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When can complex ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where species abundances keep fluctuating without going to extinction? We show that high-diversity spatially-extended systems, in…
A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak-Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into…
This paper examines the spatial agglomeration of workers and income in a continuous space-time framework. Local markets feature spatial spillovers and both exogenous and endogenous amenities. Workers relocate to maximise their instantaneous…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
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…
Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
Personality traits, such as boldness and shyness, play a significant role in shaping the survival strategies of animals. Industrial pollution has long posed serious threats to ecosystems and is typically distributed heterogeneously.…
The spatial structure of modern cities exhibits highly diverse patterns and keeps evolving under numerous constraints. Two key dimensions have recently achieved prominence in characterizing this diversity: heterogeneity and spreading.…
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments.…
We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that…
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.…
We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the…
In both natural and artificial studies, evolution is often seen as synonymous to natural selection. Individuals evolve under pressures set by environments that are either reset or do not carry over significant changes from previous…