  We consider here a logistic equation, modeling processes of nonlocal
character both in the diffusion and proliferation terms.
  More precisely, for populations that propagate according to a L\'evy process
and can reach resources in a neighborhood of their position, we compare (and
find explicit threshold for survival) the local and nonlocal case.
  As ambient space, we can consider: bounded domains, periodic environments,
and transition problems, where the environment consists of a block of
infinitesimal diffusion and an adjacent nonlocal one. In each of these cases,
we analyze the existence/nonexistence of solutions in terms of the spectral
properties of the domain. In particular, we give a detailed description of the
fact that nonlocal populations may better adapt to sparse resources and small
environments.
