Biodiversity and Conservation Set-3

Q1. Using the species–area relationship $S=cA^z$, where $c=10$ and $z=0.25$, if habitat area increases from $A_1=100\ \mathrm{km}^2$ to $A_2=400\ \mathrm{km}^2$, by what factor does species richness change ($S_2/S_1$)?

Q2. A community has species counts A:50, B:30, C:15, D:5 (total 100). Simpson's diversity index is $D=1-\sum p_i^2$, where $p_i$ are relative abundances. Which of the following management actions will produce the largest increase in Simpson's diversity index?

Q3. Three isolated populations each have census size $N=100$. Their sex compositions are: (i) 50 males & 50 females; (ii) 10 males & 90 females; (iii) 40 males & 60 females. Using $N_e=\dfrac{4N_mN_f}{N_m+N_f}$, which population will lose genetic variation most slowly (i.e., has the largest effective population size $N_e$)?

Q4. Assertion (A): Genetic rescue—translocating unrelated/less-related individuals into a small inbred population—often increases genetic diversity and fitness, thereby reducing extinction risk.
Reason (R): Introducing individuals from different populations never causes long-term negative effects such as disruption of local adaptations or outbreeding depression.

Q5. A conservation agency must allocate $400\ \mathrm{km}^2$ either as one square reserve or as four equal square reserves (total area same). Edge effects extend $w=1\ \mathrm{km}$ inward from all reserve boundaries, rendering the outer $1\ \mathrm{km}$ strip unsuitable for an edge-sensitive species. Core side length is $\text{core side}=\sqrt{A}-2w$ and core area $=(\sqrt{A}-2w)^2$. Which configuration provides the greater total core habitat for the species?

Q6. A region follows the species–area relationship $S = cA^z$ with $c=8$ and $z=0.25$. If the protected area increases from $A_1 = 100\ \mathrm{km}^2$ to $A_2 = 400\ \mathrm{km}^2$, by what factor will species richness change?

Q7. Two terrestrial communities each contain 100 individuals. Community P has species abundances [40, 30, 20, 10]; Community Q has abundances [25, 25, 25, 25]. Using Shannon diversity $H' = -\sum p_i \ln p_i$ (where $p_i$ is the proportion of individuals of species $i$), which statement is correct?

Q8. Two proposed reserves each have area $A = 100\ \mathrm{km}^2$. Reserve S is compact (square, side $=\sqrt{A}$ km) and Reserve R is highly elongated ($1\ \mathrm{km}\times 100\ \mathrm{km}$). If edge effects extend a strip of width $w=1\ \mathrm{km}$ from the boundary, the core area for a compact reserve can be estimated as $(\sqrt{A}-2w)^2$. Which comparison of core areas is correct?

Q9. Assertion (A): A population founded by a very small number of individuals will necessarily show increased allelic diversity relative to its source population within a few generations.
Reason (R): Founder events reduce effective population size $N_e$, so genetic drift becomes strong; the expected per-generation loss of heterozygosity is approximately $\dfrac{1}{2N_e}$, and mutation is usually too slow to restore lost alleles rapidly.

Q10. You must choose a reserve design for a landscape of total area $100\ \mathrm{km}^2$. There are 20 area-sensitive species that require a single contiguous reserve of at least $50\ \mathrm{km}^2$ to persist; they cannot survive in smaller isolated fragments. Generalist species follow the species–area relationship $S_{gen}=3A^{0.25}$ (with $A$ in km$^2$). Compare two designs: Design 1 — one contiguous reserve of $100\ \mathrm{km}^2$; Design 2 — four isolated reserves of $25\ \mathrm{km}^2$ each (totalling $100\ \mathrm{km}^2$), assumed far enough apart to have independent species sets. Which design will conserve more species overall?