Best Selling Books by David Harrington

Sea lice are a threat to the health of both wild and farmed salmon and an economic burden for salmon farms. Open-net salmon farms act as reservoirs for sea lice in near coastal areas, which can lead to elevated sea louse levels on wild salmon. With a free living larval stage, sea lice can disperse tens of kilometers in the ocean, both from salmon farms onto wild salmon and between salmon farms. This larval dispersal connects local sea louse populations on salmon farms and thus modelling the collection of salmon farms as a metapopulation can lead to a better understanding of which salmon farms are driving the overall growth of sea lice in a salmon farming region. In this thesis I use metapopulation models to specifically study sea lice on salmon farms in the Broughton Archipelago, BC, and more broadly to better understand the transient and asymptotic dynamics of marine metapopulations. I begin in Chapter 1 by presenting a brief background on the mathematical concepts used in this thesis and on the biological systems on which it is focused. In Chapter 2 I create a stage-structured metapopulation model for sea lice on salmon farms using age-density equations to capture the complexities of the sea louse life cycle. To identify which salmon farms are acting as sources or sinks of sea lice in a salmon farming region I create a next-generation matrix which distills the essential elements of sea louse dispersal and demography into a single operator. Using the next-generation matrix I investigate the effect of interfarm spacing and environmental variables on the source-sink distribution of salmon farms and show that on the generational scale it is possible for transient dynamics to be different than the long term dynamics of this metapopulation. In Chapter 3 I further explore the transient dynamics which can occur in general marine and other birth-jump metapopulations. I demonstrate that even in simple linear metapopulation models the transient dynamics can be very different from the asymptotic dynamics of these populations. I show how to connect reactivity and attenuation, measures of the maximum and minimum growth rates that can occur following perturbations, to the source-sink distribution of habitat patches and how reactivity and attenuation can differ from the actual population growth rates when measured in the commonly used l2 norm. I then demonstrate how to meaningfully measure reactivity in marine metapopulations, where adults typically produce a large number of offspring and thus most would be considered reactive under the classical definition. In Chapter 4 I use the next-generation matrix developed in Chapter 2 to calculate which salmon farms are acting as the largest source of sea lice in the Broughton Archipelago, BC. The Broughton Archipelago has been ground zero for studying the effects of sea lice on wild salmon and several of the farms are currently being removed in an agreement between the provincial government and local First Nations. I find that several of the farms that are not slated to be removed are acting as the largest sources of sea lice in this region and occur in two distinct clusters. I also find that warming temperatures coupled with high salinities could lead to increased sea louse growth in the Broughton. In Chapter 5 I calculate the distribution of arrival times for sea lice dispersing between salmon farms in the Broughton Archipelago to disentangle the factors affecting dispersal and cross-infection of sea lice in this region. First, I calculate the arrival time distribution directly using a hydrodynamic model of the Broughton to which I then parameterize a simple advection diffusion model of the arrival time distribution. I use the simple model to show that there an intermediate distance between farms can maximize cross infection, and the specific distance which maximizes cross infection depends on the magnitude of the current and temperature of the ocean. I conclude the thesis in Chapter 6 by contextualizaing the results within the broader literature and discussing limitations, potential for future work, and management implications of sea lice on salmon farms.

The goal of Howitt''s positive mathematical programming procedure is to calibrate a mathematical programming model so that it will reproduce a set of base data for the primal variables. This article develops an analogous procedure allowing one to specify the levels of both primal and dual variables. This article also sheds light on a potential ambiguity of Howitt''s procedure (with attendant policy evaluation impacts). The procedure is illustrated through application to an equilibrium displacement model focused on evaluating the consequences of the reluctance of U.S. trading partners to accept genetically modified crop products for U.S. production patterns and net farm income.