Mathematics, Department of


Date of this Version



Posted 9 March 2007.

Subsequently published as “’The Time Invariance Principle, the absence of ecological chaos, and a fundamental pitfall of discrete modeling,” Ecological Modelling 215 (2008) 287–292. doi: 10.1016/j.ecolmodel.2008.03.013 Copyright 2008 Elsevier B.V.


Copyright 2008 Elsevier B.V.


This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.