Lecture #15—Population Genetics

We usually gage how much change has occurred in an animal’s history by looking at the fossils and see changes in anatomy. Or can evaluate the change in terms of differences in DNA, RNA or protein. In this lecture, we look at another approach: population genetics.This is the field of study where we measure genetic differences within and between populations.

An important concept in this study is the idea of agene pool; i.e. populations are a collection of alleles. And we can treat them mathematically. So, take a simple example like a trait that only has 2 alleles. In humans, the ability to curl your tongue, was originally believed to be such an example. But since identical twins don’t always have the same ability to curl, other factors are involved.

But for the sake of this lecture let’s assume that tongue curling is entirely due to a dominant allele, R. Thus, a person can either be RR, Rr, rR, or rr. This means that the gene pool of humans is filled with people who can and cannot tongue roll. Anyone who can tongue roll will either be a RR or Rr genotype, but anyone who cannot tongue roll we can be sure is a rr.

Two individuals, G.H. Hardy and Wilhelm Weinberg, established a simple mathematical expression that explains the theoretical distribution of the different genotypes if evolution is not occurring.

p2+2pq + q2

where p2 represents the frequency of RR individuals in a population

2 pq represents the frequency of Rr individuals in a population

q2 represents the frequency of rr individuals in a population

Clearly if one knows either p or q you can calculate the other values.

One other point: if p2is the frequency of RR, then p is the frequency of R in the gene pool. And if q2 represents rr, then q is the frequency of r in the gene pool.

Let’s try an example: suppose we know that there is no advantage of being a tongue roller. And let’s further assume that a population’s gene pool consists of 36% rollers (RR +Rr combined) and

64% non-rollers (rr) = q2

36% rollers (RR & Rr) = p2 + 2pq

We cannot simply determine the frequency of RR or Rr separately because the 36% is a combination of the two values, but we can do it for rr. Thus, since the frequency of rr is 0.64,we can take the square root of q = 0.8.

This means that if 80% of the gene pool are r alleles, then 20% must R.

q = 0.8.

p = 0.2

p + q = 1 or 0.2 + 0.8 = 1

Now with these values we can complete the Hardy-Weinberg calculation:

p2+2pq + q2 or in this case

0.4 + 2 (0.2 x 0.8) + 0.64 = 1

So with this in mind, then if nothing intervenes to disturb the values of p and q the alleles will remain constant from generation to generation. This means that evolution will not be occurring. Hardy and Weinberg said these are the stringent conditions that must be true to prevent evolution:

  1. No natural selection
  2. No differential migration in or out of the population –immigration and emigration of alleles must be absent or balanced
  3. No differential mutation of r or R alleles into or out of the population.
  4. Random mating
  5. Large population needs to exist because random effects might distort the frequency of alleles between generations.

There are several types of cases where the effect of small populations can be seen.

a)Founder effect—a distorted allele frequency can occur if only a few individuals start a new colony. They are unlikely to have the same allele frequency as the parent population.

b)Bottle neck effect—if the population crashes and only a few individuals survive then the allele frequency is unlikely to be the same as the original population.

c)Genetic drift—chance breeding will produce odd allele distributions just like flipping a coin will sometimes lead to several heads or tails in a row.

The Hardy-Weinberg conditions are seldom in effect—something is likely to always be distorting the allele frequency over time. But the Hardy-Weinberg ideal gives biologists something to use as a standard for comparison.

But if this all seems to be confusing try looking at these videos:

Terms/Concepts to Define

Population Genetics

Gene pool

Hardy-Weinberg principle

Hardy-Weinberg equation

p2+2pq + q2

Founder Effect

Bottle neck principle

Genetic Drift

Can you answer these questions?

  1. Suppose you had a very large mixed barrel of marbles, 80 % are brown and 20% are white. If you reached in blindly and took out two marbles at random, what are the chances of you removing two white marbles? Or a brown first and then a white?
  2. In the Hardy-Weinberg equation what symbol represents the frequency of heterozygous individuals in the population?
  3. Explain why the Hardy-Weinberg principle says that mating must be random.
  4. Suppose there are 1000 animals in a population and that the homozygous recessive animals make up 89% of the group. If the population is in Hardy-Weinberg equilibrium, then what is the frequency of the recessive allele in the gene pool? In the next generation what would you expect the frequency to be?
  5. Populations on small islands are often unusual and genetic drift, the founder effect are said to be part of the reason. Explain why this argument makes sense.
  6. There are 500 dragons in a population and 495 are red and 5 blue. Red is the dominant allele with complete dominance.How many dragons in the population carry the blue allele but are red? i.e. How many are Rr ?
  7. What is the frequency of heterozygotes Aa in a randomly mating population in which the frequency of all dominant phenotypes is 0.19?
  8. Suppose we have a population with the following phenotypes frequencies:

9% dominant phenotype, 66% heterozygous phenotype, 25% recessive phenotype. Is this population is Hardy-Weinberg equilibrium?

If you look in the Internet under Hardy-Weinberg problems you will find many more examples with answers worked out.