A Micro-Level 'Consumer Approach' to Species Population Dynamics

47 Pages Posted: 28 Sep 2005

See all articles by Thomas Christiaans

Thomas Christiaans

University of Siegen

Thomas Eichner

University of Siegen - School of Economic Disciplines

Rudiger Pethig

University of Siegen - School of Economic Disciplines; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: August 2005

Abstract

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: species, growth, extinction, predator-prey relations, resource competition

JEL Classification: Q20

Suggested Citation

Christiaans, Thomas and Eichner, Thomas and Pethig, Rudiger, A Micro-Level 'Consumer Approach' to Species Population Dynamics (August 2005). CESifo Working Paper Series No. 1530. Available at SSRN: https://ssrn.com/abstract=812327

Thomas Christiaans

University of Siegen ( email )

Hoelderlinstrasse 3
57068 Siegen, NRW 57068
Germany

Thomas Eichner

University of Siegen - School of Economic Disciplines ( email )

Hoelderlinstrasse 3
57068 Siegen
Germany

Rudiger Pethig (Contact Author)

University of Siegen - School of Economic Disciplines ( email )

Hoelderlinstrasse 3
57068 Siegen
Germany

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

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