Question

Researchers studying a small milkweed population note that some plants produce a toxin and other plants do not. They identify the gene responsible for toxin production. The dominant allele (T) codes for an enzyme that makes the toxin, and the recessive allele (t) codes for a nonfunctional enzyme that cannot produce the toxin. Heterozygotes produce an intermediate amount of toxin. The genotypes of all individuals in the population are determined (TT = 0.56; Tt = 0.28; tt = 0.16) and used to determine the actual allele frequencies in the population. Is this population in Hardy-Weinberg equilibrium? Calculate the T and t.

Answer 1

The population isn't in the Hardy-Weinberg equilibrium because researchers are studying a small milkweed populatión and one of the conditions of the Hardy-Weinberg equilibrium is that it happens in large populations. The frequencies for the T allele is 0.7 and for the t allele is 0.3

Step-by-step explanation:

To calculate the frequencies of T and t alleles in the population we need to take into account that the following probabilities for each allele to be expressed:

TT => p(T) = 1.0 p(t) = 0.0

Tt => p(T) = 0.5 p(t) = 0.5

tt => p(T) = 0.0 p(t) = 1.0

To calculate the frequencies for each allele we need to use the following expressions

For T:

f(T) = 1.0 (TT) + 0.5 (Tt)

f(T) = 1.0 (0.56) + 0.5 (0.28)

f(T) = 0.56 + 0.14

f(T) = 0.7

For t:

f(t) = 1.0(tt) + 0.5 (Tt)

f(t) = 1.0(0.16) + 0.5 (0.28)

f(t) = 0.16 + 0.14

f(t) = 0.3

The actual allele frequencies in the population are f(T) = 0.7 and f(t) = 0.3.

Now the Hardy - Weinberg equilibrium states that a population will remain the same if it isn't modified by external factors. For this to happen it must fulfill the following conditions:

- There must be no selection

- No mutation

- It should be a large population.

- No random mating

- No migration.

As the researchers are studying a small milkweed population it doesn't fulfills the conditions of a large population and in consequence we can't say this population is in the Hardy - Weinberg equilibrium.