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Species interactions through cross-feeding via leakage and uptake of chemicals are important in microbial communities, and play an essential role in the coexistence of diverse species. Here, we study a simple dynamical model of a microbial…
Two symmetrically coupled logistic equations are proposed to mimic the competitive interaction between two species. The phenomena of coexistence, oscillations and chaos are present in this cubic discrete system. This work, together with two…
While fields like Artificial Life have made huge strides in quantifying the mechanisms that distinguish living systems from non-living ones, particular mechanisms remain difficult to reproduce in silico. Known as open-endedness, we've been…
Standard models of population dynamics focus on the the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the…
We develop a theoretical framework to understand the persistence and coexistence of competitive species in a spatially explicit metacommunity model with a heterogeneous dispersal kernel. Our analysis, based on methods from the physics of…
The interdependence between an individual strategy decision and the resulting change of environmental state is often a subtle process. Feedback-evolving games have been a prevalent framework for studying such feedback in well-mixed…
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
Explaining coexistence in species-rich communities of primary producers remains a challenge for ecologists because of their likely competition for shared resources. Following Hutchinson's seminal suggestion, many theoreticians have tried to…
Mays celebrated theoretical work of the 70s contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here Mays random-matrix modelling approach is generalized to realistic…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Understanding the emergence and sustainability of cooperation is a fundamental problem in evolutionary biology and is frequently studied by the framework of evolutionary game theory. A very powerful mechanism to promote cooperation is…
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…
Persistent economic competition is often justified as a mechanism of innovation, efficiency, and welfare maximization. Yet empirical evidence across disciplines reveals that competition systematically generates fragility, inequality, and…
Ecosystems frequently display the coexistence of diverse species under resource competition, typically resulting in skewed distributions of rarity and abundance. A potential driver of such coexistence is environmental fluctuations that…
This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge…
Similarity of competitors has been proposed to facilitate coexistence of species because it slows down competitive exclusion, thus making it easier for equalizing mechanisms to maintain diverse communities. On the other hand, chaos can…
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…
The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev.…