Related papers: The two-clock problem in population dynamics
Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the…
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…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
Consider a branching Markov process with values in some general type space. Conditional on survival up to generation $N$, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by…
Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics…
We consider a population with two types of individuals, distinguished by the resources required for reproduction: type-$0$ (small) individuals need a fractional resource unit of size $\vartheta \in (0,1)$, while type-$1$ (large) individuals…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
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…
Genetic diversity is central to the process of evolution. Both natural selection and random genetic drift are influenced by the level of genetic diversity of a population; selection acts on diversity while drift samples from it. At a given…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…