Predicting the Spread of Plant Disease: Analysis of an Infinite-Dimensional Leslie Matrix Model for Phytophthora infestans

James A. Powell¹ and Ivan Slapnicar²
Department of Mathematics and Statistics
Utah State University
Logan, Utah 84322-3900 USA - Wopke van der Werf
Crop and Weed Ecology Group
Wageningen University
Bode 98, Postbus 430
6700 AK Wageningen
The Netherlands

Abstract:

A model for the size class distribution of plant disease on plant tissues is developed, inspired by late blight lesions on potato and tomato caused by Phytophthora infestans. In the absence of spatial dispersal the model becomes an infinite-dimensional Leslie matrix, and when spatial dispersal is considered several elements of the Leslie matrix are convolution operators accounting for the spread of spores and generation of new lesions. The maximum predicted speed at which lesions spread is calculated by extending the method of Neubert and Caswell [15], which determines maximum possible front speed for propagation of invasions of an age-structured population, to the case of infinite-dimensional matrices. Observed speeds agree with predicted speeds to within errors resulting from convergence to the stable age distribution and to the asymptotic front speed.

Keywords: Phytophthora, integrodifference equations, Leslie matrices, fronts, invasion, rates of spread

AMS Subjects: 92D25, 92D99

Running Head: Spread of Plant Disease

Submitted to SIAM J. Applied Math