Detecting Levy walks without turn designation

作者：Reynolds Andy M^*

来源：Behavioral Ecology and Sociobiology, 2014, 68(11): 1893-1899.

DOI：10.1007/s00265-014-1819-3

• Levy walks
• Fractal clocks
• Composite correlated random walks
• Movement patterns
• Foraging

Many organisms have been reported to have movement patterns that are well approximated as Levy walks. This is typically because distributions of straight line distances between consecutive significant turns in movement paths have heavy power law tails. This diagnostic tool has been called into question because there is currently no standard, unambiguous way to identify significant turns. Even if such a way could be found, statistical analyses based on significant turns cannot account for actual movements made between turns and as a consequence cannot distinguish between true Levy walks and other fractal random walks such as Levy modulated correlated random walks where organisms randomly meander rather than move in straight lines between consecutive reorientation events. Here, I show that structure functions (i.e. moments of net displacements made across fixed time intervals) can distinguish between different kinds of Levy walks and between Levy walks and random walks with a few scales such as composite correlated random walks and correlated random walks. Distinguishing between these processes will lead to a better understanding of how and why animals perform Levy walks and help bridge the apparent divide between correlated random walks and Levy walks. Structure functions do not require turn identification and instead take account of entire movement paths. Using this diagnostic tool, I bolster previous claims that honeybees use a movement strategy that can be approximated by Levy walks when searching for their hive. I also show how structure functions can be used to establish the extent of self-similar behaviour in meandering Levy walks.

• 出版日期2014-11