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

Explanation

Alexander von Humanboldt ( German naturalist and geographer ) whil working on wilderness of south American jungles found that at specific places species richness increased with increasing explored area.but at such places, this increase in species richness was only up to certain extent. A rectangular hyperbola is obtained for relation between species and region. this happens for wide range of taxa like birds, bats, freshwater fishes and angiosperms.
Realtionship is of straight line on logarithmic scale e.g.
`log S= log C+Zlog A`
[S=species richness, A=area, Z= regression coefficient (slops of line ) and C= Y - intercept ]
In any type of taxonomic group or region value of Z comes in between 0.1 to 0.2. This value is similar e.g. for plants in U.K. birds in california and molluscs in New York. however if large continents are taken into account for this type of studies, value of Z differs e.g. it comes in between 0.6 to 1.2. even the slope of line is much steeper. when Z value is studied, it comes equal to 1.15 for frugivorous ( fruit eating ) birds and mammuals of tropical forests of different continents.