Hardy-Weinberg equilibrium The equation Requirements Five Requirements for a population to

be in equilibrium and not evolve:

1. No natural selection occurs

(all traits are neutral)

2. Mutations do not occur

3. There is no gene flow (population is isolated)

4. The population must be infinitely large.

5. Mating is completely random. Populations undergo change

over time through genetic

variation. A mathematical model of a population that

does not change genetically from one generation to the next. Evolution of Populations To apply the Hardy-Weinberg principle to a gene with alleles Aa:

The dominant allele A has a frequency expressed as p.

The recessive allele a has a frequency expressed as q. Because a population doesn't change genetically, all alleles sum to 100% or 1.

p + q = 1

The chances of all possible combinations of alleles occurring randomly is (p + q)^2 = 1

or

p^2 + 2pq + q^2 = 1 Frequency of homozygotes:

Dominant homozygote AA is p^2

Recessive homozygote aa is q^2

Frequency of heterozygotes Aa is 2pq The Hardy-Weinberg

Principle One way to determine how a real

population does change over time... .....is through the model of a population that does not change genetically from one generation to the next.

This population is in genetic equilibrium. Determining if Populations are

Changing and Evolving Example A population of birds consists of 84% of red birds and 16% white birds. Assuming that the red allele(R) is dominant and the white allele (r) is recessive, what is the allele frequency of the red allele? To Solve: We know that q^2 equals 0.16 = white birds (rr trait)

and p^2 + 2pq = 0.84 =red birds (RR and Rr trait)

We are looking for p, the allele frequency of the red allele.

Since the percentage of the white color traits is equal to those exhibiting the rr trait or q^2, we can determine the allele frequency, or q, by finding the square root of q^2.

q = 0.4

p = 1 - q

Therefore, p must equal 0.6. the allele frequency of the red

allele is 0.6.

How Does the Hardy-Weinberg equation help us? Evolutionary Processes occur on a very large time scale.

We are unable to observe the results of most evolutionary processes directly.

So how do we determine whether evolution (change in allele frequency in a population) is occurring? Using the Hardy-Weinberg equation , the allele frequency distribution of a large population can be found and used to estimate the allele frequency of a different population.

If the frequency of the 2nd population mirrors the known frequencies of the 1st, then little change in the alleles at that locus is occurring.

However, if the frequencies are quite different, it indicates that the allele frequency at that locus is changing, and evolution is occurring.

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# Hardy-Weinberg Principle

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