Biology Set-1

Q1. In a large randomly mating population under Hardy–Weinberg equilibrium the frequency of a recessive phenotype is $0.09$. What is the expected frequency of heterozygotes?

Q2. Consider a large randomly mating population with alleles A and a at initial frequencies $p=0.5$ and $q=0.5$. Fitnesses are $w_{AA}=0.8,\; w_{Aa}=1.0,\; w_{aa}=0.6$. After one generation of selection (no other forces), the new frequency $p'$ of allele A is given by $p'=\dfrac{p^2 w_{AA} + p q w_{Aa}}{\bar W}$ where $\bar W=p^2w_{AA}+2pq w_{Aa}+q^2 w_{aa}$. The value of $p'$ is closest to:

Q3. From a sample of $N=200$ diploid individuals the genotype counts are AA = 72, Aa = 56, aa = 72. Using $F=1-\dfrac{H_{obs}}{H_{exp}}$ with $H_{exp}=2pq$ under Hardy–Weinberg (where $p,q$ are estimated from the sample), the inbreeding coefficient $F$ is approximately:

Q4. In a very large population a recessive allele $a$ is lethal in homozygotes ($s=1$) and arises by mutation from $A$ at rate $\mu=2\times10^{-6}$ per generation. Under mutation–selection balance the equilibrium frequency is approximately $q^*\simeq\sqrt{\mu/s}$. The equilibrium $q^*$ is approximately:

Q5. Two equally sized subpopulations have allele frequencies $p_1=0.8$ and $p_2=0.6$ for allele A. Using Wright's $F_{ST}=\dfrac{H_T-H_S}{H_T}$ where $H_T=2\bar p\bar q$ (with $\bar p$ the mean allele frequency) and $H_S$ the average within-subpopulation heterozygosity, the $F_{ST}$ for these two subpopulations (equal size) is approximately:

Q6. In a large, randomly mating population the frequency of individuals showing a recessive phenotype is $q^2 = 0.09$. Assuming Hardy–Weinberg equilibrium, what percentage of the population is expected to be heterozygous carriers ($2pq$)?

Q7. A population has allele frequencies $p=0.6$ (allele A) and $q=0.4$ (allele a). Viability selection acts with fitnesses $w_{AA}=1$, $w_{Aa}=0.9$, $w_{aa}=0.7$. Using
$p'=\dfrac{p^2 w_{AA} + p q w_{Aa}}{\bar w}$ and $\bar w = p^2 w_{AA} + 2 p q w_{Aa} + q^2 w_{aa}$,
calculate the frequency of allele A after one generation of selection ($p'$) (round to three decimals).

Q8. In a molecular-clock model divergence between two lineages is given by $D = 2 r t$ where $D$ is sequence divergence, $r$ the per-lineage substitution rate and $t$ the time since split. If species X and Y show $D_{XY}=3\%$ and diverged $t_{XY}=4$ million years ago, estimate the divergence time $t_{MN}$ for species M and N that show $D_{MN}=6\%$ (assume the same molecular clock).

Q9. Assertion (A): A completely recessive deleterious allele can persist at a non-negligible equilibrium frequency in a large population despite strong selection against homozygotes.
Reason (R): For a completely recessive deleterious allele with mutation rate $\mu$ and selection coefficient $s$ against homozygotes, mutation–selection balance gives an equilibrium frequency $q^* \approx \sqrt{\dfrac{\mu}{s}}$.

Q10. The following binary character matrix (0 = ancestral, 1 = derived) is observed for four species W, X, Y and Z across five characters:

W: 1 1 0 1 1
X: 1 1 0 0 0
Y: 0 0 1 0 1
Z: 0 0 1 1 0

Which unrooted tree is the most parsimonious (fewest total character changes)?