Johan Metz

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  Effective population sizes and the canonical equation of adaptive dynamics
  Johan Metz
  Deterministic population dynamical models connect to reality through their interpretation as limits for systems size going to infinity of stochastic processes in which individuals are represented as discrete entities. In structured population models individuals may be born in different states (e.g. locations in space) after which they proceed through their h(eterogeneity)-state space, e.g. spanned by their i(dividual)-state and location. On such models one can graft evolutionary processes like random genetic drift or adaptive evolution by rare repeated substitutions of mutants in heritable traits affecting the state transition and reproduction processes of individuals. From this general perspective I will derive the so-called Canonical Equation of adaptive dynamics, a differential equation for evolutionary trait change derived under the additional assumption that mutations have small effect. In the CE approximation the rate of evolution is found to correspond to the product of a parameter $n_{e,A}$, equal to the population size times a dimensionless product of life history parameters (including spatial movements), times the gradient of the invasion fitness of potential mutants with respect to their trait vector. From a heuristic connection with the diffusion approximation for genetic drift it follows that $n_{e,A} = n_{e,D}$, the effective population size from population genetics.
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  The interplay of infectivity that decreases with virulence and limited cross-immunity: (toy) models for respiratory disease evolution
  Johan Metz
  Models for the evolution of virulence traditionally assume a trade-off between inverse disease-induced mortality rate and infectivity, resulting in intermediate virulence. The underlying intuition is that faster growing agent populations do both more damage and produce more infective particles. This intuition implicitly assumes a well-mixed host body. In reality both damage and infectivity depend mainly on the location in the body where the agents lodge. This is related i.a. to the surface proteins that allow agents to dock on and penetrate into different cell types. The typical example is respiratory diseases where more deeply seated ones are both less infective and more harmful. With the other standard assumption, full cross-immunity between disease strains, this would lead to evolution towards the tip of the nose. In reality cross-immunity depends on surface antigens and hence is at least in part connected to depth. In this talk I discuss a simple adaptive dynamics style model taking on board the aforementioned considerations. The inference is that disease diversity should decrease with depth.
  
  (The reported work was done in collaboration with Kevin Kleine and Juan E. Keymer Vergara of Delft University of Technology.)