Biology Set-1

Q1. In a 1 m^2 grassland quadrat the counts of four plant species were 10, 30, 30 and 30 individuals. Using the Shannon diversity index $H'=-\sum p_i\ln p_i$ where $p_i$ is the proportion of species $i$, what is the approximate value of $H'$ (round to two decimal places)?

Q2. A conservation planner must choose between one large reserve of area $A$ and four equal smaller reserves whose total area equals $A$. Using the species–area relationship $S=cA^z$ and assuming species in different small reserves are completely distinct (no overlap), the ratio of total species in the four small reserves to species in the single large reserve equals $4^{1-z}$. For $z=0.3$, which of the following values is closest to that ratio?

Q3. A population has effective population size $N_e=25$ and initial heterozygosity $H_0=0.80$. Using the formula $H_t=H_0\left(1-\dfrac{1}{2N_e}\right)^t$, what is the expected heterozygosity after $t=10$ generations (round to two decimal places)?

Q4. Assertion (A): For critically small wild populations (census size < 20), transferring individuals into a well-managed captive breeding program is often more effective at maintaining genetic heterozygosity over several decades than leaving them in situ when habitat continues to degrade.
Reason (R): In captivity, controlled breeding and husbandry can increase the effective population size $N_e$ and reduce environmental and demographic stochasticity, thereby slowing the per‑generation loss of heterozygosity described by $H_t=H_0\left(1-\dfrac{1}{2N_e}\right)^t$.

Q5. Assertion (A): Establishing a wildlife corridor between two isolated habitat patches generally reduces extinction probability for species with limited dispersal by facilitating recolonization and gene flow.
Reason (R): Corridors reduce extinction risk primarily by increasing the edge‑to‑area ratio of habitat patches, which enhances habitat heterogeneity at patch boundaries.

Q6. Using the species–area relationship $S=cA^z$ with $z=0.25$, a forest fragment loses half its area while originally supporting 100 species. According to the model, approximately how many species would remain after the area is halved?

Q7. Two communities each have total individuals $N=100$. Community I has species counts $[25,25,25,25]$; Community II has species counts $[70,10,10,10]$. Using Simpson's index of diversity
$D = 1 - \dfrac{\sum n_i(n_i-1)}{N(N-1)}$, which statement is correct?

Q8. Two isolated populations have effective population sizes $N_e=500$ and $N_e=50$. Using the approximate rate of loss of heterozygosity per generation $\Delta H \approx \dfrac{1}{2N_e}$, by what factor does the smaller population lose heterozygosity faster than the larger one?

Q9. Assertion (A): According to the species–area relationship $S=cA^z$ with a typical exponent $0<z<1$, fragmenting a continuous habitat of area $A$ into several smaller patches (keeping total area constant) will predict a larger combined species richness (by summing $S$ for each fragment) than the richness predicted for the unfragmented area.
Reason (R): For $0<z<1$ the function $f(A)=A^z$ is concave, and for positive parts $A_i$ with $\sum A_i = A$ one has $\sum A_i^z > A^z$, so $\sum cA_i^z > cA^z$.

Q10. A captive-breeding programme maintains 24 adults. Compare two strategies: X with $N_m=6$, $N_f=18$; Y with $N_m=12$, $N_f=12$. Using $N_e \approx \dfrac{4N_mN_f}{N_m+N_f}$, which statement is correct about effective population size and its implication for retaining genetic diversity?