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The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We discuss the differences and analogies of gravitational clustering in finite and infinite systems. The process of collective, or violent, relaxation leading to the formation of quasi-stationary states is one of the distinguished features…
We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into…
Clustering methods based on deep neural networks have proven promising for clustering real-world data because of their high representational power. In this paper, we propose a systematic taxonomy of clustering methods that utilize deep…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
A major aim of evolutionary biology is to explain the respective roles of adaptive versus non-adaptive changes in the evolution of complexity. While selection is certainly responsible for the spread and maintenance of complex phenotypes,…
We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the…
Computer modelling for evolutionary systems consists in: 1) to store in the memory the individual features of each member of a large population; and 2) to update the whole system repeatedly, as time goes by, according to some prescribed…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…