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We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary…

Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring…

Phenotypes of individuals in a population of organisms are not fixed. Phenotypic fluctuations, which describe temporal variation of the phenotype of an individual or individual-to-individual variation across a population, are present in…

Experimental studies of microbial communities routinely reveal that they have multiple stable states. While each of these states is generally resilient, certain perturbations such as antibiotics, probiotics and diet shifts, result in…

This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…

Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has…

The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev.…

The proliferation of diverse, high-leverage trading instruments in modern financial markets presents a complex, "noisy" environment, leading to a critical question: which trading strategies are evolutionarily viable? To investigate this, we…

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The dynamics of this selection is studied using a simple linear model. It has similarities to…

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider…

Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that…

Microbial ecosystems exhibit a surprising amount of functionally relevant diversity at all levels of taxonomic resolution, presenting a significant challenge for most modeling frameworks. A long-standing hope of theoretical ecology is that…

Hubbell's neutral theory of biodiversity has successfully explained the observed composition of many ecological communities but it relies on strict demographic equivalence among species and provides no room for evolutionary processes like…

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…

Understanding the stability of complex communities is a central focus in ecology, many important theoretical advancements have been made to identify drivers of ecological stability. However, previous results often rely on the…

Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well documented to much more tightly than traditionally assumed,…

We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…

Apparent biodiversity on earth exists only if we compare different species separated from their environments. Meanwhile coexisting species have to be identical in terms of energetic interactions. Consider the biosphere as a network of…

A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…