New paper on the structure of personal relationships

I have a new paper out with Ignacio Tamarit and José A. Cuesta on the structure of personal relationships. In short: we extend the idea of Dunbar circles to the continuum so all types of data can be considered. In more detail: In the early 2000's Robin Dunbar and co-authors showed that our personal relationships are organized in circles: 3-5 very close relationships, add 10-12 for the circle of close friends, another 30-40 join as friends, and acquaintainces add up to about 150. Note that the size of circles scale by a factor of 3: the sequence is approximately 5-15-50-150. Beyond that, there is evidence for a larger circle of ~500 people, see e.g., the paper by Miranda Lubbers, José Luis Molina and Hugo Valenzuela. There is a lot of empirical evidence that the circles exist. But in 2018, our team along with Robin Dunbar showed mathematically that this is the only way relationships of different intensities can be organized if cognitive capacity is limited. In fact, our theory predicted the circles as we know it, but also another regime that should be observed in small populations, where almost everybody is in the first circle for lack of enough people to be friends with (inverted regime). Data from José Luis Molina confirmed it.

However, the division on circles is somewhat arbitrary, and often data on relationships is continuous, like duration of phone calls or of face-to-face encounters. In our new paper we develop the corresponding mathematical theory to describe this. We check our theory with data from phones (Sune Lehmann et al), from face-to-face encounters (Ciro Cattuto, Alain Barrat et al) and from facebook (Arnaboldi et al). The theory describes pretty well all these datasets, and a majority of the individuals in the data are well described by one-parameter theory, with parameter value 6, which is in exact correspondance with the 3 factor of the discrete Dunbar circles. Thus, the model captures a universal feature of how we manage our relationships, and makes it clear that their structure exhibits the signature of a resource allocation problem both in the discrete and in the continuum versions. Stay tuned for further, awesome evidence of this limited resource mechanism in other contexts, hopefully coming out soon in a journal near you. Thanks to Ignacio and Jose, and to Robin Dunbar for support.