Ecology 2.0: Coexistence and Domination among Interacting Networks

Online social networks are in constant competition to attract and retain users' attention. From this point of view, OSNs and other digital services can be understood as forming a complex digital ecosystem of interacting species that compete for the same resource, our digital time. In this work, we introduce a very general and flexible framework to model such ecosystem. Akin to standard ecological theories of competing species, the fitness of OSNs increases with their performance following a preferential attachment (or rich-get-richer) mechanism. However, unlike in standard ecology, the total fitness of the system is a conserved quantity, which induces diminishing returns in the fitness of each network. In a range of parameters, the combination of these two mechanisms leads to stable coexistence states of many networks, in stark contrast to the competitive exclusion principle. However, stable coexistence is only possible in a region of the parameter space, which is delimited by a critical line. At this critical line the system undergoes a subcritical pitchfork bifurcation akin to a first order phase transition. Our model thus predicts that a minimal change or perturbation in the interactions between the different networks can induce a catastrophic effect in the fate of the system. In any case, due to the stochastic nature of the dynamics and the multitude of fixed points, a stable coexistence solution is not always reached. The probability to reach such solution is an indicator of the diversity observed in the digital ecosystem. Interestingly, we find that in a large fraction of the parameter space the most probable outcome is the coexistence of a moderate number of digital services, in agreement with empirical observations. References [1] Kaj-Kolja Kleineberg and Marián Boguñá. Evolution of the digital society reveals balance between viral and mass media influence.