Date of Award:

5-2018

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Luis Gordillo

Committee

Luis Gordillo

Committee

Brynja Kohler

Committee

Claudia Nischwitz

Committee

Dave Brown

Abstract

Alfalfa is a major cash crop in the western United States, where fields that are infested with the alfalfa stem nematode (Ditylenchus dipsaci) can be found. With no nematicides available to control alfalfa stem nematode spread, growers can use nematode resistant varieties of alfalfa to manage nematode populations in a field. A deterministic, discrete-time, host-parasite model is presented that describes the spread of alfalfa stem nematodes on resistant hosts that was fit to experimental data obtained in Weber County, Utah. Numerical results obtained from simulations with the model are used to compare how varying levels of resistance can affect harvest yield.

Resistant varieties can also affect the invasion speeds of epidemics in crops. A continuous time, spatial model is presented that describes how these resistant varieties affect invasion speeds in general crop systems. Speeds of traveling wave fronts are determined for simple epidemics in crops that contain a mixture of resistant and non-resistant hosts. For the model, it was found that the wave speeds will slow down as highly nematode resistant varieties of alfalfa are used.

The speed of invasion for the alfalfa stem nematode can be determined by using a mathematical relationship that is know as the contact distribution. We present a spatial model for the spread of alfalfa stem nematodes that uses a Gaussian distribution as the contact distribution of the alfalfa stem nematodes, which was determined by experimental data. Using this contact distribution we are able to approximate the speed of nematode invasive fronts in absence of advection, i.e. without nematode trans-port through flood irrigation. The contact distribution is then used to calculate front speeds when resistant varieties of alfalfa are introduced. We found that, unsurprisingly, invasive speeds are relatively low and cannot support the rapid dispersal of the disease among fields as seen in practice. However, this result leads to conjecture that changing current irrigation practices, from flood to sprinkle irrigation, could effectively contribute to control the spread of alfalfa stem nematodes.

Resistant varieties of alfalfa can be used to effectively control the spread of the alfalfa stem nematode. In this work we have shown that using resistant varieties of alfalfa can increase yield up to 83%, they can slow down invasion speeds of nematodes, and switching from flood to sprinkler irrigation could effectively contribute to the control of the alfalfa stem nematode.

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