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Species-area curve

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SUMMARY
=======
The species–area relationship or species–area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and empirically, the relative numbers seem to follow systematic mathematical relationships. The species–area relationship is usually constructed for a single type of organism, such as all vascular plants or all species of a specific trophic level within a particular site. It is rarely, if ever, constructed for all types of organisms if simply because of the prodigious data requirements. It is related but not identical to the species discovery curve.
Ecologists have proposed a wide range of factors determining the slope and elevation of the species–area relationship. These factors include the relative balance between immigration and extinction, rate and magnitude of disturbance on small vs. large areas, predator–prey dynamics, and clustering of individuals of the same species as a result of dispersal limitation or habitat heterogeneity. The species–area relationship has been reputed to follow from the 2nd law of thermodynamics. In contrast to these "mechanistic" explanations, others assert the need to test whether the pattern is simply the result of a random sampling process.Authors have classified the species–area relationship according to the type of habitats being sampled and the census design used. Frank W. Preston, an early investigator of the theory of the species–area relationship, divided it into two types: samples (a census of a contiguous habitat that grows in census area, also called "mainland" species–area relationships), and isolates (a census of discontiguous habitats, such as islands, also called "island" species–area relationships). Michael Rosenzweig also notes that species–area relationships for very large areas—those collecting different biogeographic provinces or continents—behave differently from species–area relationships from islands or smaller contiguous areas. It has been presumed that "island"-like species–area relationships have higher slopes (in log–log space) than "mainland" relationships, but a 2006 metaanalysis of almost 700 species–area relationships found the former had lower slopes than the latter.Regardless of census design and habitat type, species–area relationships are often fit with a simple function. Frank Preston advocated the power function based on his investigation of the lognormal species-abundance distribution. If



S


{\displaystyle S}
is the number of species,



A


{\displaystyle A}
is the habitat area, and



z


{\displaystyle z}
is the slope of the species area relationship in log-log space, then the power function species–area relationship goes as:




S
=
c

A

z




{\displaystyle S=cA^{z}}

Here



c


{\displaystyle c}
is a constant which depends on the unit used for area measurement, and equals the number of species that would exist if the habitat area was confined to one square unit. The graph looks like a straight line on log–log axes, and can be linearized as:




log
⁡
(
S
)
=
log
⁡
(
c

A

z


)
=
log
⁡
(
c
)
+
z
log
⁡
(
A
)


{\displaystyle \log(S)=\log(cA^{z})=\log(c)+z\log(A)}

In contrast, Henry Gleason championed the semilog model:




S
=
log
⁡
(
c

A

z

...