A pattern-analysis study of free-ranging dogs has come up with an interesting result that compares the language used by dogs with that of humans and other phenomena. The interdisciplinary study, which used a dataset of about 5,000 sightings of stray dogs, showed the existence of a power law dependence of dog behaviour that was a lot similar to graphs of human language.
A member of the team walked on randomly chosen streets and whenever a dog was seen, its behaviour at that instant was noted by them. “This way, we got a population-level random sample of behaviours of dogs at different places and times. We had a corpus of 93 unique [examples of] behaviour,” says Arunita Banerjee, a PhD student at the Behaviour and Ecology Lab, in the Department of Biological Sciences at Indian Institute of Science Education and Research, Kolkata. She is an author of the paper describing the work which has been accepted for publication in the journal Heliyon and has been posted online.
Power laws
Power law dependences are seen in many places in nature and in structures made by humans. An example of this is the set of words in a corpus – namely, if you take each word, count its frequency of occurrence and rank the words according to their frequency, and then make a log-log plot of the rank on the X-axis and frequency on the Y-axis, you will see that the plotted points all fall on a straight line with a slope -1 (minus one).
“Power-law dependencies suggest that there is, or are, underlying mechanisms(s), but extracting those mechanisms is not enabled by the power-law distribution, and requires further analyses of the time series,” says Ayan Banerjee from the Department of Physical Sciences of Indian Institute of Science Education and Research, Kolkata, who is a corresponding author of the paper.
The present study works on the premise that the dogs’ language is a complex one involving intricate behavioural displays – gestures, vocalisations, movements, mating rituals etc. From the dataset of 5,000 sightings, the group ranked the gestures according to the frequency of use and constructed a log-log plot. The plot approximated a straight line with a slope equal to -1.7 (minus 1.7).
Multifractal behaviour
The group also observed a multifractal characteristic of the data. As explained by Nirmalya Ghosh, from the Department of Physical Sciences, IISER Kolkata, and an author of the paper: “When we plot the rank-frequency curve in a log-log scale, we observe that different sections of the data fit different straight lines (that is, they have different slopes). This implies they have different power law dependencies which is indicative of a multi-fractal nature.”
As Ayan Banerjee explains, “From a pure probability-based statistical analysis, one would expect that a high probability event would be the most likely to happen, and thus a rare-occurence event would be immediately followed by a common one.”
Thus, it would seem likely that a dog barking, would be followed by it sleeping – which is not what actually occurs in reality. “However, the multifractal analysis tells us that behaviours of particular ranks are clustered together. This implies that a behaviour of a particular rank is likely to be followed by one of a similar rank,” he adds.
The idea for this study came up to Anindita Bhadra, a corresponding author of the paper, from the Behaviour and Ecology Lab, Department of Biological Sciences at IISER Kolkata, when she heard a talk by Ronojoy Adhikari, of The Institute of Mathematical Sciences, Chennai. He presented a very interesting piece of work in which they had used the Zipf-Mandelbrot law to claim that the markings of the Indus valley seals are a language. She says, “I started wondering, whether we could do the same with data on animal behaviour and proposed doing this with Arunita's data. She had been collecting the data for a different study, and she jumped in.”
According to Dr. Bhadra, this is a tool that can be explored by other behavioural biologists to understand the mysteries of their model systems.
