## 3rd session, December 9th & 10th 2013

__Monday 9__

9h30 - 10h : Coffee

10h - 11h : Mark Lewis

*(**Canada Research Chair in Mathematical Biology / University of Alberta*)

**Mathematics behind stream population dynamics**Human activities change the natural flow regimes in streams and rivers and this impacts ecosystems. In this talk I will mathematically investigate the impact of changes in water flow on biological populations. The approach I will take is to develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and then to analyze the equations so as to assess the effect of impacts of water flow on population dynamics. The mathematical framework is based on new theory for the net reproductive rate Ro as applied to advection-diffusion-reaction equations. I will then connect the theory to populations in rivers under various flow regimes. This work lays the groundwork for connecting Ro to more complex models of spatially structured and interacting populations, as well as more detailed habitat and hydrological data. This is achieved through explicit numerical simulation of two dimensional depth-averaged models for river population dynamics.

11h - 12h : Julien Berestycki (

*UPMC*)

**he extremal point process of the branching Brownian motion and the KPP equation**Branching Brownian motion is a particle system without interaction in which particles move in $R$ according to Brownian motions and split into two offspring particles at some rate $beta>0,$ which start in turn to diffuse and to branch. It is well known that there is a deep connection between the KPP equation and branching diffusions. A classical example is the distribution function of the position of the rightmost particle at time $t, M_t$

$$

u(t,x) := mathbb{P}(M_tle x)

$$

solves the KPP equation

$$

u_t =frac12 u_{xx} +beta(x^2-x)

$$

with Heaviside initial condition.

In this talk I'll show how this connection help to shed light on the extremal point process of the branching Brownian motion, i.e. the limiting configuration of particles near $M_t$, thus answering a conjecture of Lalley and Sellke.

Tuesday 10

Tuesday 10

9h30 - 10h : Coffee

10h - 11h : Mark Lewis

*(**Canada Research Chair in Mathematical Biology / University of Alberta*)

**First passage time: Connecting random walks to functional responses**In this talk I will outline first passage time analysis for animals undertaking complex movement patterns, and will demonstrate how first passage time can be used to derive functional responses in predator prey systems. The result is a new approach to understanding functional responses based on a random walk model and anisotropic parabolic partial differential equations. I will extend the analysis to complex heterogeneous environments to assess the effects of man-made linear landscape features on functional responses in wolves and elk. (This work is joint with Hannah McKenzie, Evelyn Merrill and Ray Spiteri).

11h - 12h : Jian Fang

*(ReaDi post-doc)*

**Pathogen spread in a wave-like environment**We consider the issue whether pathogen can keep pace with the invasion of its host. This is modeled as a scalar reaction diffusion equation with logistic nonlinear term involvoing the wave-like carrying capacity. The obtained threshold result is then used to analyze two generalized eigenvalues of an elliptic operator in unbounded domain. This talk is based on a joint work with Yijun Lou and Jianhong Wu.

15h - 16h : Mark Lewis

*(**Canada Research Chair in Mathematical Biology / University of Alberta*)Dans le cadre du séminaire du CAMS La question de la modélisation en sciences humaines