the allele that causes achondroplasia is a dominant mutation: 10 out of 102,246

Question

the allele that causes achondroplasia is a dominant mutation: 10 out of 102,246 births. since this is a dominant mutation what is the frequency of the gene in newborns? The relative number of progeny from 110 achondroplastic parents is 35, while 531 of their unaffected siblings had 740 progeny. Homozygous individuals for tje achondroplastic allele die early in life. Given that the population is in mutation-selection balance, what mutation rate would lead to this frequency of the achondroplastic allele?

Explanation / Answer

Mutation-selection balance is an equilibrium in the no. of deleterious alleles in a population. The rate, at which the deleterious alleles are created by mutation equals to the rate at which they are eliminated by selection.

Let "m" is the ratio of rate to generation at which "A" (531) mutates to "a" (740) and

"n" is the ratio of rate to genration at which "a" (110) mutates back to "A"(35).

According to the given information, the 'm' and 'n' are calculated as follows:

mp = nq - p

= 0.71

nq = p - mp

= 3.14

The frequency of the allele is calculated as follows:

P = p - mp + nq

delta p = nq - mp

= 3.14 (0) - 0.71(1)

= -0.71

q* = q + mp - nq

delta q = mp - nq

= 0.71 (1) - 3.14 (0)

= 0.71

Thus, the frequency of q is 0.71. If the disease is at mutation-selectio balance, then the mutation rate is 0.71.

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