Reply to Comment on "Inverse Square L\'evy Walks are not Optimal Search Strategies for d \geq 2 "

TL;DR

This paper refutes previous claims about the optimality of inverse-square Levy walks in search strategies, clarifying the conditions under which they are optimal and arguing these conditions are biologically unlikely.

Contribution

It clarifies the validity range of inverse-square Levy walks' optimality and specifies the unlikely biological conditions for their optimality.

Findings

Inverse-square Levy walks are not generally optimal for search.

Optimality conditions are narrowly defined and biologically unlikely.

The paper clarifies the validity range of previous results.

Abstract

We refute here the concernes raised in the Comment of our letter. This reply states clearly the validity range of our results and shows that the optimality of inverse-square Levy walks at the basis of the Levy flight foraging hypothesis is generically unfounded. We also give the precise set of conditions for which inverse-levy square Levy walks turn to be optimal, conditions which are unlikely to be verified biologically.