Marker Transport Through Ecosystem Energy Flow

Markers are substances which are artificially introduced into ecosystems in small quantities and which have no acute effects on energy flow. A marker might be a pollutant which affects life significantly only over long time frames. Alternatively, a marker might be a benign substance easily detected in small amounts and introduced in order to trace energy flow and so evaluate energy flow models. The flow of markers can be modeled in parallel to energy flow by assuming that energy flowing out of a compartment carries with it a proportional mass of marker. The purpose of this paper is to derive qualitative conditions on the food-web structure and the consumption functions of a model which guarantee stability of energy and marker flows. We will show that many consumption functions used in mathematical ecology lead to sign-stable models of energy flow and furthermore that such models enjoy inherent stability of associated marker flows.