Mark Lewis

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  Population Dynamics in Moving Environments
  Mark Lewis
  Classical population dynamics problems assume constant unchanging environments. However, realistic environments fluctuate in both space and time. My lecture will focus on the analysis of population dynamics in environments that shift spatially, due either to advective flow (eg., river population dynamics) or to changing environmental conditions (eg., climate change). The emphasis will be on the analysis of nonlinear advection-diffusion-reaction equations and related models in the case where there is strong advection and environments are heterogeneous. I will use methods of spreading speed analysis, net reproductive rate and inside dynamics to understand qualitative outcomes. Applications will be made to river populations in one- and two-dimensions and to the genetic structure of populations subject to climate change.
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  Using Mathematics to Understand Animal Movement Patterns
  Mark Lewis

  Animal movement patterns have long been the subject of mathematical and ecological interest. How do individual behavioral decision rules translate into macroscale patterns of space use such as foraging, patrolling or territories? I will show how mechanistic models, using random walks, stochastic processes, first passage time analysis and partial differential equations can be used to connect underlying processes to the observed patterns. Here interactions are complex and may involve memory of past events, as well as a cognitive map. I will make applications to a spectrum of different emerging patterns, ranging from territories in Amazonian birds to patrolling in wolves.

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  Connecting models to data for animal movement models in ecology
  Mark Lewis

  Animal movement patterns have long fascinated mathematicians and ecologists alike. One type of primarily mathematical investigation focuses on pattern formation. How do individual behavioural decision rules translate into macroscale patterns of space use? Here mechanistic models, using random walks, stochastic processes and partial differential equations have connected pattern to process. Another type of primarily ecological investigation correlates space use patterns to underlying environmental features. Here statistical models, based on resource selection have connected patterns to environmental features. In this talk I will build a bridge between mechanism and resource selection using the concept of coupled step selection functions. The approach is based on a mechanistic underpinning for the movement process, but is also amenable to easy statistical inference regarding space use. I will demonstrate how each type of model can be connected to detailed movement data to give new insight about animal behaviour. Applications will be made to a spectrum of different animals ranging from Amazonian birds to caribou to coyotes.

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  Models and Data for Invasive Spread Across Lake Networks
  Mark Lewis
  In this talk I will outline a recent interdisciplinary effort to model and understand the spread of invasive copepods across lake networks in North America. This 5-year project, developed through the Canadian Aquatic Invasive Species Network (CAISN), tracked the invasion status of approximately 500 interconnected lakes in the Canadian shield. Here the invader, spiny waterflea, is spread by recreational boaters moving between the lakes. The water flea modifies the trophic structure of lake it encounters and has a major ecological impact.
  
  To understand spread we used a stochastic gravity model, parameterized by boater survey data. In this model, the number of trips linking lakes is a random variable whose magnitude is a nonlinear function of empirically measured quantities such as lake size and distance between lakes. In our work, the gravity model was used to infer the total propagule pressure experienced by each lake. This propagule pressure was then linked to an establishment model. The establishment model estimates the probability that a propagule will establish at a given lake, depending upon local physical and chemical conditions. Fitting our hybrid model to large datasets has been an interesting challenge. As I will show, our hybrid gravity/establishement modelling approach has proved to be very effective at determining which lakes become invaded as the invasion spreads across the complex network.
  
  This work is collaborative with Subhash Lele, Jim Muirhead, Alex Potapov and Norm Yan.
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  Aquaculture and Sustainability of Coastal Ecosystem
  Mark Lewis

  Aquaculture and Sustainability of Coastal Ecosystem

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  Ecological dynamics of a salmon parasite
  Mark Lewis

  In this talk I will outline the impact that parasitic sea lice have on the ecology of pacific salmon and the role that parasite spill over and spill back with aquaculture has taken in modifying the ecology of pacific salmon. These modifications are far reaching, and include changes in salmon returns, establishment of nonlinear population thresholds such as Allee effects, and shifts in predator prey dynamics. My talk will involve a mixture of modelling and data, based on over a decade of intensive field work.