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The role of dispersal on the stability and synchrony of a metacommunity is a topic of considerable interest in theoretical ecology. Dispersal is known to promote both synchrony, which enhances the likelihood of extinction, and spatial…
This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…
Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and…
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…
Self-organization of heterogeneous particle swarms is rich in its dynamics but hard to design in a traditional top-down manner, especially when many types of kinetically distinct particles are involved. In this chapter, we discuss how we…
Microbiome-based stratification of healthy individuals into compositional categories, referred to as "community types", holds promise for drastically improving personalized medicine. Despite this potential, the existence of community types…
We propose a mathematical model for collective sensing in a population growing in a stochastically varying environment. In the population, individuals use an information channel for sensing the environment, and two channels for signal…
In real-life complex systems, individuals often encounter multiple social dilemmas that cannot be effectively captured using a single-game model. Furthermore, the environment and limited resources both play a crucial role in shaping…
Understanding what and how causal dynamical mechanisms generate collective phenomena is a central challenge in complexity science. Recent studies have focused on identifying the mechanisms underlying the synergistic interdependencies that…
Classical approaches to ecological stability rely on fully connected interaction models, yet real ecosystems are sparse and structured--a feature that qualitatively reshapes their collective dynamics. Here, we establish a thermodynamically…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…
A great number of biological organisms live in aqueous environments. Major evolutionary transitions, including the emergence of life itself, likely occurred in such environments. While the chemical aspects of the role of water in biology…
Cooperation is ubiquitous ranging from multicellular organisms to human societies. Population structures indicating individuals' limited interaction ranges are crucial to understand this issue. But it is still at large to what extend…
The significant role of space in maintaining species coexistence and determining community structure and function is well established. However, community ecology studies have mainly focused on simple competition and predation systems, and…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…