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Answer :
a) Frequency of Heterozygous Cats:In the next generation, the frequency of heterozygous cats (Tt) will be 2pq.
b) Frequency of Homozygous Recessive Cats:In the next generation, the frequency of homozygous recessive cats (tt) will be q^2.
c) Frequency of Recessive Allele (t):Since homozygous recessive cats (tt) represent q^2 of the population, and we know tt arises from two recessive alleles (t), we can estimate the frequency of the recessive allele (t) in the population by taking the square root of q^2. Therefore, the frequency of the recessive allele (t) is approximately **√q**.
The Hardy-Weinberg equation (p² + 2pq + q² = 1) describes the relationship between allele frequencies (p and q) and genotype frequencies (p², 2pq, and q²) in a population at genetic equilibrium. Here,
- p represents the frequency of the dominant allele (T) for long fur.
- q represents the frequency of the recessive allele (t) for short fur.
a) Heterozygous Cats (Tt):
The term 2pq in the Hardy-Weinberg equation represents the frequency of heterozygous individuals (Tt). This term reflects that two alleles contribute to a heterozygous genotype: one from each parent. The 2 accounts for the possibility of inheriting either the dominant (T) or recessive (t) allele from either parent.
b) Homozygous Recessive Cats (tt):
The term q² in the Hardy-Weinberg equation represents the frequency of homozygous recessive individuals (tt). This term reflects that both alleles in an individual must be recessive (t) for the short fur phenotype to appear. Since q represents the frequency of the recessive allele (t), squaring it (q²) gives the probability of inheriting two recessive alleles (tt).
c) Estimating Recessive Allele Frequency:
Since homozygous recessive cats (tt) represent individuals with two copies of the recessive allele (t), their frequency (q²) relates directly to the overall frequency of the recessive allele (t) in the population. By taking the square root of q² (√q), we can estimate the proportion of the total allele pool that is made up of the recessive allele (t).
Question
"In a population of cats, the allele for long fur (T) is dominant over the allele for short fur (t). Use the Hardy-Weinberg equation to predict the frequency of genotypes in the next generation, assuming the population is in genetic equilibrium.
a) Use the Hardy-Weinberg equation to predict the frequency of heterozygous cats in the next generation.
b) Use the Hardy-Weinberg equation to predict the frequency of homozygous recessive cats in the next generation.
c) Use the Hardy-Weinberg equation and your answer to question b to estimate the frequency of the recessive allele (t) in the population."
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