Abstract
The correlated random walk paradigm is the dominant conceptual framework for modeling animal movement patterns. Nonetheless, we do not know whether the randomness is apparent or actual. Apparent randomness could result from individuals reacting to environmental cues and their internal states in accordance with some set of behavioral rules. Here, we show how apparent randomness can result from one simple kind of algorithmic response to environmental cues. This results in an exponential step-length distribution in homogeneous environments and in generalized stretched exponential step-length distributions in more complex fractal environments. We find support for these predictions in the movement patterns of the Australian bull ant Myrmecia midas searching on natural surfaces and on artificial uniform and quasi-fractal surfaces. The bull ants spread their search significantly farther on the quasi-fractal surface than on the uniform surface, showing that search characteristics differed as a function of the substrate on which ants are searching. Further tentative support comes from a re-analysis of Australian desert ants Melophorus bagoti moving on smoothed-over sand and on a more strongly textured surface. Our findings call for more experimental studies on different surfaces to test the surprising predicted linkage between fractal dimension and the exponent in the step-length distribution.Significance statementAnimal search patterns often appear to be irregular and erratic. This behavior is captured by random walk models. Despite their considerable successes, extrapolation and prediction beyond observations remain questionable because the true nature and interpretation of the randomness in these models have until now been elusive. Here, we show how apparent randomness can result from simple algorithmic responses to environmental cues. Distinctive predictions from our theory find support in analyses of the search patterns of two species of Australian ants.
Highlights
Systematic searching is found ubiquitously in insects
M. midas move slowly, but when released, all ants in all conditions exited their tube in time and started looping around in search
The larger search range in daylight is reflected in the segment lengths (Fig. 4e), which appear longer for searches in daylight compared with searches in twilight
Summary
Systematic searching is found ubiquitously in insects. In navigating to a goal, such as the nest, it serves as a back-up systemCommunicated by J. Systematic searching is found ubiquitously in insects. To their other strategies (Schultheiss et al 2015), such as path integration (Wehner and Srinivasan 1981; Müller and Wehner 1988) and landmark guidance (Cheng 2012; Collett et al 2013). Systematic searching has been especially well-studied in hymenopteran insects, primarily in ants and bees. The focus species of this account, perform loops that return occasionally to the starting point of search, with the loops increasing in size as the search goes on (Schultheiss and Cheng 2011; Wehner and Srinivasan 1981). The expanding pattern is found even when ants are searching in the restricted environment of a long narrow channel that essentially reduces the movement to one dimension (Cheng and Wehner 2002; Narendra et al 2008)
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