Studying the effects of viruses and toxins on honey bees is important in order to understand the danger these important pollinators are exposed to. Hives exist in various environments, and different colonies are exposed to varying environmental conditions and dangers. To properly study the changes and effects of seasonality and pesticides on the population dynamics of honey bees, the presence of each of these threats must be considered. This study aims to analyze how infected colonies grapple more deeply with changing, seasonal environments, and how toxins in pesticides affect population dynamics. Thus, it addresses the following questions: How do viruses within a colony affect honey bee population dynamics when the environment is seasonal? How can the effects of pesticides be modeled to better understand the spread of toxins? This project is a continuation of my own undergraduate work in a previous class, MAT 350: Techniques and Applications of Applied Mathematics, with Dr. Yun Kang, and also utilizes previous research conducted by graduate students. Original research focused on the population dynamics of honey bee disease interactions (without considering seasonality), and a mathematical modeling approach to analyze the effects of pesticides on honey bees. In order to pursue answers to the main research questions, the model for honey bee virus interaction was adapted to account for seasonality. The adaptation of this model allowed the new model to account for the effects of seasonality on infected colony population dynamics. After adapting the model, simulations with arbitrary data were run using RStudio in order to gain insight into the specific ways in which seasonality affected the interaction between a honey bee colony and viruses. The second portion of this project examines a system of ordinary differential equations that represent the effect of pesticides on honey bee population dynamics, and explores the process of this model’s formulation. Both systems of equations used as the basis for each model’s research question are from previous research reports. This project aims to further that research, and explore the applications of applied mathematics to biological issues.

Understanding learning in fruit flies (D. melanogaster) can lead to many important discoveries about learning in humans due to the large overlap of shared DNA and the appearance of the same diseases in both species. Fruit flies have already been test subjects for many influential research experiments, some of which earned Nobel Prizes. This study seeks to investigate inhibitory conditioning in a way that differs from the traditional forward pairing inhibitory conditioning. Specifically, this experiment aims to establish inhibitory learning in fruit flies using backward association. The results show that when fruit flies are trained using backward conditioning as opposed to forward conditioning, there is a pattern of preference that differs substantially from the results showing an aversion to the associated odor in forward conditioning. When comparing the data using Two-Factor ANOVA of forward versus backward conditioning, it clearly indicates that the results are significant. Simply by altering the temporal placement of an unconditioned stimulus and a conditioned stimulus, the fruit flies learn significantly differently, switching from an aversion to the paired odor to a preference. Based on these results, fruit flies can be considered capable of inhibitory learning via backward pairing. Further research will consider whether responses become stronger after more repetitions of the training, and summation and retardation tests can be done in order to confirm that the response is, in fact, due to inhibitory conditioning and not just habituation.

In the face of widespread pollinator decline, research has increasingly focused on ways that pesticides could be harming bees. Fungicides are pesticides that are used in greater volumes than insecticides, yet significantly fewer studies have investigated the effects of these agrochemicals. The fungicide Pristine® is commonly used on bee-pollinated crops and has been shown to be detrimental to physiological processes that are key to honey bee foraging, such as digestion and learning. This study seeks to investigate how Pristine® exposure affects the amount of water, nectar, and pollen that honey bees collect. Colonies were fed either plain pollen patties or pollen patties containing 23 ppm Pristine®. Exposure to fungicide had no significant effect on corbicular pollen mass, the crop volumes of nectar or water foragers, or the proportions of foragers collecting different substances. There was a significantly higher sugar concentration in the crop of Pristine®-exposed nectar foragers (43.6%, 95% CI [38.8, 48.4]) compared to control nectar foragers (36.3%, 95% CI [31.9, 40.6]). The higher sugar concentration in the nectar of Pristine®-treated bees could indicate that the agrochemical decreases sucrose responsiveness or nutritional status in bees. Alternatively, fungicide exposure may increase the amount of sugar that bees need to make it back to the hive. Based on these results, it would appear that fungicides like Pristine® do not strongly affect the amounts of substances that honey bees collect, but it is still highly plausible that treated bees forage more slowly or with lower return rates.