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The process of `Evolutionary Diffusion', i.e. reproduction with local mutation but without selection in a biological population, resembles standard Diffusion in many ways. However, Evolutionary Diffusion allows the formation of local peaks…
The Moran process is a random process that models the spread of genetic mutations through graphs. If the graph is connected, the process eventually reaches "fixation", where every vertex is a mutant, or "extinction", where no vertex is a…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
We investigate the process of fixation of advantageous mutations in an asexual population. We assume that the effect of each beneficial mutation is exponentially distributed with mean value $\omega_{med}=1/\beta$. The model also considers…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two…
The continuous interest in the social network area contributes to the fast development of this field. The new possibilities of obtaining and storing data facilitate deeper analysis of the entire network, extracted social groups and single…
The continuous interest in the social network area contributes to the fast development of this field. The new possibilities of obtaining and storing data facilitate deeper analysis of the entire social network, extracted social groups and…
We propose a model for evolutionary game dynamics with three strategies $A$, $B$ and $C$ in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a…
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,…
Evolutionary dynamics have been traditionally studied in the context of homogeneous populations, mainly described my the Moran process. Recently, this approach has been generalized in \cite{LHN} by arranging individuals on the nodes of a…
Complex spatial structure, with partially isolated subpopulations, and environment heterogeneity, such as gradients in nutrients, oxygen, and drugs, both shape the evolution of natural populations. We investigate the impact of environment…
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes…
We propose a continuous model for evolutionary rate variation across sites and over the tree and derive exact transition probabilities under this model. Changes in rate are modelled using the CIR process, a diffusion widely used in…
We are often interested in clustering objects that evolve over time and identifying solutions to the clustering problem for every time step. Evolutionary clustering provides insight into cluster evolution and temporal changes in cluster…
We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…
A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100 fold have been observed to spontaneously…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…
We consider the modified Moran process on graphs to study the spread of genetic and cultural mutations on structured populations. An initial mutant arises either spontaneously (aka \emph{uniform initialization}), or during reproduction (aka…