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In a population with two alleles for a gene locus (P and p), the allele frequency of $P$ is $0.7$ what would be the frequency of heterozygotes if the population is in the hardy Weinberg equilibrium?
a. $0.49$
b. $0.42$
c. $0.21$
d. $0.09$

Last updated date: 29th Feb 2024
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Hint: In population genetics, the Hardy–Weinberg precept, additionally called the Hardy–Weinberg equilibrium, model, theorem, or regulation, states that allele and genotype frequencies in a population will continue to be steady from generation to generation within the absence of other evolutionary impacts. These effects encompass genetic flow, mate choice, assortative mating, herbal choice, sexual selection, mutation, gene waft, meiotic pressure, genetic hitchhiking, population bottleneck, founder effect and inbreeding.

Complete answer:
• In the simplest case of Hardy Weinberg equilibrium, a locus with two alleles denoted $A$ and $a$ with frequencies $f(A) = p$ and $f(a) = q$
• The predicted genotype frequencies below random mating are $f(AA) = p2$ for the $AA$ homozygotes, $f(aa) = q2$ for the $aa$ homozygotes, and $f(Aa) = 2pq$ for the heterozygotes. In the absence of choice, mutation, genetic waft, or different forces, allele frequencies $p$ and $q$ are consistent between generations, so equilibrium is reached.
• The principle is named after G. H. Hardy and Wilhelm Weinberg, who first verified it mathematically.
• Hardy's paper changed into targeted on debunking the then-generally held view that a dominant allele could routinely generally tend to boom in frequency; nowadays, confusion among dominance and selection is less commonplace.
• Today, checks for Hardy–Weinberg genotype frequencies are used in most cases to check for population stratification and different types of non-random mating.
• Frequency of allele $P = 0.7$ or $70\% $ Frequency of allele $p = 0.3$ or $30\% $
• From Hardy-Weinberg equilibrium: $({p^2} + 2pq + {q^2})$
• $2pq$ (Heterozygous genotype) $ = 2 \times 0.7 \times 0.3 = 0.42$ or $42\% $

Hence, the correct answer is option (B).

Note: Hardy's statement starts with a recurrence relation for the frequencies $p$, $2q$, and $r$. These recurrence relations observe from fundamental principles in probability, especially independence, and conditional probability. For instance, take into account the possibility of an offspring from the technology being homozygous dominant. A dominant allele can be inherited from a homozygous dominant discern with possibility $1$, or from a heterozygous figure with opportunity $0.5$.