A mutation has occurred in an animal population so that the homozygous recessive condition (ff) is a fatal disease for the animal. Affected individuals die soon after birth. The homozygous dominant (FF) and the heterozygous (Ff) individuals live normally. A study of the population over one year found that 4% of the new born individuals died soon after birth. An equal number of males and females died. Assume that all victims were due to the recessive condition.

A. What is the frequency for the recessive allele?
B. What is the frequency for the dominant allele?
C. What is the frequency of the FF genotype?
D. What is the frequency of the Ff genotype?
E. Assume that 100 individuals were born in the animal population. How many of these would probably be carriers (heterozygous) of the allele for the recessive trait?
F. How many of these 100 animals would NOT carry the allele for the recessive trait?
G. Natural selection is operating against which allele?
H. What happened in a single generation to both allele frequencies?
I. If this condition were to continue for several more generations, what would happen to the allele frequencies?

Answer and Explanation:

Available data:

The allelic frequencies in a locus are represented as p and q, referring to the allelic dominant or recessive forms. The genotypic frequencies after one generation are p² (Homozygous dominant), 2pq (Heterozygous), q² (Homozygous recessive). Populations in H-W equilibrium will get the same allelic frequencies generation after generation. The sum of these allelic frequencies equals 1, this is p + q = 1.

In the same way, the sum of genotypic frequencies equals 1, this is

p² + 2pq + q² = 1

Being

p the dominant allelic frequency,

q the recessive allelic frequency,

p²the homozygous dominant genotypic frequency

q² the homozygous recessive genotypic frequency

2pq the heterozygous genotypic frequency

A. What is the frequency of the recessive allele?

4% of individuals with the recessive allele died. This means that the genotypic frequency for the trait, ff, is 0.04

If F(ff) = 0.04, then the allelic frequency for the recessive allele, f(f) is √0.04. This is:

ff=q²=0.04

f=q=√ 0.04

f=q=0.2

So, the frequency for the recessive allele is 0.2

B. What is the frequency of the dominant allele?

By clearing the equation: p + q = 1, we can calculate the allelic frequency for the dominant allele. This is:

p + q = 1

p + 0.2 = 1

p = 1 - 0.2

p = 0.8

F = p = 0.8

The frequency for the dominant allele, f(F) is 0.8

C. What is the frequency of the FF genotype?

The genotypic frequency equals  p². So, knowing that p = 0.8, then the genotypic frequency for the trait, F (FF) is

p = 0.8

F (FF) = p² = 0.8 ² =0.64

So, the frequency of the FF genotype is 0.64

D. What is the frequency of the Ff genotype?

We can calculate the frequency for the heterozygote genotype by clearing the following equation:

F (Ff) = 2xpxq = 2 x 0.8 x 0.2

                        = 0.32

The frequency of the Ff genotype is 0.32

To corroborate these results, we can add all the genotypic frequencies, and the sum should equal one. This is:

p2 + 2pq + q2 = 1

0.64 + 0.32 + 0.04= 1

E. Assume that 100 individuals were born in the animal population. How many of these would probably be carriers (heterozygous) of the allele for the recessive trait?

The frequency of the Ff genotype is 0.32. This means that 32% of the population are carriers.

If 100 individuals equal 100% of the population, then by developing the "three simple" rule, we can calculate how many individuals are heterozygous in this population. This is:

100% population 100 Total individuals

32% population X = 32 Heterozygous individuals

32 animals would probably be carriers of the allele for the recessive trait

F. How many of these 100 animals would NOT carry the allele for the recessive trait?

100% population 100 Total individuals

64% population X = 64 dominant homozygous individuals

64 animals would NOT carry the allele for the recessive trait

G. Natural selection is operating against which allele?  

Natural selection is operating against the recessive allele, f.

H. What happened in a single generation to both allele frequencies?

The frequency of the recessive allele will decrease and the frequency of the dominant allele will increase.

As all ff individuals die when they are born, in one generation, the genotype ff will not contribute in the same way to the next generation, with respect to the expected contribution according to Hardy-Weinberg equilibrium.

This means that if the genotypic frequency of the recessive allele decreases, the heterozygous and homozygous genotypic frequency will increase.

Directional natural selection is operating.

I. If this condition were to continue for several more generations, what would happen to the allele frequencies?

If the condition continues for several more generations, the recessive allele will tend to disappear, and the dominant allele will tend to establish. The population will be in equilibrium after several generations.

                     This is, f(F) = p = 1

                                 f (f) = q = 0

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