Viswanathan G M, Buldyrev S V, Havlin S, da Luz M G, Raposo E P, Stanley H E
Center for Polymer Studies and Department of Physics, Boston University, Massachusetts 02215, USA.
Nature. 1999 Oct 28;401(6756):911-4. doi: 10.1038/44831.
We address the general question of what is the best statistical strategy to adapt in order to search efficiently for randomly located objects ('target sites'). It is often assumed in foraging theory that the flight lengths of a forager have a characteristic scale: from this assumption gaussian, Rayleigh and other classical distributions with well-defined variances have arisen. However, such theories cannot explain the long-tailed power-law distributions of flight lengths or flight times that are observed experimentally. Here we study how the search efficiency depends on the probability distribution of flight lengths taken by a forager that can detect target sites only in its limited vicinity. We show that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Lévy flight motion, is an optimal strategy. We test the theory by analysing experimental foraging data on selected insect, mammal and bird species, and find that they are consistent with the predicted inverse square power-law distributions.
我们探讨了一个普遍问题，即采用何种最佳统计策略才能高效搜索随机分布的物体（“目标位点”）。在觅食理论中，通常假定觅食者的飞行长度具有特征尺度：基于此假设，出现了高斯分布、瑞利分布以及其他具有明确方差的经典分布。然而，这类理论无法解释实验中观察到的飞行长度或飞行时间的长尾幂律分布。在此，我们研究了搜索效率如何取决于觅食者的飞行长度概率分布，该觅食者仅能在其有限范围内探测到目标位点。我们表明，当目标位点稀疏且可被多次访问时，对应于列维飞行运动的飞行长度的反平方幂律分布是一种最优策略。我们通过分析选定昆虫、哺乳动物和鸟类物种的实验觅食数据来检验该理论，发现它们与预测的反平方幂律分布一致。
