As climate warms, different phenotypes, such as different flowering time in plants or breeding date in birds, are favored by natural selection. To persist, species must therefore change their geographical distribution to track the climate to which they were adapted to, and/or their phenotypic distribution to adapt to new climates. Quantitative genetics models describing joint changes in phenotypic and geographical distributions have been developed in the nineties to better understand the challenges faced by species under climate change. We have built on this work by examining how the life cycle of species affects and jointly evolves with these dynamics: I will present a few examples of work in progress where collaboration between mathematicians and evolutionary biologists have led to new insights on how age-structure, mode of reproduction, mutation and dispersal affect the response of species to climate change.

A primary goal of evolution biology is to understand the mechanisms that generate and shape the vast diversity of life. From stable polymorphisms at susceptibility loci to the maintenance of sexual reproduction, pathogens are thought to play an import role in the maintenance of genetic diversity of their hosts. Indeed as evidenced by the death toll of the Plague in 14th century Europe to the decimation of African undulates by Rinderpest, infectious pathogens can exert strong selective pressures on their hosts. Using methods from Epidemiology we modelled coevolution between hosts and their infectious pathogens. We explore how coevolution, epidemiology, and stochasticity shape the genetic diversity of hosts.

Cellular movement plays important roles in many (patho)physiological processes, such as immune cell response, growth of neuronal axons and cancer. The regulation of this movement depends on the interaction of several key proteins implicated in the development of cellular polarity (consisting of a front and a back) and the formation of protein complexes called adhesions. Adhesions anchor the cell to its substrate, allowing it to migrate. In CHO cells, three classes of adhesion can be identified based on size and dynamic properties: nascent adhesions, focal complexes and focal adhesions. When cells extends forward at the front, nascent adhesions assemble and anchor the leading edge to the substrate, while focal adhesions at the back disassemble, allowing detachment, retraction and forward movement. The dynamics of these processes are controlled by a number of regulatory factors, occurring on both cell-wide and adhesion-level scales. The coordination of these regulatory factors is complex, but insights into their dynamics can be gained from the use of mathematical/biophysical modeling techniques which integrate many of these components together. In this talk, I will present our recently developed molecularly-explicit and mechanosensitive models of cell polarity and adhesion dynamics to explore how local regulation of key adhesion proteins (including paxillin, rho family of GTPases and integrin) produce cell-wide polarization and nascent adhesion assembly/disassembly. The dynamics associated with various parameter regimes will be presented and insights into the mechanisms regulating adhesion dynamics will be provided.

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