  We develop general heterogeneous nonlocal diffusion models and investigate
their connection to local diffusion models by taking a singular limit of
focusing kernels. We reveal the link between the two groups of diffusion
equations which include both spatial heterogeneity and anisotropy. In
particular, we introduce the notion of deciding factors which single out a
nonlocal diffusion model and typically consist of the total jump rate and the
average jump length. In this framework, we also discuss the dependence of the
profile of the steady state solutions on these deciding factors, thus shedding
light on the preferential position of individuals.
