  The overwhelming success of online social networks, the key actors in the Web
2.0 cosmos, has reshaped human interactions globally. To help understand the
fundamental mechanisms which determine the fate of online social networks at
the system level, we describe the digital world as a complex ecosystem of
interacting networks. In this paper, we study the impact of heterogeneity in
network fitnesses on the competition between an international network, such as
Facebook, and local services. The higher fitness of international networks is
induced by their ability to attract users from all over the world, which can
then establish social interactions without the limitations of local networks.
In other words, inter-country social ties lead to increased fitness of the
international network. To study the competition between an international
network and local ones, we construct a 1:1000 scale model of the digital world,
consisting of the 80 countries with the most Internet users. Under certain
conditions, this leads to the extinction of local networks; whereas under
different conditions, local networks can persist and even dominate completely.
In particular, our model suggests that, with the parameters that best reproduce
the empirical overtake of Facebook, this overtake could have not taken place
with a significant probability.
