Bulletin of Mathematical Biology

, Volume 78, Issue 11, pp 2165–2185 | Cite as

Expansion Under Climate Change: The Genetic Consequences

  • Jimmy Garnier
  • Mark A. Lewis
Original Article


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.


Neutral genetic diversity Range shift Range expansion Climate change Travelling wave Reaction–diffusion model 



MAL gratefully acknowledges a Canada Research Chair, a Killam Research Fellowship, Discovery and Accelerator grants from the Canadian Natural Sciences and Engineering Research Council, and the Natural Science and Engineering Research Council of Canada (Grant No. NET GP 434810-12) to the TRIA Network, with contributions from Alberta Agriculture and Forestry, Foothills Research Institute, Manitoba Conservation and Water Stewardship, Natural Resources Canada - Canadian Forest Service, Northwest Territories Environment and Natural Resources, Ontario Ministry of Natural Resources and Forestry, Saskatchewan Ministry of Environment, West Fraser and Weyerhaeuser. JG gratefully acknowledges the NONLOCAL project from the French National Research Agency (ANR-14-CE25-0013).


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.LAMACNRS – Université Savoie Mont-BlancChambéryFrance
  2. 2.Department of Mathematical and Statistical Sciences, Centre for Mathematical BiologyUniversity of AlbertaEdmontonCanada
  3. 3.Department of Biological SciencesUniversity of AlbertaEdmontonCanada

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