Masters Theses

Date of Award

6-1986

Degree Type

Thesis

Degree Name

Master of Science

Major

Management Science

Major Professor

Louis J. Gross

Abstract

Yield maximization in modern agriculture depends in part upon successful control of pathogen infestations. Disease control depends upon limiting infective incidents and, if one occurs, isolation of the infective agent from the remainder of the field. Carefully selected spatial patterns of two plant strains may offer a low cost, relatively easy to implement method of controlling pathogenic disease.

To test this idea, I developed a spatial simulation to model the inception and spread of disease in a plant field. Length of the season, field dimensions and maximum plant size and growth rates are input parameters. The resistant strain has a reduced growth rate. This is the cost of incorporating the resistant strain into the field.

Per capita pathogen birth and death rates determine maximum pathogen population. Spore dispersal and disease spread are stochastic events. Monte Carlo techniques are used to determine the distribution of crop yields in unpatterned and patterned fields. Chi square tests are used to test the hypothesis that patterning has no effect on crop yields and to test the differences between yields of various patterns. Finally, I examine a simple optimization problem and offer extensions to this model.

Sensitivity analysis was used to ascertain the operating characteristics of this model. Using unpatterned fields and checkered, striped and bordered patterns, I measured the total yield, the viable fraction of plants and mean pathogen population at the end of the season. Patterning resulted in a 30 percent increase in mean yields at the end of the season. The checkered field had both higher mean yield and lower pathogen population than either the striped or bordered fields. For a fixed total yield K, the checkered field was shown to be least likely to be less than this yield K at the end of the season.

The model revealed that the resistant plants should probably be modelled with a smaller maximum biomass, as well as a reduced growth rate, to more precisely exact a cost for the use of the resistant strain. Furthermore, total yield may be a more useful decision criterion than viable fraction of plants for judging the efficacy of spatial patterns. Total yield represents the gross output of the field, not just a proportion of plants which are healthy at the end of the season.

The model showed that a spatial simulation approach to plant epidemiology can be used to analyze crop patterns in a field. The model would benefit from empirical data. In its current form, the model can be used to analyze such topics as the relative importance of host density and mean spore dispersal distance in the spread of plant disease. Much more work can be done to determine both the optimal crop pattern and the optimal fraction of resistant plants, and to explore the relationship between these two variables.

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