A recessive lethal gene in chickens causes circulatory failure and death of the embryo at 70 hours.A commercial hatchery finds that a hatching failure due to this gene of greater than 4% is unacceptable.What is the upper limit for the frequency of this allele in the breeding population of fowls that is acceptable to the hatchery managers?

Hardy-Weinberg Law

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

p = frequency of the dominant allele in the population
q = frequency of the recessive allele in the population

p^2 = percentage of homozygous dominant individuals
q^2 = percentage of homozygous recessive individuals
2pq = percentage of heterozygous individuals

so in this problem, q^2=.04, which implies p=1-q=1-.2=.8
and 2pq=2*.8*.2=.32

So the upper limit for those carrying the gene in the breeding population is 32 percent.

Thank you so much. I don't really understand this law at all.

To determine the upper limit for the frequency of the recessive lethal allele that is acceptable to the hatchery managers, we need to calculate the frequency at which hatching failure exceeds 4%.

Let's assume the frequency of the recessive lethal allele in the breeding population is represented by "q". Since this allele is recessive, its frequency can be represented by the square root of the hatching failure (4%) or 0.04.

q = √(hatching failure) = √0.04 = 0.2

Therefore, the upper limit for the frequency of the recessive lethal allele in the breeding population that is acceptable to the hatchery managers is 0.2 or 20%. Any frequency higher than this would result in a hatching failure greater than 4%, which is deemed unacceptable.

To find the upper limit for the frequency of the recessive lethal allele in the breeding population of fowls, we need to consider the probability of an individual carrying this allele and the probability of the allele being passed down to the next generation.

Let's assume that the breeding population is in Hardy-Weinberg equilibrium, meaning that the frequency of the recessive lethal allele remains constant from generation to generation.

In this case, we can use the Hardy-Weinberg equation to determine the frequency of the recessive lethal allele, denoted as q. The equation is:

p² + 2pq + q² = 1,

where p is the frequency of the dominant allele, and p², 2pq, and q² represent the proportions of the three possible genotypes (dominant homozygous, heterozygous, and recessive homozygous) in the population.

Since the recessive lethal gene causes hatching failure in embryos at a frequency greater than 4% (0.04), we can calculate the maximum acceptable frequency for the recessive lethal allele, denoted as q_max.

1 - q_max² = 0.04.

Rearranging the equation, we have:

q_max² = 1 - 0.04,

q_max² = 0.96,

q_max = √0.96,

q_max ≈ 0.9798.

Therefore, the upper limit for the frequency of the recessive lethal allele in the breeding population of fowls that is acceptable to the hatchery managers is approximately 0.9798, or 97.98%.