Cities and biodiversity: Spatial efficiency of land use

Biologically important but dangerous wildlife creatures encroach into cities, which causes human-wildlife conflicts. To explore the effect of the encroachment of wildlife into cities on equilibrium land use and its efficiency, we develop an equilibrium theory of land used for humans and wildlife by combining an ecosystem model with urban economics model. Humans choose their housing location and size in response to the risk of encountering wildlife in cities, and animals optimize their food intake by spreading out in response to heterogeneous feeding grounds in both urban areas and natural habitats, which determines the spatial heterogeneous distribution of both agents. We first prove the existence and uniqueness of the spatial equilibrium in a linear city adjacent to natural habitats. Next, our theory provides new insights for the wildlife conservation: (i) this spatial heterogeneity generates inefficient predator-prey interactions, leading to an inefficient steady state population equilibrium of animals; (ii) With the spatial inefficiency, the equilibrium city size is not always too big. We numerically demonstrate how both the equilibrium and the optimal solution are affected by the scale of conflicts and the value of wildlife.