The Narragansett Bay Model

Abstract

One of the basic problems in formulating mathematical expressions for detailed ecological processes is how to combine into a single expression the influences of several factors that operate simultaneously. The approach chosen here, and in many other similar models (Canale et al, 1974; DiToro et al, 1971; O’Brien and Wroblewski, 1972), is to postulate a maximum rate as a function of one factor, usually temperature, and to determine the effects of the remaining factors as unitless fractions which reduce the maximum. Functionally, this is the same assumption implicit in commonly used equations for even a single factor. For example, the hyperbolic Monod (1942) expression for substrate-limited growth of microorganisms (also used in enzyme reaction kinetics by Michaelis and Menten, 1913) is the product of a maximum growth rate, μ_max, and a fraction:

$$ \mu = {\mu_{\max }}(\frac{S}{{{K_s} + S}}) $$

Note that numerator and denominator have the same units (concentration), and the fraction is therefore a unitless number between 0 and 1. This logic may be easily extended to include more limiting fractions, each of which may be independently derived.