- Home
- 20. Mechanisms of Change
- Hardy-Weinberg principle

All UK Exam Boards included

How could we keep track of the frequency of each allele for a given trait when we have a dominant-recessive interaction? More specifically, how could we account for the visible dominant traits as homozygous or heterozygous, since both look the same?

This is where the **Hardy-Weinberg principle** comes in. Firstly, there are criteria for when this principle may be applied to a population:

**1. Random mating** must take place.

**2. No migration** must occur either inwards or outwards of the population.

**3. No mutations** must arise in the population.

**4. No natural selection** must take place due to one trait being better or worse adapted to the environment.

It’s apparent that this is simply rarely, if ever, the case in a real wild population. However, the Hardy-Weinberg principle is useful at predicting allele frequencies in a reliable mathematical model.

The *frequency* of the dominant allele is noted **p **while that of the recessive allele is noted **q**. Both must necessarily account for the whole population, therefore:

**p + q = 1**

The values are frequencies, so they are noted as *percentages*. 1 is 100% while 0.5 is 50% and 0.05 is 5%, etc.

**Worked exercise**

If we know that the frequency of the allele for dark fur in a population of koala bears is 0.2, and this allele is dominant over the one for light fur, work out the frequency of the allele for light fur in the population.

**p = 0.2**

**p + q = 1**

Therefore, **0.2 + q = 1 **so **q = 1 – 0.2**

**q = 0.8 **or 80%.

Now the *allele frequency* has been worked out, how could we work out the actual **phenotype** of the koala bears in the population. How many are actually dark-furred? How many of the dark-furred ones are homozygous?

For this we use the same equation as before, but **squared**: (p + q)2

This is equivalent to **p ^{2} + 2pq + q^{2} = 1**

Where **2pq** is the frequency of **heterozygotes**, and **p ^{2}** and

We want to know how many koala bears have dark fur. We know that the allele frequency for dark fur is 0.2, so 0.2^{2} is the percentage of homozygous dark fur individuals; = 0.04 (4%).

This trait being dominant, the heterozygotes must also have dark fur. The frequency of heterozygous dark fur is 2pq = 2*0.2*0.8 = 0.32 (32%).

**So overall, there are (0.4 + 0.32) 0.36 or 36% dark-furred koala bears in the population.**

This leaves the remaining 64% with light fur. Note the contrast between the light *phenotype* only being 64% while the *allele frequency* for light fur is 80%. If the allele were dominant over dark fur, the frequency would be *higher* rather than *lower*.

I got A* in A-level biology (Cambridge), thanks! I love your videosSherif Negm Facebook

You're such a G. Helped me so much, finally found someone who breaks biology down into something I can understand!!!Alex Contact Form

Good topic notes and cool videos. I'll definitely recommend it to my students.Seema Sehgal AQA Examiner and biology teacher on LinkedIn

OMG that’s great! Actually just helped me with my homeworkmabelbarc The Student Room

You explain everything so simply!SecretDuck The Student Room