Density Function Solutions of Population Size Models

• Activity Number: 453
• Type: Contributed
• Date/Time: Wednesday, August 6, 2008 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): James Matis*+ and Thomas Kiffe and Timothy Matis and Wopke van der Werf and Alejandro Costamagna and G. Jerry Michels, Jr.
• Companies: Texas A&M University and Texas A&M University and Texas A&M University and Wageningen University and The University of Minnesota and Texas A&M University
• Keywords: mechanistic models ; aphids ; Normal curve ; logistic curve ; differential equations

Abstract

We develop two mechanistic models for describing insect population growth curves. The first is a diff. equation in which the rate of population growth decreases linearly over time, reflecting the aging of the host plants, a 'bottom-up' model. The surprising solution, readily obtained using calculus, is a scaled Normal pdf, hence the Normal curve is fitted directly to growth curve data. The second model is a diff. equation in which the death rate is a function of the cumulative past population size, reflecting environmental degradation over time, a 'top-down' model. Its solution is a scaled logistic pdf, hence the logistic function is fitted directly to data. The models are illustrated by fitting them to data on the soybean and greenbug aphids. The model derivations and fittings are interesting exercises on 'real-world' applications of mechanistic models and on novel uses of pdfs.