Related papers: A branching model for intergenerational telomere l…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
The GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume $L$-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural…
The lengths of the telomere regions of chromosomes in a population of cells are modelled using a chemical master equation formalism, from which the evolution of the average number of cells of each telomere length is extracted. In…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
Do biological cells sense time by the number of their divisions, a process that ends at senescence? We consider the question "can the cell's perception of time be expressed through the length of the shortest telomere?" The answer is that…
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and, when they reach a critical length, the cell will enter permanent cell cycle arrest - a state known…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and…
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies)…