Related papers: Extremal events dictate population growth rate inf…
Solving population balance equations, we derive analytical steady-state cell size distributions for single-lineage experiments, such as the mother machine. These experiments are fundamentally different from batch cultures where populations…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
Bootstrap methods are increasingly accepted as one of the common approaches in constructing confidence intervals in bibliometric studies. Typical bootstrap methods assume that the statistical population is infinite. When the statistical…
We propose a dynamical mechanism for a scale dependent error growth rate, by the introduction of a class of hierarchical models. The coupling of time scales and length scales is motivated by atmospheric dynamics. This model class can be…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
Single-cell experiments revealed substantial variability in generation times, growth rates but also in birth and division sizes between genetically identical cells. Understanding how these fluctuations determine the fitness of the…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…
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…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
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…
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…
The growth of a population is often modeled as branching process where each individual at the end of its life is replaced by a certain number of offspring. An example of these branching models is the Bellman-Harris process, where the…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…