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A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
Many biological populations exhibit diversity in their strategy for survival and reproduction in a given environment, and microbes are an example. We explore the fate of different strategies under sustained environmental change by…
Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…
Ecological systems are emergent features of ecological and adaptive dynamics of a community of interacting species. By natural selection through the abiotic environment and by co-adaptation within the community, species evolve, thereby…
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and…
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 propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
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 discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of…
Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic, and mounting experimental evidence raises the intriguing…
Recent work draws attention to community-community encounters ("coalescence") as likely an important factor shaping natural ecosystems. This work builds on MacArthur's classic model of competitive coexistence to investigate such…
Group formation and coordination are fundamental characteristics of living systems, essential for performing tasks and ensuring survival. Interactions between individuals play a key role in group formation, and the impact of resource…
Living systems are thermodynamically open but closed in their organization. In other words, even though their material components turn over constantly, a material-independent property persists, which we call organization. Moreover,…
We demonstrate diversification rather than optimisation for highly interacting organisms in a well mixed biological system by means of a simple model and reference to experiment, and find the cause to be the complex network of interactions…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…