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Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
We present a general theoretical model for the spatio-temporal dynamics of animal contests. Inspired by interactions between physical particles, the model is formulated in terms of effective interaction potentials, which map typical…
The concept of hierarchy in complex systems is tightly linked to co-evolutionary processes. We propose here to explore it in the case of the co-evolution between transportation networks and territories. More precisely, we extend a…
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…
Range migrations in response to climate change, invasive species and the emergence of novel ecosystems highlight the importance of temporal turnover in community composition as a fundamental part of global change in the Anthropocene.…
In recent years, we are seeing the formulation and use of elaborate and complex models in ecological studies. The questions related to the efficient, systematic and error-proof exploration of parameter spaces are of great importance to…
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…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
This paper proposes a systems theory approach to the modeling of onset and evolution of criminality in a territory, which aims at capturing the complexity features of social systems. Complexity is related to the fact that individuals have…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
The aim of this manuscript is to contain the arguments and define the theoretical objects for building a general framework to model population dynamics from the ground up, relying mainly on the probabilistic landscapes defining the dynamics…
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…
Collective behaviours often need to be expressed through numerical features, e.g., for classification or imitation learning. This problem is often addressed by proposing an ad-hoc feature set for a particular swarm behaviour context,…
With the influx of complex and detailed tracking data gathered from electronic tracking devices, the analysis of animal movement data has recently emerged as a cottage industry amongst biostatisticians. New approaches of ever greater…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might…
Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
This paper presents a unified mathematical theory of swarms where the dynamics of social behaviors interacts with the mechanical dynamics of self-propelled particles. The term behavioral swarms is introduced to characterize the specific…