Effect of Crop Growth and Canopy Filtration on the Dynamics of Plant Disease Epidemics Spread by Aerially Dispersed Spores

Abstract

Most mathematical models of plant disease epidemics ignore the growth and phenology of the host crop. Unfortunately, reports of disease development are often not accompanied by a simultaneous and commensurate evaluation of crop development. However, the time scale for increases in the leaf area of field crops is comparable to the time scale of epidemics. This simultaneous development of host and pathogen has many ramifications on the resulting plant disease epidemic. First, there is a simple dilution effect resulting from the introduction of new healthy leaf area with time. Often, measurements of disease levels are made pro rata (per unit of host leaf area or total root length or mass). Thus, host growth will reduce the apparent infection rate. A second, related effect, has to do with the so-called "correction factor," which accounts for inoculum falling on already infected tissue. This factor accounts for multiple infection and is given by the fraction of the host tissue that is susceptible to disease. As an epidemic develops, less and less tissue is open to infection and the initial exponential growth slows. Crop growth delays the impact of this limiting effect and, therefore, tends to increase the rate of disease progress. A third and often neglected effect arises when an increase in the density of susceptible host tissue results in a corresponding increase in the basic reproduction ratio, R(0), defined as the ratio of the total number of daughter lesions produced to the number of original mother lesions. This occurs when the transport efficiency of inoculum from infected to susceptible host is strongly dependent on the spatial density of plant tissue. Thus, crop growth may have a major impact on the development of plant disease epidemics occurring during the vegetative phase of crop growth. The effects that these crop growth-related factors have on plant disease epidemics spread by airborne spores are evaluated using mathematical models and their importance is discussed. In particular, plant disease epidemics initiated by the introduction of inoculum during this stage of development are shown to be relatively insensitive to the time at which inoculum is introduced.