A micro-level 'consumer approach' to species population dynamics - Thomas Christiaans; Thomas Christiaans; Rüdiger Pethig (Center for Economic Studies and ifo Institute (CESifo), 2005)
In this paper we develop a micro ecosystem model whose basic entities are representative organisms which behave as if maximizing their net offspring under constraints. Net offspring is increasing in prey biomass intake, declining in the loss of own biomass to predators and Allee's Law applies. The organism's constraint reflects its perception of how scarce its own biomass and the biomass of its prey is. In the short-run periods prices (scarcity indicators) coordinate and determine all biomass transactions and net offspring which directly translates into population growth functions. We are able to explicitly determine these growth functions for a simple food web when specific parametric net offspring functions are chosen in the micro-level ecosystem model. For the case of a single species our model is shown to yield the well-known Verhulst-Pearl logistic growth function. With two species in predator-prey relationship, we derive differential equations whose dynamics are completely characterized and turn out to be similar to the predator-prey model with Michaelis-Menten type functional response. With two species competing for a single resource we find that coexistence is a knife-edge feature confirming Tschirhart's (2002) result in a different but related model.
Keywords: Q20; 330; species; growth; extinction; predator-prey relations; resource competition; Erneuerbare Ressourcen; Bioökonomik; Mikroökonomische Fundierung; Theorie; Räuber-Beute Modell