Related papers: Allee dynamics: Growth, extinction and range expan…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…
We present a novel exactly solvable ordinary differential equation model for rate-induced tipping: a dynamic phenomenon of dynamical systems where a time-dependent parameter triggers the transition of stability of a system. Our model…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and…
We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the…
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…
Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…
In this paper, we focus on studying the passivity properties of different versions of replicator dynamics (RD). RD is an important class of evolutionary dynamics in evolutionary game theory. Evolutionary dynamics describe how the population…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
Reaction-diffusion analytical modeling of predator-prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. Few…
Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…
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 paper is concerned with a reaction--diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has…
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,…