Ecological modelling: The mathematical mirror to animal nature

Environmental context explains Lévy and Brownian movement patterns of marine predators

“…We tested the spatial occurrence of these two principal patterns and found Lévy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Lévy-flight foraging hypothesis 1,7 , supporting the contention 8,9 that organism search strategies naturally evolved in such a way that they exploit optimal Lévy patterns.…”

“…Lévy flights and walks are theorized to be the most efficient movement pattern for locating patchy prey in low concentrations on spatial scales beyond a searcher's sensory range, with an optimal search having a power-law exponent of m < 2 (refs 4, 13). It is proposed that organisms have therefore naturally evolved search patterns that can be modelled as optimal Lévy flights 1,7,13 .However, burgeoning empirical support for this hypothesis recently foundered following studies suggesting methodological shortcomings in the estimation of power-law exponents and in determining the goodness of fit to the data 5,6,14-16 , thus casting doubt on some, if not all, of the empirical studies that used such methods 8,9 . Hence, controversy remains over whether Lévy behaviour occurs in nature 6,9,17 , despite many empirical studies 1,18 .…”

“…However, burgeoning empirical support for this hypothesis recently foundered following studies suggesting methodological shortcomings in the estimation of power-law exponents and in determining the goodness of fit to the data 5,6,[14][15][16] , thus casting doubt on some, if not all, of the empirical studies that used such methods 8,9 . Hence, controversy remains over whether Lévy behaviour occurs in nature 6,9,17 , despite many empirical studies 1,18 .…”

“…Hence, controversy remains over whether Lévy behaviour occurs in nature 6,9,17 , despite many empirical studies 1,18 . Furthermore, long time series of movements (over weeks to months) derived from animalattached electronic tags will very probably capture complex movement data resulting from different types of behaviour (for example searching, travelling and resting) as animals respond to various biotic and abiotic factors over time.…”

“…Previous studies analysing movement data 6,12,13 on free-ranging animals for Lévy motion used data collected over long time periods and different habitat types, without giving sufficient consideration to the issue of there being different types of behaviour interspersed within the time series. The lack of analysis of separate behaviour-pattern types may be at least one reason why evidence for Lévy flights in animal behaviour has proved challenging to detect unequivocally 9,17 .…”