ECOP Subgroup Contributed Talks

Arwa Baabdulla

University of Alberta

"Homogenization of a Reaction Diffusion Equation can Explain Influenza A Virus Load Data"

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L^-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. These show different antiviral activity. When arranged in a checker board pattern, the total viral load significantly depends on the spatial arrangement of the cells. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities.

Emil Frølich

Ph.D. Student at Technical University of Denmark

"A new approach to multispecies population games in continuous space and time"

Population dynamics are generally modelled without taking behaviour into account. This in spite of the largest daily feeding times for predators, namely at dawn and dusk, being driven by behaviour. This is usually explained by prey avoiding visual predators, and visual predators seeking to find prey. We develop a game-theoretical model of predator-prey interactions in continuous time and space, finding the Nash equilibrium at every instant. By using the general resolution of polymatrix games, and an efficient discretization, we solve the spatial game nearly instantaneously. Our approach allows a unified model for the slow time-scale of population dynamics, and the fast time-scale of behaviour. We use the diel vertical migration as a case, examining emergent phenomena from the introduction of the fast dynamics. On the behavioural time-scale, we see the emergence of a deep scattering layer from the game dynamics. On the longer time-scale of population dynamics, the introduction of optimal behaviour has a strong stabilizing effect. In a seasonal environment, we observe a change in daily migration patterns throughout the seasons, driven by changes in population and light levels. The framework we propose can easily be adapted to population games in inhomogeneous terrestrial environments, and more complex food-webs.

Abdel Halloway

University of Illinois -- Urbana Champaign

"Unstable Population Dynamics in Obligate Cooperators"

Cooperation significantly impacts a species' population dynamics as individuals choose with whom to associate based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely disperse between groups which works well for facultative co-operators like flocking birds, schooling fish, and swarming locusts. However, obligate co-operators like canids, cetaceans, and primates may be more discerning and selective over their associations, rejecting new members and even removing current members, thereby limiting dispersal. Incorporating such aspects into population models may better reflect the population dynamics of obligately cooperative species. We created and analyzed a model of the population dynamics of obligate co-operators where a behavioral game determines within-group population dynamics that then spill over into between-group dynamics. We identify a fundamental mismatch between the stability of the behavioral dynamics and the stability of the population dynamics; when one is stable, the other is not. Our results suggest that group turnover may be inherent to the population dynamics of obligate co-operators. If our model is true. the instability arises from a non-chaotic deterministic process, and such dynamics should be predictable and testable. Furthermore, we identify four key features that impact the conservation of obligate cooperative species and make recommendations on such.

Peter Thompson

University of Alberta Department of Biological Sciences

"Using movement models to identify spatial memory in animals"

Spatial memory, the storage and recovery of the locations of important landmarks on the landscape, plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in their environments allows for an increased understanding of animal cognition. We developed a model that accounts for the memory of seasonal or ephemeral qualities of an animal's environment. The model builds on existing research to test hypotheses about the mechanisms driving animal movement behavior. Our model allows for comparison of four different hypotheses that detail the important of resource selection and spatial memory in animal movement. We used simulation analyses to verify that our model appropriately identifies memory and resource selection in simulated movement data, and these analyses have been informative about the data required to use the model properly. This model has potential to identify cognitive mechanisms for memory in a variety of ecological systems where periodic or seasonal revisitation patterns within a home range may take place.