Emergence of scaling in complex substitutive systems

Abstract

Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth.Here, we find that, ranging from mobile handsets to automobiles, from smart-phone apps to scientific fields, early growth patterns follow a power law with non-integer exponents. We test the hypothesis that mechanisms specific to substitution dynamics may play a role, by analyzing a unique data tracing 3.6M individuals substituting for different mobile handsets. We uncover three generic ingredients governing substitutions, allowing us to develop a minimal substitution model, which not only explains the power-law growth, but also collapses diverse growth trajectories of individual constituents into a single curve. These results offer a mechanistic understanding of power-law early growth patterns emerging from various domains and demonstrate that substitution dynamics are governed by robust self-organizing principles that go beyond the particulars of individual systems.2 Diffusion processes impact broad aspects of human society 1-5 , ranging from the spread of biological viruses 3, 6-8 to the adoption of innovations 4,[9][10][11][12][13][14] and knowledge 15, 16 and to the spread of information [17][18][19] , cultural norms and social behavior [20][21][22][23] . Despite numerous studies that span multiple disciplines, our knowledge is mainly limited to spreading processes in non-substitutive systems. Yet, a considerable number of ideas, products and behaviors spread by substitution-to adopt a new one, agents often need to give up an existing one. For example, the development of science hinges on scientists' relentlessness in abandoning a scientific framework once one that offers a better description of reality emerges 24 . The same is true for adopting a new healthy habit or other durable items, like mobile phones, cars or homes.While substitutions play a key role from science to economy, our limited understanding of such processes stems from the lack of empirical data tracing their characteristics. To study the dynamics of substitutions, we explore growth patterns in four different substitutive systems where detailed dynamical patterns are captured with fine temporal resolution (See Supplementary Note 1 for detailed data descriptions). Our first dataset captures, with daily resolution, 3.6 Million individuals choosing among different types of mobile handsets, recorded by a Northern European telecommunication company from January 2006 to November 2014. Since an individual is unlikely to keep more than one mobile phone at a time, his or her adoption of a new handset is typically associated with discontinuance of the old one. Here, we focus on handsets that have been released for at least 6 months and used by at least 50 users in total (885 different handset models). Our second dataset captures monthly transaction records of 126 automobiles sold in the North America between 2010 and 2016. These automobiles have been released for at least four mont...

On the Dual Nature of Adoption Processes in Complex Networks

“…Researchers have been tackling the problem of the emergence of innovation from different angles. For example, some studies have been focusing on the dynamics of substitutive systems, in which the new always replaces the old [84]. Here instead, we keep the focus on the dynamics leading to the emergence of the new; we frame the problem in a cumulative way such that the new, intentionally very broadly defined always comes as an addition to the existing.…”

“…This implies that the last novelty found will remain unchanged for some time. As for processes of individual and collective attention in social and substitutive systems [84], individuals will focus on a single novelty at the time. A simple way to couple discovery and contagion is illustrated in Figure 3, where each individual tries to spread this last novelty to her/his neighbors through the links of the social network by means of a simple SI contagion process.…”

Scaling laws in natural conversations among elderly people

“…Scaling laws, which are generally defined as f ( x ) ∼ x μ , where μ is a scaling exponent (here, “∼” means that the left side is proportional to the right side), are ubiquitous in natural phenomena [ 17 ]. Interestingly, they are observed widely in brain and behavioral phenomena, such as neural dynamics, decision-making, semantic memory, memory retrieval, cognition, movements, language, and social dynamics [ 18 – 26 ]. The most famous example can be seen in the word patterns of human language [ 18 ].…”

The Strength of Structural Diversity in Online Social Networks

“…As the backbone of so many online social systems, network structure is becoming a complex and subtle force that drives the dynamics of a wide variety of social processes. In some cases, we seek to leverage social networks to maintain social capital, encourage the adoption of new products, or promote positive behaviors like cooperation and physical exercise [1][2][3][4][5][6][7][8][9][10], while in others to eliminate the spread of infectious diseases and fake news or change negative behaviors like conflict and unhealthy eating [11][12][13][14][15].…”