Application of various mathematical models to data from the uptake of methyl mercury in bluegill sunfish ( Lepomis macrochirus)

Abstract

Evaluated and compared are the results of various mathematical models to data from the uptake of methyl mercury in bluegill sunfish ( Lepomis macrochirus). Data were obtained from the direct uptake of methyl mercury from water in bluegill at 9°C and at a CH 3HgCl concentration of 0.2 ppb. The models considered are: (1) linear uptake relationship; (2) first-order kinetics, one-compartment or single-exponential model; (3) combination of first-order kinetics and the linear uptake relationship, designated as slope-exponential model; (4) two-compartment or double-exponential model; (5) three-compartment model, including a storage compartment for the build up of contaminant, designated as storage model; (6) three-compartment model, allowing two routes of elimination, designated the “Y” model; (7) an empirical uptake relationship having the form of a rectangular hyperbola. A comparison of the nonlinear models showed that the empirical model had fewer convergence problems in obtaining parameter estimates and its parameter values had less variation. The best fit was made by the “Y” model, the empirical model gave one of the smaller values of the residual mean squares, and other nonlinear models had computational convergence difficulties. The lack of computational problems and the comparitively small residual mean squares resulted in the selection of and the preference for the empirical model for use in describing the individual and interactive effects of temperature and methyl mercury concentration on the direct uptake of methyl mercury from water by bluegill.