  The escape trajectories animals take following a predatory attack appear to
show high degrees of apparent 'randomness' - a property that has been described
as 'protean behaviour'. Here we present a method of quantifying the escape
trajectories of individual animals using a path complexity approach. When fish
(Pseudomugil signifer) were attacked either on their own or in groups, we find
that an individual's path rapidly increases in entropy (our measure of
complexity) following the attack. For individuals on their own, this entropy
remains elevated (indicating a more random path) for a sustained period (10
seconds) after the attack, whilst it falls more quickly for individuals in
groups. The entropy of the path is context dependent. When attacks towards
single fish come from greater distances, a fish's path shows less complexity
compared to attacks that come from short range. This context dependency effect
did not exist, however, when individuals were in groups. Nor did the path
complexity of individuals in groups depend on a fish's local density of
neighbours. We separate out the components of speed and direction changes to
determine which of these components contributes to the overall increase in path
complexity following an attack. We found that both speed and direction measures
contribute similarly to an individual's path's complexity in absolute terms.
Our work highlights the adaptive behavioural tactics that animals use to avoid
predators and also provides a novel method for quantifying the escape
trajectories of animals.
