Related papers: Power laws for family sizes in a duplication model
The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
Given $n$ samples of a regular discrete distribution $\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type) which implies a typical power law when $\pi$ is heavy-tailed. Constructing a (random)…
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment…
In many situations, the gene expression signature is a unique marker of the biological state. We study the modification of the gene expression distribution function when the biological state of a system experiences a change. This change may…
We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
The Yule model and the coalescent model are two neutral stochastic models for generating trees in phylogenetics and population genetics, respectively. Although these models are quite different, they lead to identical distributions…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
A fundamental issue discussed in evolutionary biology is the transition from unicellular to multicellular organisms. Here we develop non-robust models provided in [1] and attempt to get robust models investigated how differentiation of…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the…
Isogenic Escherichia coli growing exponentially in a constant environment display large variation in growth-rates, division-sizes and generation-times. It is unclear how these seemingly random cell cycles can be reconciled with the precise…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation.…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population…