I am a PhD candidate with Rebecca Tyson and I started my PhD in September 2008.I have two projects with Dr. Tyson, one studying the effect of fragmentation of habitat on cyclic population dynamics, and one studying the impact of park management strategies on the spread of Mountain Pine Beetle.
Habitat fragmentation is known to be a key factor affecting population dynamics. We studied the effect of habitat fragmentation on cyclic population dynamics using spatially explicit predator–prey models with four different sets of reaction terms. We employ a simplification procedure based on a Fourier series first-term truncation of the spatially explicit models to obtain spatially implicit models. These simpler models capture the main features of the spatially explicit models and can be used to explain the dynamics observed by Strohm and Tyson.
The current Mountain Pine Beetle (MPB) outbreak has reached the highest population levels in recorded history. Parks Canada has spent significant funds on management actions, but the effectiveness of these measures is mostly unknown, and is difficult to determine with field work alone. Mathematical modelling is a useful tool in this work, as it can be used to investigate the effect of different management strategies without damage to the landscape or economy. I have developed a mathematical model describing MPB population dynamics and dispersal over multiple years to show the progression of MPB attack over time. This model incorporates the interaction between MPB, susceptible Lodgepole Pine trees, and the pheromones produced by MPB. Management actions are simulated over multiple years to inform when each particular management action is most effective at stemming the infestation of MPB. This model was additionally used to study the spacing in between attacks of MPB in the same year, and has been validated by data.
Garrett has worked on projects involving the modelling of insect dispercal, specifically the dispercal of codeling moths, using odrinary and partial differential equations. Garrett has also worked on an temperature dependent developmental model for Mecinus Janthformis, a biological control agent for an invasive plant species Dalmatian Toadflax. Extending this model to incorporate population incorporate population dynamics and
Katrina was a masters student with Dr. Tyson between 2010 and 2012. Her research focused on post-harvest disease in apple fruit, and had two main components, a statistical model which was used to predict incoming infection risk for apples going into storage, and a Gaussian plume model used to describe spore dispersal in apple orchards, and to examine trends seen in experimental data collection. Combining biology, mathematics, and statistics resulted in a truly interdisciplinary thesis.
I am currently working on animal movement and optimal foraging strategy. In particular, I am interested in how physiological and environmental constraints such as predation success and landscape fragmentation shape different movement strategies of predators. I am using correlated composite random walks (CCRWs) and large scale simulations to find optimal movement strategies for varying constraints to investigate how changes in the environment can affect a predators movement.
I am also interested in how results from optimal foraging strategy can be used to assist field ecologists with their work. Hence I develope tools that predict ranges for predator-prey interactions if information about environmental and physiological constraints is noisy. I plan to use these tools on Grey Seal movement tracks on the Eastern Coasten Shelf in Nova Scotia, Canada, to help ecologist who work on seal-cod interaction to prepare field experiments.
Haley Dirksen graduated from UBC Okanagan with a Bachelor of Science in Medical Biochemistry, Honours Program in June 2012. Haley learned of Dr. Tyson’s modelling work in her second year of university when she was pursuing a Major in Mathematics. While in Dr. Tyson’s Differential Equations class she had the opportunity to hear of a fellow student’s Undergraduate Research Award (URA) project which combined the fields of microbiology and mathematics. After changing her major halfway through her second year, this concept of marrying multiple disciples in a single project prompted Haley to pursue such a project combining her passion for biochemistry with her deeply held love of mathematics. After expressing interest in such a project to Dr. Tyson, it was suggested that Haley undertake a URA like the project that had inspired her. After discussing topics with a variety of potential supervisors, a project was finally settled upon and in May 2011 the research began with Enologist Dr. Cédric Saucier, Microbiologist Dr. Louise Nelson, and Dr. Rebecca Tyson’s combined expertise to guide the project.
This URA project, entitled “Modeling Botrytis cinerea growth using metabolic and enzymatic parameters”, studied the necrotrophic fungus Botrytis cinerea which is the causative agent of two types of rot in grapes used to make wine: bunch rot (detrimental) and noble rot (advantageous). This project was specifically designed to assess changes in the concentrations of several biochemical components of wine grapes that occur due to B. cinerea infection. A mathematical model quantifying the functional relationship between Botrytis infections and wine quality was then developed.
Based on the results of this URA project, it was determined that further research was necessary. Thus, after revisions were made, it became the premise of Haley’s Honours Thesis, entitled “Modeling Botrytis cinerea growth as a function of enzymatic and metabolic parameters” which began in November 2011. The aims of this research were three-fold: (1) To assess the effect of glucose, gallic acid, and gluconic acid on fungal growth and the production of the enzyme laccase by B. cinerea; (2) To develop and refine a mathematical model capable of predicting the change in glucose, gallic acid, gluconic acid, and laccase with respect to the growth rate of the fungus; (3) To use the mathematical model to elucidate the mechanisms behind laccase activity. The activity of the enzyme was determined with respect to the amount of gallic acid present in the growth medium. Gallic acid was found to induce the growth and laccase production rates of B. cinerea at high concentrations, the former of which appeared to be a novel result. In this study, it was also determined that B. cinerea was capable of producing laccase in the absence of gallic acid. These results were then compared with the mathematical model simulations to ascertain the efficacy of the model. The model that was developed was determined, in general, to be consistent with the experimental results.
Since gallic acid was found to have an unexpected effect on the growth rate of the fungus, Haley returned in July 2012 to continue her research, this time aimed at determining the limit of this effect and improving the developed mathematical model.