They turn up weekly in my inbox, gnawing away at my soul. The kind words, the smiling faces, the ego-stroking invitations to connect, all of which I guiltily ignore. The thing is, I buy into the idea of Dunbar’s number — that our primate brains limit us to meaningful social contact with no more than about 150 people — and I am already exceeding 200 on LinkedIn.

Professor Robin Dunbar, the Oxford university anthropologist who came up with the eponymous figure after noting the strikingly similar sizes of human groupings ranging from Neolithic villages to Roman legions to an average Christmas card list, has posited that our social attention is not distributed evenly among those 150 confidantes but instead layered like an onion; five closest contacts in the innermost layer, then 10 in the next, followed by 35 and 100.

Now a study of mobile phone calls has attempted to test Prof Dunbar’s hypothesis about our Russian doll-like shells of emotional intimacy, providing insight into how we stratify our social connections. Along with colleagues at Finland’s Aalto University School of Science, Prof Dunbar looked at a 2007 data set of European mobile phone calls, comprising 35m users making a total of 6bn calls. The frequency of calls between two people was a proxy for emotional closeness. Those who made just emergency or business calls were excluded; only those making reciprocal calls to at least 100 people were included.

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The paper has limitations: it looked at just one year of data. Friendships can be impermanent, varying across time and place, and reflecting our lives at particular stages. Frequency of contact does not always correlate with depth of relationship; longstanding bonds often do not need intensive tending to bloom.

But it is also possible that this study captures a unique picture of friendship: a 2007 data set represents the social world before smartphone ubiquity, and before people routinely began maintaining friendships on Facebook and other online sites on their mobile devices. There is also a persuasive consistency in the numbers, the researchers note. This intuitively mirrors real life: even if a house move or a job change forces a change of circumstances, old acquaintances are superseded by new ones. The exact components of the layers may change but the layers themselves remain intact.

Few of us, it should be noted, exceed 200 meaningful social relationships. This limit should prompt networking sites to refine their services in a digitally promiscuous age. The enduring human need to connect — a desire that can now be expressed at the touch of a button — should ideally be balanced against the inability of our brains to cope with an excessive degree of digital schmoozing.

Instead of the usual binary options to either accept or decline an invitation, there could be a third box to click that is both more gracious and scientifically accurate. It would read: “It’s not that I don’t want you to join my network, but I’m just waiting for some space to come up on my fourth layer.”