English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is widely accepted that inverse square L\'evy walks are optimal searchstrategies because they maximize the encounter rate with sparse, randomlydistributed, replenishable targets when the search restarts in the vicinity ofthe previously visited target, which becomes revisitable again with highprobability, i.e., non-destructive foraging [Nature 401, 911 (1999)]. Theprecise conditions for the validity of this L\'evy 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 raisedrecently for $d \geq 2$: (i) the capture rate $\eta$ has linear dependence onthe target density $\rho$ for all values of the L\'evy index $\alpha$; (ii)"the gain $\eta_{max}/\eta$ achieved by varying $\alpha $ is bounded even inthe limit $\rho \to 0 $" so that "tuning $\alpha$ can only yield a marginalgain"; (iii) depending on the values of the radius of detection $a$, therestarting distance $l_c$ and the scale parameter $s$, the optimum is realizedfor a range of $\alpha$ [Phys. Rev. Lett. 124, 080601 (2020)]. Here we answereach of these three criticisms in detail and show that claims (i)-(iii) do notactually invalidate the LFH. Our results and analyses restore the originalresult of the LFH for non-destructive foraging.

Comment on "Inverse Square L\'evy Walks are not Optimal Search Strategies for d $\geq$ 2" [Phys. Rev. Lett. 124, 080601 (2020)]