Cecilia Berardo, Coevolution of a patient predator and its reckless prey
The war of attrition in game theory is a model for a stand-off situation between two opponents where victory goes to the one who continues longer. In the asymmetric version of the game where the opponents assume different unambiguous roles, the evolutionarily stable strategy is a pure strategy where one gives up immediately while the other is prepared to wait indefinitely.
We model a stand-off between a predator and a prey when the prey is hiding and the predator is waiting for the prey to come out from its refuge, or more dramatically, when the two are locked in a situation of mutual threat of injury or even death by the predator’s teeth and claws or the horns and hooves of the prey. The stand-off is resolved when the predator gives up or when the prey tries to escape. Instead of using the asymmetric war of attrition, we embed the stand-off as an integral part of the predator-prey model of Rosenzweig and MacArthur derived from first principles. We apply this model to study the coevolution of the giving-up rates of the prey and the predator, using the adaptive dynamics approach. As we will see, some results are the same as for the asymmetric war of attrition, but others are quite different.
Samuel Bernard, Multiscale approaches for clock-driven cell population dynamics
Multiscale modelling approaches in biology are useful to take into account the complex interactions between different organisation levels in those systems. This is especially important when there a lot of heterogeneity between individual units. We will discuss a few examples from cell population dynamics where interaction between cells alters the behavior of singles-cells: i) how interaction between cells can transform a collection of sloppy oscillators into a robust, noise resistant clocks. ii) how synchrony in the cell division cycle can affect tissue growth, promote tissue regeneration and suppress tumours.
Vasiliki Bitsouni, Stationary aggregation and travelling wave patterns in heterogeneous cancer cell populations
Abstract: Cellular adhesion, i.e., cell-cell and cell-matrix adhesion, and cellular proliferation are fundamental features of multicellular organisms, linked to maintenance of order in the organisms. The breaking and forming of the adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. We present a model of nonlocal partial differential equations coupled with ordinary differential equations, describing cancer cell invasion and movement as a result of integrin-controlled cellular adhesion, for two cancer cell populations with different levels of mutation. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion. We discuss different possible cell aggregation patterns, as well as travelling wave patterns, and we investigate the effect of cancer mutation rate on the speed of cancer invasion.
Joint work with D. Trucu (University of Dundee), M.A.J. Chaplain (University of St Andrews) and R. Eftimie (Université de Franche-Comté).
Laura Kanzler, Kinetic Modelling of Colonies of Myxobacteria
Abstract: Myxobacteria are rod-shaped, social bacteria that are able to move on flat surfaces by ’gliding’ and form a fascinating example of how simple cell-cell interaction rules can lead to emergent, collective behavior. Observed movement patterns of individual bacteria in such a colony include straight runs with approximately constant velocity, alignment interactions and velocity reversals. Experimental evidence shows that above mentioned behavior is a consequence of direct cell-contact interaction rather than diffusion of chemical signals, which indicates the suitability of kinetic modeling.
In this talk a new kinetic model of Boltzmann-type for such colonies of myxobacteria will be introduced and investigated. For the spatially homogeneous case an existence and uniqueness result will be shown, as well as exponential decay to an equilibrium for the Maxwellian collision operator. Further, model extensions and their analysis will be addressed and numerical simulations will be shown.