Who observed that within a region species richness increase with increasing explored area?

Alexander von Humboldt

The correct answer is Option (4) -Alexander von Humboldt

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. On a logarithmic scale, the relationship is a straight line described by the equation

log S = log C + Z log A

where S= Species richness

A= Area

Z = slope of the line (regression coefficient)