Structured Population Dynamics: An Introduction to Integral Modeling

Authors

Joseph Briggs, North Carolina State University, Raleigh
Kathryn Dabbs, University of Tennessee - Knoxville
Michael Holm, University of Nebraska-Lincoln
Joan Lubben, University of Nebraska-LincolnFollow
Richard Rebarber, University of Nebraska - LincolnFollow
Brigitte Tenhumberg, University of Nebraska - LincolnFollow
Daniel Riser-Espinoza, Swarthmore College

Document Type

Article

Date of this Version

2010

Citation

Mathematics Magazine 83 (2010) 243-257. doi:l0. 4169/002557010X521778

Comments

Copyright © 2010 Mathematical Association of America. Used by permission.

Abstract

In this article we illuminate the differences and similarities between matrix population models and integral population models for single-species stage structured populations. We illustrate the use of integral models with an application to Platte thistle, following Rose et al. [22], showing how the model is determined by basic life history functions. PPMs are ubiquitous in ecology, but for many purposes an IPM might be easier and/or more accurate to use. In TABLE 1 we summarize the similarities between PPMs and IPMs. In order to compare the predictions for PPMs and IPMs, enough data must be available to find the parameters in both models. This is done for models for the plant monkshood in Easterling et al. [9]. We should mention that if time is treated as a continuous variable, the analogue of a PPM model is an ordinary differential equation, and the analogue of a IPM is an integro-differential equation.