Modeling the dynamics of nutrient limited consumer populations using constant elasticity production functions

Abstract

The marginal rate of technical substitution is a well-defined and important concept in economic production theory. It describes the ability of a firm to maintain levels of production while substituting one factor of production for another. Ecological stoichiometry has considered a similar problem—how organismal production is affected when incoming nutrients are not available in ideal proportions. However, the dominant models of analysis have assumed homeostatic nutrient ratios on the part of consumers. This is equivalent to fixed-factor production in economics with no substitutability. This work demonstrates how models of production from economic theory that incorporate factor substitutability provide a more realistic representation of consumer production under nutrient limitation. I demonstrate how economic analysis tools can be used to assess nutrient limited production. I also describe the changes in individual and systems dynamics as the ability to substitute carbon for another nutrient increases. In particular, substitution is shown to promote ecosystem resilience by broadening the threshold element ratio at which a nutrient becomes limiting.