Lévy walks evolve through interaction between movement and environmental complexity

de Jager, M., Weissing, F. J., Herman, P. M., Nolet, B. A., & van de Koppel, J. (2011). Lévy walks evolve through interaction between movement and environmental complexity. Science, 332(6037), 1551-1553.

The formation of specific spatial patterns on landscapes generally results from positive feedbacks on conspecific density at local scales and negative feedbacks at larger scales. These specific mechanisms differ from system to system; in the formation of patterns in mussel beds, previous studies have shown that short-distance facilitation results from a decrease in wave stress and predation risk for mussels in aggregation, and long-distance inhibition stems from intraspecific competition for food. In this paper, de Jager et al. (2011) explore the mechanism of this pattern formation. Specifically, they ask what movement strategy best explains aggregation on a small scale.

Multiple models have been proposed to statistically explain animal movements. Lévy walks and Brownian walks are two such models, in which step lengths (i.e., distance moved between reorientation events) are drawn from a power-law or exponential distribution, respectively. Though not always mechanistic, Lévy walks fit a wide range of animal movement patterns, particularly searching behavior. Since pattern develops in response to the existing distribution of mussels (i.e. habitat) and resources, the authors hypothesize that movement patterns of mussels might be important for pattern formation.

In order to test this hypothesis, the authors first use a mesocosm experiment to confirm that mussels do, in fact, move in a pattern that fits a Lévy walk. To do so, they measured step lengths of moving mussels and fit them to a power-law distribution; the Lévy walk was the best fit. After doing so, they were then able to build an individual-based model to ask whether this movement strategy facilitated formation of spatially aggregated mussel beds. This model incorporated their observation from the mesocosm experiment that mussel movement decreases with short-range density (i.e., mussels move less in aggregations) and increases with long-range density (i.e., mussels move more when in a large group). In doing so, the authors showed that, compared to ballistic or Brownian movement, a Lévy walk resulted in a faster rate of pattern formation. Mechanistically, this pattern occurred because ballistic movement (i.e. large steps) prevented cluster formation and Brownian movement (i.e. small steps) required more steps to create the aggregations. In one additional analysis, the authors concluded that the Lévy walk is an evolutionarily stable strategy in this system. de Jager et al. use their results to suggest that, beyond this specific system, feedbacks between animal movements and habitat complexity can determine both habitat structure and movement strategies.