Which concept did Alexander von Humboldt describe for the first time?

The correct answer is Option (3) → Species-area relationships

During his long explorations of the South American jungles, the German naturalist and geographer Alexander von Humboldt observed that within a region, species richness increased with the area explored, but only up to a limit. This is the species-area relationship, which becomes a straight line on a logarithmic scale.

Option (1) Ecological biodiversity — Incorrect. Ecological diversity is diversity at the ecosystem level, one of the levels of biodiversity. It was not Humboldt’s observation.

Option (2) Law of limiting factor — Incorrect. The law of limiting factor deals with how a factor in limited supply controls a process. It has no link with Humboldt’s explorations.

Option (3) Species-area relationships — Correct. Humboldt first described how species richness rises with the area explored, up to a limit.

Option (4) Population growth equation — Incorrect. Population growth equations describe how the size of a population changes with time. They are studied under population ecology, not as Humboldt’s work.

NCERT Extract:
Patterns of Biodiversity – “… (ii) 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 ….”