  We review localization with non-Hermitian time evolution as applied to simple
models of population biology with spatially varying growth profiles and
convection. Convection leads to a constant imaginary vector potential in the
Schroedinger-like operator which appears in linearized growth models. We
illustrate the basic ideas by reviewing how convection affects the evolution of
a population influenced by a simple square well growth profile. Results from
discrete lattice growth models in both one and two dimensions are presented. A
set of similarity transformations which lead to exact results for the spectrum
and winding numbers of eigenfunctions for random growth rates in one dimension
is described in detail. We discuss the influence of boundary conditions, and
argue that periodic boundary conditions lead to results which are in fact
typical of a broad class of growth problems with convection.
