SÉMINAIRE D'ANALYSE NUMÉRIQUE
Année universitaire 2015-2016
Mark
LEWIS (Department of Mathematical and
Statistical Sciences, University of Alberta, Canada)
Expansion under climate change:
the genetic consequences.
Range expansion and range shifts are crucial population responses to climate
change. Genetic consequences are not well understood but are clearly coupled
to ecological dynamics that, in turn, are driven by shifting climate
conditions. We model a population with a deterministic reaction--diffusion
model coupled to a heterogeneous environment that develops in time due to
climate change. We decompose the resulting travelling wave solution
into neutral genetic components to analyse the spatio-temporal dynamics of
its genetic structure. Our analysis shows that range expansions and
range shifts under slow climate change preserve genetic diversity. This is
because slow climate change creates range boundaries that promote spatial
mixing of genetic components. Mathematically, the mixing leads to so-called
pushed travelling wave solutions. This mixing phenomenon is not seen in
spatially homogeneous environments, where range expansion reduces genetic
diversity through gene surfing arising from pulled travelling wave
solutions. However, the preservation of diversity is diminished when
climate change occurs too quickly. Using diversity indices, we show that
fast expansions and range shifts erode genetic diversity more than slow
range expansions and range shifts. Our study provides analytical insight
into the dynamics of travelling wave solutions in heterogeneous
environments. This is joint work with Jimmy Garnier (CNRS and Université
Savoie Mont-Blanc).
