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Species-Area Relations

S = cA^z

or

log S = log c + z log A

where S is the number of species (richness), A the area, z the exponent, and c the constant of
proportionality or the expected number of species occurring on one unit of area (one related to
the units of measure of area, e.g., sq. mile, km², etc.).

In studies of birds:

S = 2.53 A ^0.165 (Harris)
S = 1.16 A^0.176 (British breeding birds)
S = 1.17 A^0.24 (wintering British birds)

and mammals

S = 1.19 A^0.326

where A is in square miles.

z typically ranges from 0.25 to 0.35. (It may be very close to 0.33 or a cube-root.)

when z = 0.30, a 10-fold increase in area is necessary to double the number of species. A 90% reduction in area can lead to a 50% decrease in species in the area.

Rafe et al. (1985: 332), faced with taking the logarithm of a zero area, assigned all habitats not present an arbitrary value of 0.1 ha partially on the grounds that such an area was "... too small to hold a major assemblage of species."

A typical strategy is to use the conventional transformation of species (y) and area (x) as log (y +1) and log (x + 1).

An optional view is to study mean density of species per occupied plot, an old ecological trick.

One study found a species-elevation relationship

S = 101.1 - 4.4 x 10^-3 X - 8 x 10^-7 X²

The form of the equation may be helpful in later analyses.

Rafe et al. (1985: 331) found, to no one's surprise, that a greater amount of variation in richness is explained by species-habitat relations than by species-area relationships.

Mack et al. (1997) found that remotely sensed data are of sufficient resolutiuon for coarse estimates of bird species-area relationships.

Increasing the area has an effect over and above that due to increase in habitat diversity with area (Rafe et al. 1985: 332). For sites of equal area, greatest richness will occur on the sites with the most habitat types.

Species-area curves are used for:

• estimating species present, richness, or its synonym, "diversity "
• predicting number of extinctions due to habitat destruction
• estimating the minimum size of a refuge needed to preserve a given species or number of species
• raising issues of reserve design

Beta or gamma species are found within more than one habitat type.

Species tend to be more numerous where :

• islands are close to "shore" or a source
• islands are large
• islands are diverse heterogenous
• islands have complex topography (mountainous, etc.)
• islands have several climatic extremes
• islands have many layers (foilage height diversity)
• islands are more mature (time since volcanoes etc.)

Future developments are to be found in treating regions (counties, provinces, watersheds, etc.) as "islands." and using the semivariogram to determine the limits of such islands.

Potential for future analyses: species per 100 km2may be related to percent of the area of an "island" with slopes > 30%. Several lines like the one here may reflect different aspects. Analyze for the asymptote, then study relations past this criterion of steepness, i.e., the species steepness curve, a negative logarithmic.

It also seems reasonable to analyze richness not only as a function of of area, but also of elevation differences, irregularity of the area (e.g., edges), and layers present.

The species area curve has been used to argue for preserving large areas ( estimating the minimum size area to protect a select number of species) and for estimating rates of extinction (as a function of habitat loss) (see Simberloff, Bul. Ecol. Soc of Amer, June 1987)

Assignment

Using Harris' equation and remembering there are 640 acres in a square mile, what is the likely richness of a 12,000 acre tract? Send the instructor a brief one-sentence answer.

References

Harris, L.D. 1984. The fragmented forest. Univ. Chicago Press. Chicago, IL. 211 pp.

Rafe, R.W., M.B. Usher, and R.G. Jefferson. 1985. Birds on reserves: the influence of area and habitat on species richness. J. Appl. Ecol. 22: 327-335.

Cain, S.A. 1938. The species-area curve. Amer. Midland Naturalist 19: 573-581.

Colinvaux, P. 1986. Ecology. John Wiley and Sons, Inc., New York, NY 725pp.

Connor, E.F. and E.D. McCoy. 1979. The statistics and biology of the species-area relationship. Amer. Naturalist 113: 791-833.

Curran, P.J. 1988. The semivariogram in remote sensing: an introduction. Remote Sensing Environment J. 24:493-507.

Davies, N.B. 1977. Prey selection and social behavior in wagtails (Aves:Motacillidae). Jour. Animal Ecol. 46:37-57.

Game, M. 1980. Best shape for nature reserves. Nature 287:630-631

Goff, F.G., G.A. Dawson, and J.J. Rochow. 1982. Site examination for threatened and endangered plant species. Environmental Management 6(4): 307-316.

Mack, E.L., L.G. Firbank, P>E> Bellamy, S.A. Hinsley, and N.Veitch 1997. The comparison of remotely sensed and ground-based habitat area data using species-area models. J. Appl. Ecology 34:1222-1228.

Mason, N.A. 1993. Floral richness inventory of an eastern US forest. Unpub. M.S. Thesis, Va. Poly. Inst. and State Univ., Blacksburg, Va. 107pp.

Mueller-Dombois, D. and H. Ellenberg. 1974. Aims and methods in vegetation ecology. John Wiley and Sons, New York, NY 547 pp.

Office of Technology Assessment. 1987. Technologies to maintain biological diversity. Congress of the United States, Washington, DC 334pp.

Peet, R.K. 1974. The measurement of species diversity. Annual Review of Ecology and Systemeatics 5: 285- 307

Shafer, C.L. 1990. Nature reserves: island theory and conservation practice. Smithsonian Institution Press, Washington, DC 189pp.

Simberloff, D.S. and L.G. Abele. 1976. Island biogeography theory and conservation practice Science 191:285-286.

Simberloff, D.S. and L.G. Abele. 1976. Island biogeography and conservation: strategy and limitations. Science 193: 1027-1032.

Begon, 1966. Ecology: individuals, populations and communities. Black~ell Scientific Publ., Mass. 851 pp.

Gysel, L. W. and L. J. Lyon. 1980. Habitat analysis and evaluation. Pages 305-327 in S. D. Schemnitz, ed. Wildlife management techniques. The Wildlife Society, Washington, D.C.

Krebs, C.J. 1985. Ecology: The experimental analysis of distribution and abundance. Third ed. Harper & Row, Publ., New York, N.Y. 8OOpp.

May, R. M. 1981. Theoretical ecology. Second ed. Blackwell Scientific Publ., Mass. 489pp.

Soule´, M. E. and B. A. Wilcox, editors. 1980. Conservation biology: an evolutionary-ecological perspective. Sinauer Associates, Inc., Mass. 395 pp.

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Last revision July 20, 2000.