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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 present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the…
Phenotypic plasticity is a key factor in driving the evolution of species in the predator-prey interaction. The natural environment is replete with phenotypic plasticity, which is the source of inducible defences against predators,…
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…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
The coexistence of multiple phytoplankton species despite their reliance on similar resources is often explained with mean-field models assuming mixed populations. In reality, observations of phytoplankton indicate spatial aggregation at…
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…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
We study the competition and the evolution of nodes embedded in Euclidean restricted spaces. The population evolves by a branching process in which new nodes are generated when up to two new nodes are attached to the previous ones at each…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
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…
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
We present two approaches to study invasion in growth-fragmentation-death mod- els. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
Classical models of biological invasions assess species spread in homogeneous landscapes by assuming constant growth rates and random local movement. Mounting evidence suggests, however, that demographic stochasticity, environmental…
Horizontal transfer (HT) of heritable information or `traits' (carried by genetic elements, endosymbionts, or culture) is widespread among living organisms. Yet current ecological and evolutionary theory addressing HT is limited. We present…
We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is non-local, and show that spatial structures with interesting…
Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from…