  In this paper, we analyse the structure of the set of positive solutions of
an heterogeneous nonlocal equation of the form: $$ \int_{\Omega} K(x,
y)u(y)\,dy -\int_ {\Omega}K(y, x)u(x)\, dy + a_0u+\lambda a_1(x)u
-\beta(x)u^p=0 \quad \text{in}\quad \times \O$$ where $\Omega\subset \R^n$ is a
bounded open set, $K\in C(\R^n\times \R^n) $ is nonnegative, $a_i,\beta \in
C(\Omega)$ and $\lambda\in\R$. Such type of equation appears in some studies of
population dynamics where the above solutions are the stationary states of the
dynamic of a spatially structured population evolving in a heterogeneous
partially controlled landscape and submitted to a long range dispersal. Under
some fairly general assumptions on $K,a_i$ and $\beta$ we first establish a
necessary and sufficient criterium for the existence of a unique positive
solution. Then we analyse the structure of the set of positive solution
$(\lambda,u_\lambda)$ with respect to the presence or absence of a refuge zone
(i.e $\omega$ so that $\beta_{|\omega}\equiv 0$).
