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Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…
The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness $m\in(0,\infty)$ invade a population of…
In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or "driver," mutations from "passenger" mutations that have no selective effect. Toward this end, we prove results concerning the…
The Moran process is a classic stochastic process that models invasion dynamics on graphs. A single "mutant" (e.g., a new opinion, strain, social trait etc.) invades a population of residents spread over the nodes of a graph. The mutant…
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…
In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover it is regarded as a…
Heterogeneity within tumour cell populations is associated with an increase in malignancy and appears to play an important role during cancer metastasis. Using in silico experiments, we study the interplay between collective behaviours and…
Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful…
The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…
The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
In species reproducing both sexually and asexually clones are often more common in recently established populations. Earlier studies have suggested that this pattern arises from natural selection favouring asexual recruitment in young…
Interesting theoretical problems of target search or threshold crossing, formally known as {\it first passage}, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Research into somatic mutations in cancer cell DNA and their role in tumour growth and progression between successive stages is crucial for improving our understanding of cancer evolution. Mathematical and computer modelling can provide…
This paper proposes a stochastic block model with dynamics where the population grows using preferential attachment. Nodes with higher weighted degree are more likely to recruit new nodes, and nodes always recruit nodes from their own…
We study the evolution of a population in a two-locus genotype space, in which the negative effects of two single mutations are overcompensated in a high fitness double mutant. We discuss how the interplay of finite population size, $N$,…