Heavy-tailed distributions in the intermittent motion behaviour of the intertidal gastropod Littorina littorea

The two-dimensional motion behaviour of the common intertidal gastropod Littorina littorea is investigated as a function of the immersion time from three sampling sites on an exposed rocky shore. A total of 90 individuals have been individually marked and tracked over 14 consecutive daylight low tide. Successive displacements show very intermittent behaviour, with a few localised large displacements over a wide range of small displacements. We show that successive displacements are described by flight length ld heavy-tailed distributions with P(ld)∼ld-μ. The very low values of the exponent μ (μ≈2.22, 2.43 and 2.67) indicate that L. littorea flights fall into the category of super-diffusive processes. These exponents were significantly higher than the special value μ≈2 analytically and theoretically predicted to be the most advantageous in optimising long-term encounter statistics, especially for low-prey-density scenario. As natural selection should favour flexible behaviour, leading to different optimum searching statistics, under different conditions, our results support the idea that the differences in food concentration and distribution encountered at the different sites by L. littorea led to different heavy-tailed distributions observed for the most extreme displacements.