Ecological Archives E086-104-A1

Peter B. Adler, Ethan P. White, William K. Lauenroth, Dawn M. Kaufman, Andrew Rassweiler, and James A. Rusak. 2005. Evidence for a general species–time–area relationship. Ecology 86:2032–2039.

Appendix A. The scales of equivalence equation.

In order to determine the scales at which the observed exponents of the species–area relationship (SAR) and species–time relationship (STR) are equal, we determine the form of these relationships from the full species–time–area relationship (STAR) model and then set the exponents to be equal to one another.

Starting with the full STAR model from Table 1 and rearranging gives

where S is the number of species observed at a given area (A) and time-span (T), z1 is the scaling exponent of the SAR at the unit time scale, w1 is the scaling exponent of the STR at the unit spatial scale, and u is the interaction term. Rearranging to get the form of the SAR at T and the STR at A gives

Taking the exponents from the relevant term, setting them equal to one another, and solving for A gives

Thus, for the full model, at any time span there is a spatial scale at which the exponents of the SAR and STR will be equal to one another, and that spatial scale is simply a constant multiple of the time scale. Another way of putting this that the ratio of the scales at which the exponents are equal to one another is a constant, as can be seen in the next to last step of the above solution.



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