The social brain of social media - a physiological boundary to the number of online relations

Based on the research done by Dunbar and the resulting Social Brain Hypothesis, the present study introduced a mathematical model for the development of follower numbers and the number of followed accounts regarding users/influencers of Social Media platforms. Under very simple assumptions the mathematical model suggests that an universal upper bound to follower and followed numbers exists. The theoretical upper bound is then empirically validated by using a representative data set of 255 influencers on Instagram from the field of women's fashion. The follower numbers show convergence to a common boundary for the years 2018 to 2019 and stagnation for 2019 to 2020, while the number of followed accounts show stagnation for 2018 to 2019 and convergence for 2019 and 2020. The model in conjunction with its empirical validation therefore provides the mathematical background to establish the socio-biological Social Brain Hypothesis in the field of influencer marketing in regards to Social Media platforms.