Evolution Set-4

Q1. In a large randomly mating population in Hardy–Weinberg equilibrium the frequency of a recessive phenotype is $0.16$ (i.e. $q^2=0.16$). What is the expected frequency of heterozygotes ($2pq$) in this population?

Q2. A diploid population has allele frequencies $p=0.7$ and $q=0.3$. Viability selection acts with fitnesses $w_{AA}=1,\; w_{Aa}=1,\; w_{aa}=0.6$. Using the selection recurrence
$p'=\dfrac{p^2w_{AA}+pq\,w_{Aa}}{\bar w}$ (where $\bar w$ is mean fitness), what is the allele frequency $p'$ after one generation of selection?

Q3. In a randomly mating population the autosomal recessive disease has affected frequency $q^2=0.04$. If inbreeding increases so that the inbreeding coefficient is $F=0.25$, what is the expected frequency of carriers (heterozygotes)? (Use $P(Aa)=2pq(1-F)$.)

Q4. Assertion (A): Under neutral theory the substitution rate (rate of molecular evolution) equals the neutral mutation rate $\mu$ and is independent of effective population size $N_e$.
Reason (R): The number of new neutral mutations per generation is approximately $2N_e\mu$, but the fixation probability of a single neutral mutation is about $1/(2N_e)$, so the substitution rate per generation equals $2N_e\mu\times\frac{1}{2N_e}=\mu$.

Q5. Consider an infinitely large panmictic population with two alleles A and a where $w_{AA}=1,\; w_{Aa}=0.8,\; w_{aa}=0.9$. The internal equilibrium is given by $p^*=\dfrac{w_{aa}-w_{Aa}}{w_{aa}+w_{AA}-2w_{Aa}}$. If the initial frequency of A is $p_0=0.4$, what is the long-term outcome under selection (no mutation, migration or drift)?

Q6. In a large randomly mating population under Hardy–Weinberg equilibrium the frequency of the homozygous recessive genotype ($aa$) is $q^2=0.09$. What is the expected frequency of heterozygotes ($2pq$)?

Q7. On an island the allele $A$ has frequency $p_{island}=0.10$. Each generation, a fraction $m=0.20$ of individuals are migrants from the mainland where $p_{mainland}=0.80$. Using $p'=(1-m)p_{island}+m\,p_{mainland}$, what is the allele frequency of $A$ on the island after one generation of migration (ignore selection and drift)?

Q8. Consider four taxa A, B, C, D with binary characters (1 = derived, 0 = ancestral) as follows: A: $0\;0\;1\;1$, B: $0\;1\;1\;0$, C: $1\;1\;0\;0$, D: $1\;0\;0\;1$. Which of the following unrooted trees is the most parsimonious (requires the fewest character changes)?

Q9. Two allopatric populations diverged from an ancestor fixed for $aabb$. In population I allele $A$ arose and fixed (population genotype $AAbb$); in population II allele $B$ arose and fixed (population genotype $aaBB$). Assume Dobzhansky–Muller incompatibility occurs only when both derived alleles are homozygous together ($AABB$) and that heterozygotes are viable. Which cross will produce some inviable offspring expressing the incompatibility?

Q10. A completely recessive deleterious allele $a$ has mutation rate $\mu=1\times10^{-5}$ and selection coefficient against homozygotes $s=0.002$ in a population with effective size $N_e=250$. Which statement is correct?

Q11. In a large random‑mating population the allele frequencies at a locus are $p=0.7$ and $q=0.3$. Expected heterozygosity under Hardy–Weinberg is $H_{exp}=2pq$. A sample shows observed heterozygosity $H_{obs}=0.36$. Using $H_{obs}=2pq(1-F)$, estimate the inbreeding coefficient $F$ (rounded to two decimal places).

Q12. In a large panmictic population allele $A$ has frequency $p=0.6$ and allele $a$ has $q=0.4$. Fitnesses are $w_{AA}=1$, $w_{Aa}=1$, $w_{aa}=0.6$. Using
$p'=\dfrac{p^2 w_{AA} + p q w_{Aa}}{\bar w},\quad \bar w = p^2 w_{AA} + 2 p q w_{Aa} + q^2 w_{aa},$
calculate the allele frequency $p'$ of $A$ after one generation of selection (rounded to three decimal places).

Q13. A large panmictic population is in Hardy–Weinberg equilibrium with allele $A$ frequency $p=0.4$. Assuming no evolutionary forces act, what will be the expected frequency of heterozygotes $Aa$ after two generations?

Q14. Assertion (A): Genetic drift can cause rapid fixation or loss of neutral alleles in small populations, contributing to genetic divergence between isolated populations. Reason (R): The strength of genetic drift increases with effective population size $N_e$ because sampling fluctuations are larger in bigger populations.
Which of the following is correct?

Q15. Assertion (A): For a protein‑coding gene, a ratio $K_a/K_s>1$ (nonsynonymous to synonymous substitution rate) is generally interpreted as evidence of positive selection on that gene. Reason (R): A raised $K_a/K_s$ ratio can also arise from relaxed purifying selection or increased fixation of slightly deleterious nonsynonymous mutations in populations with reduced effective size $N_e$, not only from positive selection.
Which of the following is correct?