  As a result of climate change, many populations have to modify their range to
follow the suitable areas - their "climate envelope" - often risking
extinction. During this migration process, they may face absolute boundaries to
dispersal, because of external environmental factors. Consequently, not only
the position, but also the shape of the climate envelope can be modified. We
use a reaction-diffusion model to analyse the effects on population persistence
of simultaneous changes in the climate envelope position and shape. When the
growth term is of logistic type, we show that extinction and persistence are
principally conditioned by the species mobility and the speed of climate
change, but not by the shape of the climate envelope. However, with a growth
term taking an Allee effect into account, we find a high sensitivity to the
variations of the shape of the climate envelope. In this case, the species
which have a high mobility, although they could more easily follow the
migration of the climate envelope, would be at risk of extinction when
encountering a local narrowing of the boundary geometry. This effect can be
attenuated by a progressive opening of the available space at the exit of the
narrowing, even though it transiently leads to a diminished area of the climate
envelope.

Analysis of PDEs;Populations and Evolution