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Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
Given an endogenous timescale set by invasion in a constant environment, we introduced periodic temporal variation in competitive superiority by alternating the species' propagation rates. By manipulating habitat size and introduction rate,…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…
Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals…
We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
Diverse communities of competing species are generally characterized by substantial niche overlap and strongly stochastic dynamics. Abundance fluctuations are proportional to population size, so the dynamics of rare populations is slower.…
We study a spatially homogeneous model of a market where several agents or companies compete for a wealth resource. In analogy with ecological systems the simplest case of such models shows a kind of "competitive exclusion" principle.…
A microscopic model is developed, within the frame of the theory of quantitative traits, to study both numerically and analytically the combined effect of competition and assortativity on the sympatric speciation process, i.e. speciation in…
We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…