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The fuel-driven process of replication in living systems generates distributions of copied entities with varying degrees of copying accuracy. Here we introduce a thermodynamically consistent ensemble for investigating universal population…

We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…

Orderliness, reflected via mathematical laws, is encountered in different frameworks involving social groups. Here we show that a thermodynamics can be constructed that macroscopically describes urban population flows. Microscopic dynamic…

A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…

Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without…

In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear…

In this paper, we inspect well-known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns.…

A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…

Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…

Are there multiple equilibria in the spatial economy? This paper develops a unified framework that integrates systems of cities and regional models to address this question within a general geographic space. A key feature is the endogenous…

With a steadily growing human population and rapid advancements in technology, the global human network is increasing in size and connection density. This growth exacerbates networked global threats and can lead to unexpected consequences…

Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons…

This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…

Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation, and human-driven habitat degradation. Such threats are pushing ecosystems to the brink of collapse. Because of a…

Recent advances in the urban science make broad use of the notion of scaling. We focus here on the important scaling relationship between the gross metropolitan product (GMP) of a city and its population (pop). It has been demonstrated that…

We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the…

A generalized continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way. A parameter controls the effectiveness of the transactions between the agents. We show…

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…

Supporting the health and well-being of dynamic populations around the world requires governmental agencies, organizations and researchers to understand and reason over complex relationships between human behavior and local contexts in…