KCET · BIOLOGY · STD 12 - 13. Biodiversity and Conservation

Match for M and N with species-area relationship shown in the graphic representation below and choose the correct option.

A \(M \rightarrow S = CA^Z, N \rightarrow \log S =\log C + Z \log A\)
B \(M \rightarrow S = CZ^A, N \rightarrow \log C =\log S + Z \log A\)
C \(M \rightarrow S = CA^Z, N \rightarrow \log S =\log C + A \log Z\)
D \(M \rightarrow S = AZ^C, N \rightarrow \log ZA =\log C + \log S\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(M \rightarrow S = CA^Z, N \rightarrow \log S =\log C + Z \log A\)

Step-by-step Solution

Detailed explanation

(A) \(M \rightarrow S = CA^Z, N \rightarrow \log S =\log C + Z \log A\),
The relationship between species richness and area is a rectangular hyperbola, it is a straight line on a logarithmic scale. The curve is often referred to as the species-area curve. The description of the species-area relationship is as follows:
\(S = CA ^{ Z }\)
logS= logC + ZlogA
where, S = species richness, A = area, Z = the slope the line (regression coefficient) and C = the intercept on the Y-axis.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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