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 statement: Animal 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.
Keywords: Algorithmic; Australian ants; Correlated random walks; Myrmecia midas; Randomness; Search.