An Allometric Interpretation of Species-Area Curves: The Meaning of the Coefficient

Abstract

Students of allometric growth and the species-area curve have favored the same mathematical expression, the power function, in their work. Allometricians, after much debate and error, derived satisfactory interpretations for the parameters of this function. The coefficient proved difficult because it is not invariant under change of scale and often makes no biological sense as the value of y (number of species) when x equals 1 unit. Ecologists have fallen into the same traps that plagued allometricians 30 yr ago, but have been unaware that the problems had been solved by their sister subdiscipline. Coefficients of power functions should not be neglected or ignored by ecologists (more often than not, they are not reported at all). When slopes are constant in families of related curves-a common situation in the species-area literature where slopes are so often near 0.25-ratios of coefficients are constant at all values of x (area): They record a size-independent invariant within a system. I present several invariants, previously unrecognized or identified more circuitously in other ways.