Related papers: Fast flowing populations are not well mixed
For estimating area-specific parameters (quantities) in a finite population, a mixed model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values although we often…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…
We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
In this letter, we deal with evolutionary game theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic,…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
Cooperation is fundamental to the functioning of biological and social systems in both human and animal populations, with the structure of interactions playing a crucial role. Previous studies have used networks to describe interactions and…
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…
The idea that there are any large-scale trends in the evolution of biological organisms is highly controversial. It is commonly believed, for example, that there is a large-scale trend in evolution towards increasing complexity, but…
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…
In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…
We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…
We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case,…
Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…