RESEARCH PROJECTS
Below are some synopses of my main research projects. For my full publication record, please see my Google Scholar page.
Undergraduate math education projects:
Throughout my teaching postdoc I have been involved in several projects in undergraduate math education. The main focus of these projects have been: the necessary supports for group work in large classes, the inclusion of climate science in math courses, the effect of mastery grading on student test anxiety, and a demographic analysis of the first year math program at UBC. When these projects are published, they will be posted below.
A three-pronged lesson in differential equations in a calculus course: analytical, numerical, and experimental
Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In this paper, we detail a three-pronged lesson introducing differential equations using analytical, numerical and experimental approaches in a large first-year differential calculus course. Presenting the three approaches in succession allows students to evaluate advantages and disadvantages. The lesson incorporates software and programming and provides opportunities for active, experiential, team-based learning.
Chow, A.N., Harrington, P.D., and F.S. Leung, A three-pronged lesson in differential equations in a calculus course: analytical, numerical, and experimental, Teach. Math. Its Appl. (2023)
Mathematical ecology projects:
My PhD research was in mathematical ecology and I was particularly interested in the dynamics of marine metapopulations and sea lice on salmon farms. Below are some short synopses of projects that I led during my PhD.
A next-generation approach to calculate source-sink dynamics in marine metapopulations:
Calculating source and sink patches is important to preserve or control marine species where adult subpopulations remain confined to population patches, but larval dispersal can connect subpopulations. In this paper we applied a next generation approach specifically to sea lice populations on salmon farms, which have large economic effects on the salmon farming industry.
Harrington, P.D., and M.A. Lewis, A Next-Generation Approach to Calculate Source–Sink Dynamics in Marine Metapopulations, Bull Math Biol 82, 9 (2020) doi.org/10.1007/s11538-019-00674-1
A framework for studying transients in marine metapopulations
Understanding the short-term dynamics that may occur in marine metapopulations is important in controlling the outbreak and spread of infections and invasive species. In this paper we connected the short-term dynamics to the source-sink distribution of marine metapopulations so that existing knowledge on source and sink patches can be used to identify where outbreaks may occur.
Harrington, P.D., Lewis, M.A. and P van den Driessche, Reactivity, attenuation, and transients in metapopulations, SIAM J. Appl. Dyn. Syst 21:2 (2022)
Next-generation matrices for marine metapopulations: the case of sea lice on salmon farms
In this paper we construct a next-generation matrix for a network of sea lice populations on salmon farms in the Broughton Archipelago, BC, an intensive salmon farming region on the west coast of Canada where certain salmon farms are currently being removed under an agreement between local First Nations and the provincial government. We identify the salmon farms which are acting as the largest sources of sea lice and show that in this region the most productive sea lice populations are also the most connected. We find that the farms which are the largest sources of sea lice have not yet been removed from the Broughton Archipelago, and that warming temperatures could lead to increased sea louse growth.
Harrington, P.D., Cantrell, D.L., and M.A. Lewis, Next-generation matrices for marine metapopulations: the case of sea lice on salmon farms, Ecol. Evol., 13 (2023)
Calculating arrival times for sea louse spread between salmon farms
Calculating the arrival times of sea lice spreading between salmon farms is important in controlling sea lice outbreaks in small areas with multiple salmon farms, which is typical of many salmon farming regions across the world. In this paper, we develop a simple analytical model for the dispersal of sea lice between two salmon farms. From the model, we calculate the arrival time distribution of sea lice dispersing between farms, as well as the level of cross-infection of sea lice. We also use numerical flows from a hydrodynamic model, coupled with a particle tracking model, to directly calculate the arrival time of sea lice dispersing between two farms in the Broughton Archipelago, British Columbia, in order to fit our analytical model and find realistic parameter estimates. Using the parametrized analytical model, we show that there is often an intermediate interfarm spacing that maximizes the level of cross-infection between farms, and that increased temperatures will lead to increased levels of cross-infection.
Harrington, P.D., Cantrell, D.L., Foreman, G.G., Guo, M., and M.A. Lewis, Timing and probability of arrival for sea lice dispersing between salmon farms, R. Soc. Open sci. 10, 2, (2023)
Salmon Coast Field Station
Salmon Coast Field Station has been monitoring the abundance of sea lice on wild salmon for over 20 years. As part of my PhD I have participated in this long-term monitoring program at Salmon Coast for five years. In 2018 and 2019 I was the leader of this monitoring program and was responsible for the safety of field crew and writing the publicly available yearly reports which are available at https://www.salmoncoast.org/
