  Apparently random events in nature often reveal hidden patterns when analysed
using diverse and robust statistical tools. Power-law distributions, for
example, project diverse natural phenomenon, ranging from earthquakes1 to
heartbeat dynamics2 onto a common platform of statistical self-similarity. A
large range of human languages are known to follow a specific regime of
power-law distributions, the Zipf-Mandelbrot law, in addition to showing
properties like the Pareto principle and Shannon entropy3,4. Animal behaviour
in specific contexts have been shown to follow power-law distributions5,6.
However, the entire behavioural repertoire of a species has never been analysed
for the existence of underlying patterns. Here we show that the frequency-rank
data of randomly sighted behaviours at the population level of free-ranging
dogs follow a scale-invariant power-law behaviour. While the data does not
display Zipfian trends, it obeys the Pareto principle and Shannon entropy rules
akin to languages. Interestingly, the data also exhibits robust self-similarity
patterns at different scales which we extract using multifractal detrended
fluctuation analysis7. The observed multifractal trends suggest that the
probability of consecutive occurrence of behaviours of adjacent ranks is much
higher than behaviours widely separated in rank. Since we observe such robust
trends in random data sets, we hypothesize that the general behavioural
repertoire of a species is shaped by a syntax similar to languages. This opens
up the prospect of future multifractal and other statistical investigations on
true time series of behavioural data to probe the existence of possible long
and short-range correlations, and thereby develop predictive models of
behaviour.
