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.

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations: the Susceptible-Infested-Juvenile (SIJ) model. Stability of fixed points is analyzed as a function of population growth rates, and indicates the existence of periodic outbreaks that intensify as growth rates increase. We devise analytical methods to predict outbreak severity and duration as well as outbreak return time. To assess the vulnerability of natural resources to climate change, we develop a thermally-driven mechanistic model to predict MPB population growth rates using a distributional model of beetle phenology in conjunction with criteria for successful tree colonization. The model uses projected daily minimum and maximum temperatures for the years 2025 to 2085 generated by three separate global climate models. Growth rates are calculated each year for an area defined by latitude range 42° N to 49° N and longitude range 108° W to 117° W on a Cartesian grid of approximately 4km resolution. Using these growth rates, we analyze how the optimal thermal window for beetle development is changing with respect to elevation as a result of climate change induced warming. We also use our combined model to evaluate if thermal regimes exist that would promote life cycle bivoltinism and discuss how yearly growth rates would change as a result. Outbreaks of MPB are largely driven by host tree stand demographics and spatial effects of beetle dispersal. We augment the SIJ model to account for the spatial effects of MPB dispersal throughout a forest landscape by coupling it with a Gaussian redistribution kernel. The new model generates a train of sustained solitary waves of infestation that move through a forest with constant speed. We convert the resulting integrodifference equation into a partial differential equation and search for travelling wave solutions. The resulting differential equation provides predictions of the shape of an outbreak wave profile and of peak infestation as functions of wave speed, which can be calculated analytically. These results culminate in the derivation of an explicit formula for predicting the severity of an outbreak based on the net reproductive rate of MPB and host searching efficiency.