Optimal L\'{e}vy-flight foraging in a finite landscape

摘要

We present a simple model to study L\'{e}vy-flight foraging in a finitelandscape with countable targets. In our approach, foraging is a step-basedexploratory random search process with a power-law step-size distribution $P(l)\propto l^{-\mu}$. We find that, when the termination is regulated by a finitenumber of steps $N$, the optimum value of $\mu$ that maximises the foragingefficiency can vary substantially in the interval $\mu \in (1,3)$, depending onthe landscape features (landscape size and number of targets). We furtherdemonstrate that subjective returning can be another significant factor thataffects the foraging efficiency in such context. Our results suggest thatL\'{e}vy-flight foraging may arise through an interaction between theenvironmental context and the termination of exploitation, and particularlythat the number of steps can play an important role in this scenario which isoverlooked by most previous work. Our study not only provides a new perspectiveon L\'{e}vy-flight foraging, but also opens new avenues for investigating theinteraction between foraging dynamics and environment as well as offers arealistic framework for analysing animal movement patterns from empirical data.