  We model a spatially detailed, two-sex population dynamics, to study the cost
of ecological restoration. We assume that cost is proportional to the number of
individuals introduced into a large habitat. We treat dispersal as homogeneous
diffusion. The local population dynamics depends on sex ratio at birth, and
allows mortality rates to differ between sexes. Furthermore, local density
dependence induces a strong Allee effect, implying that the initial population
must be sufficiently large to avert rapid extinction. We address three
different initial spatial distributions for the introduced individuals; for
each we minimize the associated cost, constrained by the requirement that the
species must be restored throughout the habitat. First, we consider spatially
inhomogeneous, unstable stationary solutions of the model's equations as
plausible candidates for small restoration cost. Second, we use numerical
simulations to find the smallest cluster size, enclosing a spatially
homogeneous population density, that minimizes the cost of assured restoration.
Finally, by employing simulated annealing, we minimize restoration cost among
all possible initial spatial distributions of females and males. For biased sex
ratios, or for a significant between-sex difference in mortality, we find that
sex-specific spatial distributions minimize the cost. But as long as the sex
ratio maximizes the local equilibrium density for given mortality rates, a
common homogeneous distribution for both sexes that spans a critical distance
yields a similarly low cost.
