Abstract: Understanding how collective behavior emerges from simple interactions among many components of a complex system is a central challenge in contemporary science, linking phenomena as different as the spontaneous formation of social groups and the temporal rhythms of urban systems. This work addresses this problem through two studies that examine how socio-spatial behavior, that is, social behavior shaped by and situated in physical space, gives rise to robust macroscopic structures. The first study examines casual group formation using an attractiveness-driven agent-based model in which point-like agents move randomly in a two-dimensional arena and pause near socially attractive peers. By comparing this model with a null model in which agents move continuously, we show that individual-level social appeal fundamentally reshapes the structure and dynamics of social aggregation. Whereas the null model undergoes a percolation-like transition, the attractiveness-driven model suppresses this transition, generates more compact groups, and yields an average degree that grows linearly with system size at fixed density. Crucially, this model generates a power-law group-size distribution, $P(n) \propto n^{-2.5}$, whose exponent remains stable across densities, in contrast to the null model, whose group-size distribution changes form with density. These results demonstrate that individual-level social appeal is sufficient to produce scale-free patterns of spontaneous group formation in physical space. The second study investigates whether comparable regularities emerge in the organization of urban activity. Using the SafeGraph Weekly Patterns dataset, we analyze hourly visitation profiles during a non-holiday pre-pandemic week for 603,860 buildings across the 100 U.S. cities with the highest data coverage. A two-level unsupervised pipeline first identifies building clusters within each city using K-means and then groups cities by hierarchical clustering based on their building-cluster visitation profiles. Despite allowing the number of building clusters to vary independently across cities from two to ten, all 100 cities converge on exactly four building-level activity archetypes: hospitality, institutional, commercial, and entertainment. These universal building-level clusters combine differently across cities, giving rise to five city-level urban archetypes. The resulting clusters at both levels are validated using independent spatial, visitation, functional, and socioeconomic indicators, demonstrating robust and consistent macroscopic patterns across both levels. Together, these studies show how socio-spatial behavior gives rise to emergent collective structures across scales through simple, identifiable mechanisms.

Abstract: The dynamics of casual group formation has long been a subject of interest in social sciences. While early stochastic models offered foundational insights into group size distributions, they often simplified individual behaviors and lacked mechanisms for heterogeneous social appeal. Here, we re-examine the attractiveness-driven interaction model, an agent-based framework where point-like agents move randomly in a 2D arena and exhibit varied social appeal, leading them to pause near highly attractive celebrity peers. We compare this model to a null model where the agents are continuously in movement, which resembles a Random Geometric Graph. Our extensive simulations reveal significant structural and dynamic differences: unlike the null model, the attractiveness-driven model's average degree increases linearly with system size for fixed density, resulting in more compact groups and the suppression of a percolation transition. Crucially, while the null model's group size distribution is either exponentially decaying or bimodal, the attractiveness-driven model robustly exhibits a power-law distribution, $P(n) \sim n^{-2.5}$, with an exponent independent of density. These findings, obtained through computationally intensive simulations due to long equilibration times, offer a thorough quantitative characterization of this model, highlighting the critical role of individual attractiveness in shaping social aggregation in physical space.

Abstract: The population dynamics of early replicators has revealed numerous puzzles, highlighting the difficulty of transitioning from simple template-directed replicating molecules to complex biological systems. The resolution of these puzzles has set the research agenda on prebiotic evolution since the seminal works of Manfred Eigen in the 1970s. Here, we study the effects of demographic noise on the population dynamics of template-directed (non-enzymatic) and protein-mediated (enzymatic) replicators. We borrow stochastic algorithms from evolutionary game theory to simulate finite populations of two types of replicators. These algorithms recover the replicator equation framework in the infinite population limit. For large but finite populations, we use finite-size scaling to determine the probability of fixation and the mean time to fixation near a threshold that delimits the regions of dominance of each replicator type. Since enzyme-producing replicators cannot evolve in a well-mixed population containing replicators that benefit from the enzyme but do not encode it, we study the evolution of enzyme-producing replicators in a finite population structured in temporarily formed random groups of fixed size n. We argue that this problem is identical to the weak-altruism version of the n-player prisoner’s dilemma, and show that the threshold is given by the condition that the reward for altruistic behavior is equal to its cost.