So far, we’ve talked about Mendelian genetics and Darwinian natural selection. Combining the two, we get population genetics. Population genetics is the study of the distribution and change in frequency of alleles within populations, and is the foundation of modern evolutionary biology.

In this post, we will explore how the mathematical foundation of population genetics was formed and what causes populations to change over time.

### Allele frequency

Recall that an allele is just a variant of a gene. For example, the version of a gene that produces blue eye color would be an allele. All of us receive one allele from our mother and one from our father, meaning every person carries two alleles. Consider a population of two people where the following is true:

B = brown eye color allele (dominant)

b = blue eye color allele (recessive)Person 1 = Bb

Person 2 = bbB allele frequency = 1/4 = .25

b allele frequency = 3/4 = .75

B phenotype frequency = 1/2 = .50

b phenotype frequency = 1/2 = .50

Note the difference between allele frequency and phenotype frequency. Allele frequency calculates the proportion of genes in a population that code for a certain trait. Phenotype frequency calculates the proportion of a population that expresses a certain trait. We can still pass on the gene for a trait even if we do not personally express that trait.

### Hardy-Weinberg equation

Now, consider a huge population of people where the allele frequency remains constant from generation to generation. This means no natural selection, mutations, or evolution of any kind occurs. Let’s also assume that we are still dealing with the brown eye color (B) and blue eye color (b) alleles. Let the probability of B = p, and the probability of b = q. Knowing that the probabilities have to equal 1, we can do some interesting math.

p + q = 1

(p + q)^2 = 1

p^2 + 2pq + q^2 = 1p^2 = probability of BB

2pq = probability of Bb or bB

q^2 = probability of bb

What we just did was derive the Hardy-Weinberg equation, and it has some powerful applications. For example, imagine we observe that 16% of a population has the blue eye phenotype. Using the Hardy-Weinberg equation, we can solve for the allele frequencies in the population.

p^2 + 2pq + q^2 = 1

p^2 + 2pq + .16 = 1

q = sqrt(.16) = .40

p = 1 – .40 = .60BB = 36%

Bb or bB = 48%

bb = 16%

The frequency of the blue eye allele is 40%. We can answer some other interesting questions like what percentage of the population is a carrier of the blue eye allele. The answer is 64%. Using the same logic, we could find out what percentage of a population is a carrier of a specific genetic disease.

We now have a model for understanding populations with stable allele frequencies. This is known as Hardy-Weinberg equilibrium. But what happens if allele frequencies change over time? Well, another word for changing allele frequencies is evolution.

More than anything else, the Hardy-Weinberg equation gives us a base case no evolution world to compare the real world to. In the real world, we find that allele frequencies do change in populations and there are five key factors that explain this.

### Natural selection

The alleles that best help an organism survive and reproduce will be selected for. Overtime, their frequency in the population will increase and Hardy-Weinberg equilibrium will be broken.

### Sexual selection

So long as mating isn’t random, certain traits will be more attractive to partners. These traits may have nothing to do with survival, but that fact that they help reproduction means they will increase in frequency.

### Mutation

When a mistake happens during the copying of DNA in reproductive cells, a new allele will be introduced to the population. Most of the time the mutation will kill or deform the organism, but occasionally the mutation will be useful and spread in the population.

### Genetic drift

If a population is small enough, random chance can greatly affect the frequency of alleles. For example, if a four person population all randomly passed on the blue eye color allele, all subsequent generations would have blue eye color. This has nothing to do with the fitness of allele to the environment.

### Gene flow

When populations that are separated by geographic factors mix, new alleles will be introduced. This is usually the byproduct of immigration and emigration. The new alleles will disrupt the Hardy-Weinberg equilibrium.

### Conclusion

If populations didn’t change overtime, the Hardy-Weinberg equation would remain in equilibrium. However, populations do change as the result of natural selection, sexual selection, mutation, genetic drift, and gene flow. The hardy-Weinberg equation gives us a mathematical framework for thinking about how allele frequencies can change over time. Population genetics takes this framework and applies it to the study of evolution.

References:

https://www.khanacademy.org/science/biology/her

https://youtu.be/WhFKPaRnTdQ?list=PL3EED4C1D684D3ADFhttps://en.wikipedia.org/wiki/Population_genetics