THE BIG SEVEN1. Mutation is not occurring

2. Natural selection is not occurring

3. The population is very large

4. All members of a population breed

5. All mating is totally random

6. Everyone produces the same number of offspring

7. There is no immigration or emigration happening in the population

Ok, so how realistic is this???

Not very, but we can use an equation as a model for population genetics

First you need to know that:

•ALLELES represent GENES

•Individuals receive one allele from each parent

•This makes up an individuals genes

•The genes determine the phenotype

Therefore an individual will receive a combination of alleles in the form of :

Dominant Dominant

Recessive Recessive

Dominant Recessive

The alleles are represented as letters

Capital letter = DominantLowercase Letter = Recessive

AAaaAa

AA is called: HOMOZYGOUS DOMINANT

Aa is called: HETEROZYGOUS DOMINANT

aa is called: HOMOZYGOUS RECESSIVE

The HARDY- WEINBERG Equation (s)

p + q = 1 p2 + 2pq +

q2 = 1

BREATH DEEP….here we go……

These equations figure out:

•ALLELE FREQUENCY

•GENOTYPE FREQUENCY

AA + Aa + aa = 1

p2 + 2pq + q2

= 1

Formula for GENOTYPE Frequency

A + a = 1 p + q = 1

Formula for ALLELE frequency

Now that we know what each formula represents, figuring out each problem is easy!!!!!!

You will ALWAYS be given

That the characteristic is either DOMINANT or RECESSIVE

Example: the problem will tell you that

RED = RWHITE = r

THEN you will be GIVEN

A VALUE of one of these:

A a AA aa

And you already know that:

A = p a = q

AA = p2 Aa = 2pq aa = q2

NOW all you have to do is..

Plug the values in!!!

But it’s kind of like a maze

Sooooooooo

STEP 1: write out both formulas

AA + Aa + aa = 1p2 + 2pq + q2 = 1

AND

A + a = 1 p + q = 1

Step 2: Figure out what you’ve been given and plug it in

Example: if you are given the value of aa as 50% or .5o

Plug .50 into the q2 spot

AA + Aa + aa = 1p2 + 2pq + q2 = 1p2 + 2pq + .50 = 1

Now you can figure out q

.50 = .71

A + a = 1p+ q = 1

P + .71 = 1.29 + .71 = 1

AA + Aa + aa = 1p2 + 2pq + q2 = 1

.084 + 2 (.29)(.71) + .50 = 1.084 + .41 + .50 = 1

Lets look at a problem

The gene for an intelligent dolphin is dominant to a gene for an aggressive dolphin. In a population there are 25% that have the gene for homozygous recessive aggressiveness. Figure out the gene frequency for the heterozygous intelligent.

OK, so we know that:

We’re looking or GENE FREQUENCY

Intelligent = A

Aggressive = a

Homozygous recessive = aa = 25% = .25

Heterozygous = Aa