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In the field of ecology, a well known relation between the number of species and the size of an island can be approximated by a power function of the form: $S = c A^z$

  • $S$ = number of species
  • $c$ = a fitted constant
  • $A$ = area of the island
  • $z$ = a constant equal to $\log_{10}(S) / \log_{10}(A)$

Variable $z$ is, in fact, the slope of the linear relation between $\log_{10}(S)$ and $\log_{10}(A)$. I’ve never encountered a multivariate equation where one of the independent variables consists of the slope of a linear relation where a non-linear transform has been applied to the major independent and dependent variable.

I’m curious if the previously mentioned equation belongs to a more general class of equations? Is there a special name for these types of equations?

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