Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates

Many authors have claimed to observe animal movement paths that appear to be L,vy walks, i.e. a random walk where the distribution of move lengths follows an inverse power law. A L,vy walk is known to be the optimal search strategy of a particular class of random walks in certain environments; hence, it is important to distinguish correctly between L,vy walks and other types of random walks in observed animal movement paths. Evidence of a power law distribution in the step length distribution of observed animal movement paths is often used to classify a particular movement path as a L,vy walk. However, there is some doubt about the accuracy of early studies that apparently found L,vy walk behaviour. A recently accepted method to determine whether a movement path truly exhibits L,vy walk behaviour is based on an analysis of move lengths with a maximum likelihood estimate using Akaike weights. Here, we show that simulated (non-L,vy) random walks representing different types of animal movement behaviour (a composite correlated random walk; pooled data from a set of random walks with different levels of correlation and three-dimensional correlated random walks projected into one dimension) can all show apparent power law behaviour typical of L,vy walks when using the maximum likelihood estimation method. The probability of the movement path being identified as having a power law step distribution is related to both the sampling rate used by the observer and the way that 'turns' or 'reorientations' in the movement path are designated. However, identification is also dependent on the nature and properties of the simulated path, and there is currently no standard method of observation and analysis that is robust for all cases. Our results indicate that even apparently robust maximum likelihood methods can lead to a mismatch between pattern and process, as paths arising from non-L,vy walks exhibit L,vy-like patterns.