The Lévy Flight Foraging Hypothesis In Bounded Regions: Subordinate Brownian Motions
 

The authors investigate the problem of the Lévy flight foraging hypothesis in an ecological niche described by a bounded region of space, with either absorbing or reflecting boundary conditions. To this end, they consider a forager diffusing according to a fractional heat equation in a bounded domain, and they define several efficiency functionals whose optimality is discussed in relation to the fractional exponent $s \in (0, 1)$ of the diffusive equation. Such an equation is taken to be the spectral fractional heat equation (with Dirichlet or Neumann boundary conditions).