A story on relocation strategies, the Allee effect, and the Ideal Free Distribution
It is well known that relocation strategies in ecology and in economics can make the difference between extinction and persistence. In this talk I present a unifying model for the dynamics of ecological populations and street vendors, an important part of many informal economies. I discuss the effects of chemotactic movement of populations subject to the Allee Effect by discussing the existence of equilibrium solutions subject to various boundary conditions and the evolution problem when the chemotaxis effect is small. On an interesting note, I present numerical simulations, which show that in fact chemotaxis can help overcome the Allee effect as well as some partial analytical results in this direction. I will conclude by making a connection to the Ideal Free Distribution and analyze what happens under competition, showing that the Ideal Free Distribution is locally evolutionarily stable.