Species-area relationships

Statistics on the rates of extinction have mostly been inferred from a species-area relationship and projections of habitat destruction.

$$S=CA^z$$

If we're only interested in the proportion of species remaining after some portion of the habitat has been destroyed

$${S' \over S} = {{CA'^z} \over {CA^z}}$$ (1)

$$= \left( {A' \over A} \right)^z$$ (2)

$z$ is generally between 0.15 and 0.35. So for example, if we're interested in projecting the fraction of species that will be lost from tropical rainforests as a result of deforestation, we can make the following back of the envelope calculation.

If current rates of tropical deforestation continue for another 30 years half of the remaining rain forest will be gone. If we then prevent all further deforestation, between

$$0.5^{0.35} = 0.78$$

and

$$0.5^{0.15} = 0.90$$

of the species presently there will remain, i.e., 10%-20% will go extinct. More sophisticated approaches use an exponential decay model, recognizing that the predictions of the above approach apply only after the remaining forest fragments have reach an immigration-extinction equilibrium. Notice, however, that these calculations only reflect the effects of lost habitat, not increased exposure to disease, competition with invasive exotics, overxploitation, or habitat degradation.