Evolution Set-1

Q1. In a large randomly mating population at Hardy–Weinberg equilibrium the frequency of the recessive phenotype is 0.04. Using $p^2+2pq+q^2=1$, what is the expected frequency of heterozygotes ($2pq$)?

Q2. Population A has allele 'A' frequency $p_A=0.7$ and population B has $p_B=0.2$. Each generation a fraction $m=0.1$ of individuals in B are migrants from A (gene flow A→B). Assuming random mating after migration and no selection, the allele frequency in B after one generation is $p'_B=(1-m)p_B+m p_A$. What is $p'_B$?

Q3. For a locus in an isolated population with effective population size $N_e=50$ and initial heterozygosity $H_0=0.6$, the expected heterozygosity after $t$ generations under genetic drift is $H_t = H_0\left(1-\dfrac{1}{2N_e}\right)^t$. What is the approximate value of $H_{10}$?

Q4. Assertion (A): Inbreeding (mating between close relatives) increases homozygosity in a population but does not alter allele frequencies provided there is no selection, mutation, migration or genetic drift.
Reason (R): Inbreeding raises the probability that two alleles in an individual are identical by descent, reducing observed heterozygosity according to $H_{obs}=2pq(1-F)$, where $F$ is the inbreeding coefficient.
Choose the correct option.

Q5. Assertion (A): Neutral substitutions at many sites tend to accumulate approximately linearly with time in a lineage, providing the conceptual basis for a "molecular clock".
Reason (R): The majority of point mutations are deleterious and are removed by purifying selection, which lowers the observed substitution rate in many genes.
Choose the correct option.

Q6. In a large randomly mating population of 1000 individuals the genotypes at a locus are counted as $AA=490,\;Aa=420,\;aa=90$. Calculate the allele frequencies $p$ (frequency of $A$) and $q$ (frequency of $a$).

Q7. Two species show $6\%$ sequence divergence ($d=0.06$) in a protein. If the molecular substitution rate per lineage is $r=0.01$ substitutions per site per million years, estimate the time $t$ (in million years) since their divergence using $t=\dfrac{d}{2r}$.

Q8. Species P with $2n=14$ (so $n=7$) and species Q with $2n=18$ (so $n=9$) hybridize to give a sterile F1 hybrid that contains one haploid set from each parent. If this hybrid undergoes chromosome doubling to form an allopolyploid, what will be the chromosome number ($2n$) of the new fertile species?

Q9. Assertion (A): In a very small isolated population of size $N$, a mildly deleterious recessive allele can reach fixation by genetic drift faster than selection removes it.
Reason (R): In small populations random sampling causes large allele-frequency fluctuations, and when $2Ns\ll1$ (i.e. $s\ll\dfrac{1}{2N}$) the efficacy of selection is negligible compared to drift.
Choose the correct option.

Q10. Consider two alleles $A$ and $a$ with fitnesses $w_{AA}=0.9,\;w_{Aa}=1.0,\;w_{aa}=0.8$. For heterozygote advantage the equilibrium frequency of allele $A$ is given by $p^{*}=\dfrac{w_{aa}-w_{Aa}}{w_{AA}-2w_{Aa}+w_{aa}}$. Calculate $p^{*}$.