Related papers: A singular limit for an age structured mutation pr…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
Although species longevity is subject to a diverse range of selective forces, the mortality curves of a wide variety of organisms are rather similar. We argue that aging and its universal characteristics may have evolved by means of a…
The complexity of gene regulatory networks in multicellular organisms makes interpretable low-dimensional models highly desirable. An attractive geometric picture, attributed to Waddington, visualizes the differentiation of a cell into…
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We have simulated the evolution of age structured populations whose individuals represented by their diploid genomes were distributed on a square lattice. The environmental conditions on the whole territory changed simultaneously in the…
Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur,…
Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…
A superprocess limit for an interacting birth-death particle system modelling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…