Describe species-area relationships.

(N/A) The great German naturalist and geographer Alexander von Humboldt,during his pioneering and extensive explorations in the wilderness of South American jungles,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,represented by the equation $S = CA^Z$.
On a logarithmic scale,the relationship becomes a straight line described by the equation $\log S = \log C + Z \log A$.
Where:
$S = \text{Species richness}$
$A = \text{Area}$
$Z = \text{Slope of the line (regression coefficient)}$
$C = Y\text{-intercept}$
Ecologists have discovered that the value of $Z$ lies in the range of $0.1$ to $0.2$,regardless of the taxonomic group or the region (whether it is the plants in Britain,birds in California,or molluscs in New York state,the slopes of the regression line are amazingly similar).
However,if we analyze the species-area relationship among very large areas like entire continents,we will find the slope of the line to be much steeper ($Z$ values in the range of $0.6$ to $1.2$).
For example,for frugivorous (fruit-eating) birds and mammals in the tropical forests of different continents,the slope is found to be $1.15$.