Consequences of limited availability of resources on scaling exponents of interrelated macroecological laws
Empirical evidence of scaling relationships between ecological quantities are abundant: population abundances (Damuth’s law) and metabolic rates (Kleiber’s law) scale with body mass, the number of species in an ecosystem scales with its area (species-area relationship), etc.
In an ecosystem in stationary conditions abundances, body mass and total metabolic rate (summed over all individuals) are controlled by the same limiting factor: the availability of resources. In any ecosystem, in fact, the rate of resource supply is necessarily finite. Consequently, there is a limit to the total metabolic rate the ecosystem can sustain. Given the above-mentioned connection between metabolism and body mass, and between body mass and abundance, the limit on total metabolic rate implies that resource availability will also impose constraints on body mass and abundance distributions. It is thus clear that species traits (body mass, metabolic rates) and ecological quantities (population abundances, number of species) must be tightly linked to each other, but how does this link reflect on scaling laws and their exponents?
We present a theoretical framework, based on methods of statistical physics and finite-size scaling theory, which accounts for the limiting effect of resources and allows exploring and quantifying the inter-relatedness of widespread macroecological laws.
In this framework the exponents of the above-mentioned scaling relationships are interconnected. In particular, the number of independent scaling exponents is smaller than the number of scaling relationships observed empirically (e.g. the species-area relationship, the scaling of the total biomass with area, the community size spectrum, the scale of the maximum organismic mass, the species-mass relationship, the relative species abundance), an issue that has been often overlooked in the literature. Consequently, estimates of one exponent will give information also on the other exponents. A interesting result of this investigation is that, depending on the exponent of metabolic rate scaling vs body mass, the total biomass could scale super-linearly with the ecosystem area. This is a testable hypothesis, which may have profound implications for ecology. Most importantly, a super-linear scaling of total biomass with ecosystem area may be of interest to conservation ecology. Among other consequences, in fact, super-linearity would suggest the creation of a small number of large protected areas rather than a large number of small ones.