Species-area Relationships
The Unified Theory unifies biodiversity, as measured by species-abundance curves, with biogeography, as measured by species-area curves. Species-area relationships show the rate at which species diversity increases with area. The topic is of great interest to conservation biologists in the design of reserves, as it is often desired to harbour as many species as possible.
The most commonly encountered relationship is the power law given by
where S is the number of species found, A is the area sampled, and c and z are constants. This relationship, with different constants, has been found to fit a wide range of empirical data.
From the perspective of Unified Theory, it is convenient to consider S as a function of total community size J. Then for some constant k, and if this relationship were exactly true, the species area line would be straight on log scales. It is typically found that the curve is not straight, but the slope changes from being steep at small areas, shallower at intermediate areas, and steep at the largest areas.
The formula for species composition may be used to calculate the expected number of species present in a community under the assumptions of the Unified Theory. In symbols
where θ is the fundamental biodiversity number. This formula specifies the expected number of species sampled in a community of size J. The last term, is the expected number of new species encountered when adding one new individual to the community. This is an increasing function of θ and a decreasing function of J, as expected.
By making the substitution (see section on saturation above), then the expected number of species becomes .
The formula above may be approximated to an integral giving
This formulation is predicated on a random placement of individuals.
Read more about this topic: Unified Neutral Theory Of Biodiversity