Parameter Estimates in Differential Equation Models for Population Growth

Abstract

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer Mathematica code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist, G. F. Gause, and estimate growth rates, carrying capacities, and “coefficients for the struggle for existence.”

Keywords:

• Parameter estimation
• differential equations
• population modeling
• logistic
• competition
• G. F. Gause
• optimization
• sum of square errors

Acknowledgments

The author is very grateful to the referees for careful readings and meticulous comments and suggestions, all of which improved the exposition, mathematics, and modeling. He is most thankful to the new Editor-in-Chief, Joanna A. Ellis-Monaghan, for shepherding this manuscript through the referee and publication stages. As an editor for many years, it is always good to be on the other side and to receive attention, feedback, and suggestions, (lots of them!) all of which make for better writing. Finally, he thanks his students over many years for taking the modeling journey with him, time and time again, and learning with him.

Notes

This article is not subject to US copyright law.

The views expressed here in are those of the author and do not reflect the position of the United States Military Academy, the Department of the Army, or the Department of Defense.