Question

1. in caucasian humans, hair straightness or curliness is thought to be governed by a single pair of alleles showing partial dominance. individuals with straight hair are homozygous for the $i_s$ allele, while those with curly hair are homozygous for the $i_c$ allele. individuals with wavy hair are heterozygous ($i_si_c$). in a population of 1,000 individuals, 245 were found to have straight hair, 393 had curly hair, and 362 had wavy hair.

(a) calculate the allelic frequencies of the $i_s$ and $i_c$ alleles.

phenotype (genotype)	# $i_s$ alleles	# $i_c$ alleles
wavy ($i_si_c$)
curly ($i_ci_c$)
total:
frequency

Explanation:

Step1: Calculate the total number of alleles

Since there are 1000 individuals and each individual has 2 alleles for this trait, the total number of alleles is $1000\times2 = 2000$.

Step2: Calculate the number of $I_s$ alleles

Individuals with straight hair ($I_sI_s$) have 2 $I_s$ alleles each. There are 245 individuals with straight hair, so the number of $I_s$ alleles from them is $245\times2=490$. Individuals with wavy hair ($I_sI_c$) have 1 $I_s$ allele each. There are 362 individuals with wavy hair, so the number of $I_s$ alleles from them is 362. The total number of $I_s$ alleles is $490 + 362=852$.

Step3: Calculate the frequency of $I_s$ alleles

The frequency of $I_s$ alleles, $p=\frac{852}{2000}=0.426$.

Step4: Calculate the number of $I_c$ alleles

Individuals with curly hair ($I_cI_c$) have 2 $I_c$ alleles each. There are 393 individuals with curly hair, so the number of $I_c$ alleles from them is $393\times2 = 786$. Individuals with wavy hair ($I_sI_c$) have 1 $I_c$ allele each. There are 362 individuals with wavy hair, so the number of $I_c$ alleles from them is 362. The total number of $I_c$ alleles is $786+362 = 1148$.

Step5: Calculate the frequency of $I_c$ alleles

The frequency of $I_c$ alleles, $q=\frac{1148}{2000}=0.574$.

Answer:

The frequency of $I_s$ allele is 0.426 and the frequency of $I_c$ allele is 0.574.