Related papers: A multitype Galton-Watson model for rejuvenating c…
We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying Galton-Watson process to describe the evolution of…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
Consider a population evolving as a discrete-time supercritical multi-type Galton--Watson process. Suppose we run the process for $T$ generations, then sample $k$ individuals uniformly at generation $T$ and trace their genealogy backwards…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
1 Sharp prediction of extinction times is needed in biodiversity monitoring and conservation management. 2 The Galton-Watson process is a classical stochastic model for describing population dynamics. Its evolution is like the matrix…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is…
We describe a percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Tissues are considered as structures made of regular healthy,…
The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales -- from the molecular to cellular to whole…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…
The Galton-Watson process is a Markov chain modeling the population size of independently reproducing particles giving birth to $k$ offspring with probability $p_k$, $k\ge0$. In this paper we consider {\it defective} Galton-Watson processes…
What is aging? Mechanistic answers to this question remain elusive despite decades of research. Here, we propose a mathematical model of cellular aging based on a model gene interaction network. Our network model is made of only non-aging…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…
In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of different types. We assume that this function is superadditive,…