What is the significance of the slope of regression in a species - area relationship?

Explanation

German Naturalist and Geographer Alexander von Humboldt explored the wilderness of south American jungles and found that within a region the species richness increased with increasing area but upto a certain limit. The relationship between species richness and area for a wide variety of taxa (angiosperm plants, birds, bats and freshwater fishes) turned out to be the 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)
C= Y-intercept Regression coefficient Z generally has a value of 0.1-0.2 regardless of taxonomic group or region. However, in case of the species-area relationship Area in very large areas like entire continents, the slope of the line appears to be much steeper (Z-value in the range of 0.6-1.2). For example, in case of the fruit eating (frugivorous) birds and mammals in the tropical forests of different continents, the slope is found to be a steeper line.