Restoration Ecology: Two-Sex Dynamics and Cost Minimization

TL;DR

This paper develops a spatially detailed model of two-sex population dynamics to determine the minimal cost of ecological restoration, considering various initial distributions and sex-specific factors, with implications for optimizing restoration strategies.

Contribution

It introduces a novel model incorporating sex ratio, mortality differences, and Allee effects to optimize initial population distributions for cost-effective habitat restoration.

Findings

Sex-specific distributions can reduce restoration costs when sex ratios are biased.

Homogeneous distributions are nearly optimal when sex ratios maximize local equilibrium density.

Numerical and simulated annealing methods effectively identify minimal-cost restoration strategies.

Abstract

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.