The Time Invariance Principle, Ecological (Non)Chaos, andA Fundamental Pitfall of Discrete Modeling

This paper is to show that all but one discrete models used for population dynamics in ecology are inherently paradoxical that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to resolve 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.