Stability analysis of toxic substances within aquatic ecosystems and their effect on aquatic populations

Abstract

Abstract A stability analysis is presented for toxic substances introduced to aquatic ecosystems and their intercompartmental relationships to aquatic populations. A specific toxin, vinyl chloride, was used in this study because an aquatic ecosystem model that includes vinyl chloride is available. The system and compartmental stability are dependent on the magnitudes and rates of transfer of vinyl chloride into, out of, and within each compartment. An 11 compartment model is presented and set up for the system eigenvalues. Compartments whose eigenvalues equal zero are the least stable because they accumulate vinyl chloride. Intercompartmental transports of vinyl chloride into and out of the filter-feeding fish compartment is incorporated into a logistic population model. This model is analyzed for growth stability as a function of vinyl chloride in the aquatic system. It is found that the population collapses when the vinyl chloride decay rate terms are greater than the growth rate term. These techniques apply to the analysis of any aquatic population where a toxic substance is present.