Related papers: Range Expansion with Mutation and Selection: Dynam…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
Non-uniform rates of morphological evolution and evolutionary increases in organismal complexity, captured in metaphors like "adaptive zones", "punctuated equilibrium" and "blunderbuss patterns", require more elaborate explanations than a…
In the magnetic Eden model (MEM), particles have a spin and grow in contact with a thermal bath. Although Ising-like interactions affect the growth dynamics, deposited spins are frozen and not allowed to flip. This review article focuses on…
In this paper we propose a Moran model that describes the population dynamics of two types: While the first type has a selective advantage during reproduction, the second type can avoid replacement during reproduction with some positive…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…
The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front…
The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…
We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…
This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…
We have developed a mathematical model that captures stress-induced mutagenesis, a fundamental aspect of pathogenic and neoplastic evolutionary dynamics, on the fitness landscape with multiple relevant genetic traits as a high-dimensional…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
Failing to account for ecological processes such as dispersal and connectivity when modeling distributions can lead to biased inference about environmental drivers and reduced predictive performance. Spatial dynamic occupancy models are…
Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell…
A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a…
This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators…
Land use expansion is linked to major sustainability concerns including climate change, food security and biodiversity loss. This expansion is largely concentrated in so-called frontiers, defined here as places experiencing marked…
Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that…
Competition between random genetic drift and natural selection plays a central role in evolution: Whereas non-beneficial mutations often prevail in small populations by chance, mutations that sweep through large populations typically confer…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…