Related papers: Pattern formation through genetic drift at expandi…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…
We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…
We study stripe formation in two-dimensional systems under directional quenching in a phase-diffusion approximation including non-adiabatic boundary effects. We find stripe formation through simple traveling waves for all angles relative to…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
A first-principles statistical theory is constructed for the evolution of two dimensional interfaces in Laplacian fields. The aim is to predict the pattern that the growth evolves into, whether it becomes fractal and if so the…
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
In genetic drift of small population, it is well known that even when the ratio of alleles is 0.5, specific genes are fixed in or disappear from the population. It seems the reason why inbreeding is avoided. On the other hand, this…
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…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
The birth/death process with mutation describes the evolution of a population, and displays rich dynamics including clustering and fluctuations. We discuss an analytical `field-theoretical' approach to the birth/death process, using a…
We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
In nature, most microbial populations have complex spatial structures that can affect their evolution. Evolutionary graph theory predicts that some spatial structures modelled by placing individuals on the nodes of a graph affect the…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
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…