What shape best describes the relationship between species richness a…

The correct answer is Option (3) → Rectangular hyperbola

Alexander von Humboldt saw that, within a region, species richness rises with the area explored, but only up to a limit. For many taxa, such as flowering plants, birds, bats and freshwater fishes, a plot of species richness against area gives a rectangular hyperbola: it rises steeply and then levels off.

Option (1) Straight line — Incorrect. The relationship becomes a straight line only when both axes are on a logarithmic scale (log S = log C + Z log A). On an ordinary graph the curve is not straight.

Option (2) Sigmoid curve — Incorrect. A sigmoid (S-shaped) curve describes logistic population growth, where numbers level off at the carrying capacity. It is not the species-area curve.

Option (3) Rectangular hyperbola — Correct. The species-area curve is a rectangular hyperbola, S = CA^Z, for a wide variety of taxa.

Figure 13.2 Showing species area relationship. Note that on log scale the relationship becomes linear

NCERT Extract:
Patterns of Biodiversity – “… Species-Area relationships : During his pioneering and extensive explorations in the wilderness of South American jungles, the great German naturalist and geographer Alexander von Humboldt observed that within a region species richness increased with increasing explored area, but only up to a limit. In fact, the relation between species richness and area for a wide variety of taxa (angiosperm plants, birds, bats, freshwater fishes) turns out to be a rectangular hyperbola (Figure 13.2).”