Biodiversity and Conservation Set-4

Q1. Two communities X and Y each contain four species. Community X has abundances 40, 30, 20, 10; Community Y has abundances 25, 25, 25, 25. Using the Shannon diversity index $H'=-\sum p_i\ln p_i$ (natural log), which statement is correct?

Q2. A protected area of 1000 km$^2$ supports 200 species. Assuming the species–area relationship $S=cA^z$ with $z=0.25$ and the same constant $c$, estimate the expected number of species in a 250 km$^2$ reserve of identical habitat and the approximate percent decrease in species relative to the 1000 km$^2$ area.

Q3. In a breeding population there are $N_m=5$ males and $N_f=45$ females. Using $N_e=\dfrac{4N_mN_f}{N_m+N_f}$, calculate the effective population size $N_e$. Using the approximation that the fraction of heterozygosity lost per generation is $\Delta H\approx\dfrac{1}{2N_e}$, estimate the percent loss of heterozygosity per generation and compare it to a population of 50 with equal sexes (25 males & 25 females).

Q4. In the MacArthur–Wilson equilibrium model species number $S^*$ is reached when colonization equals extinction. Two islands have the same equilibrium $S^*$. Island L is large but far from the mainland (low colonization, low extinction). Island N is small but very near the mainland (high colonization, high extinction). Which island will have the higher species turnover rate (rate at which species are replaced per unit time) at equilibrium?

Q5. With identical total area for conservation, managers must choose between one large reserve (SL) and several small isolated reserves (SS). For which group of species is SL generally the better strategy to maximise long‑term persistence?

Q6. In a sampled community there are three species with abundances 6, 3 and 1 individuals respectively. Using Simpson's index of diversity defined as $1-\dfrac{\sum n_i(n_i-1)}{N(N-1)}$, calculate the Simpson's index of diversity for this sample (to two decimal places).

Q7. Two islands follow the species–area relationship $S=cA^z$. Island X has area $100\ \text{km}^2$ and supports 50 species; island Y has area $400\ \text{km}^2$ and supports 80 species. Using $z=\dfrac{\log(S_2/S_1)}{\log(A_2/A_1)}$, estimate the exponent $z$ (to two decimal places).

Q8. A protected area of total area $1\ \text{km}^2$ (1,000,000 m$^2$) must include a core zone at least 100 m away from edges to support interior forest species. Which of the following reserve designs will maximize the core area available to such interior species? (Assume simple geometric shapes and no overlap between separate reserves.)

Q9. Using the species–area relation $S=cA^z$, consider a region with $z=0.25$. Compare species richness offered by (i) one reserve of area $A$ versus (ii) two equal reserves each of area $A/2$. Which statement about total species richness in arrangement (ii) compared to (i) is correct?

Q10. A captive breeding programme has 20 breeding adults. Compare two sex-ratio strategies: (I) $N_m=2,\ N_f=18$ and (II) $N_m=10,\ N_f=10$. Effective population size is $N_e=\dfrac{4N_mN_f}{N_m+N_f}$ and heterozygosity after $t$ generations is $H_t=H_0\Big(1-\dfrac{1}{2N_e}\Big)^t$. Using these formulas, which statement best describes expected retention of heterozygosity after 10 generations?

Q11. In a sampled quadrat with 64 individuals four species have abundances: S1 = 32, S2 = 16, S3 = 8, S4 = 8. Using the Shannon–Wiener index $H = -\sum p_i \ln p_i$ (natural logarithm), what is the value of $H$ for this sample (approximately)?

Q12. A region of area 10,000 km$^2$ supports 2000 plant species. If habitat is reduced to 5,000 km$^2$ and the species–area relationship follows $S = cA^z$ with $z = 0.25$, estimate the number of species expected to persist in the reduced area. (Use $S_2 = S_1\left(\dfrac{A_2}{A_1}\right)^z$.)

Q13. Three sampled forest patches have local species counts 12, 15 and 9 respectively. The total number of distinct species across all patches (gamma diversity) is 22. Using the multiplicative definition $\beta_{mult} = \dfrac{\gamma}{\bar{\alpha}}$ where $\bar{\alpha}$ is mean local richness, what is $\beta_{mult}$ (approximately)?

Q14. For a diploid population the expected proportion of heterozygosity remaining after $t$ generations due to genetic drift is $H_t = H_0\left(1 - \dfrac{1}{2N}\right)^t$. Two isolated populations have census sizes $N_A=50$ and $N_B=10$. After $t=10$ generations, which statement is most accurate?

Q15. Consider three equal-area habitat fragments each of area $A$ where each fragment supports $S(A)=30$ species. With species–area scaling $S=cA^z$ and $z=0.25$, a single large reserve of area $3A$ would support $S(3A)=30\cdot3^{0.25}$ species. Assuming zero triple overlap (no species present in all three fragments) and that every pair of fragments shares on average $o$ species (pairwise overlap), the combined species richness of the three small reserves is $|A\cup B\cup C|=3S - 3o$. What is the minimum average pairwise overlap $o$ (rounded to nearest whole number) at which the single large reserve protects at least as many species as the three small reserves combined?