评论“平方反比Lévy Walks are not Optimal Search Strategies for d $\geq$ 2”[Phys. Rev. Lett. 124，080601（2020）]
Comment on "Inverse Square Lévy Walks are not Optimal Search Strategies for d $\geq$ 2" [Phys. Rev. Lett. 124, 080601 (2020)]
摘要：
人们普遍认为，平方反比Lévy行走是最佳搜索策略，因为当搜索在先前访问过的目标附近重新开始时，它们最大化了稀疏、随机分布、可修改的目标的遭遇率，该目标以高概率再次变得可修改，即，非破坏性觅食[Nature 401，911（1999）]。Lévy飞行觅食假说（LFH）有效性的精确条件已在文献中广泛描述[Phys. Life Rev. 14，94（2015）]。然而，最近对于$d \geq 2$已经提出了三个反对LFH的主张：（i）对于Lévy指数$α$的所有值，捕获率$η$与目标密度$ρ$具有线性相关性;（ii）“通过改变$α$实现的增益$η_{max}/η$甚至在极限$ρ\to 0 $中也是有界的“，使得“调谐$α$只能产生边际增益”;（iii）取决于检测半径$a$、重新开始距离$l_c$和尺度参数$s$的值，对于$α$的范围实现最优[Phys.Rev.Lett. 124，080601（2020）]。在这里，我们回答这三个批评的细节，并表明索赔（i）-（iii）实际上并不无效的LFH。我们的结果和分析恢复了LFH的非破坏性觅食的原始结果。
英文摘要：
It is widely accepted that inverse square Lévy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the previously visited target, which becomes revisitable again with high probability, i.e., non-destructive foraging [Nature 401, 911 (1999)]. The precise conditions for the validity of this Lévy flight foraging hypothesis (LFH) have been widely described in the literature [Phys. Life Rev. 14, 94 (2015)]. Nevertheless, three objecting claims to the LFH have been raised recently for $d \geq 2$: (i) the capture rate $η$ has linear dependence on the target density $ρ$ for all values of the Lévy index $α$; (ii) "the gain $η_{max}/η$ achieved by varying $α$ is bounded even in the limit $ρ\to 0 $" so that "tuning $α$ can only yield a marginal gain"; (iii) depending on the values of the radius of detection $a$, the restarting distance $l_c$ and the scale parameter $s$, the optimum is realized for a range of $α$ [Phys. Rev. Lett. 124, 080601 (2020)]. Here we answer each of these three criticisms in detail and show that claims (i)-(iii) do not actually invalidate the LFH. Our results and analyses restore the original result of the LFH for non-destructive foraging.
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