Related papers: A compact containment result for nonlinear histori…

We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…

We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…

Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…

Consider a supercritical birth and death process where the children acquire mutations. We study the mutation rates along the ancestral lineages in a sample of size $n$ from the population at time $T$. The mutation rate is time-inhomogenous…

A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…

In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…

We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…

Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…

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 model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…

Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…

We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…

We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations…

We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…

We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given…

We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…

In this research, we present a generalized quasispecies model in which population growth is governed by an arbitrary nonlinear function incorporating time delays. We begin by demonstrating that, under the constant population constraint, the…

Models of conformity and anti-conformity have typically focused on cultural traits with nominal (unordered) variants, such as baby names, strategies (cooperate/defect), or the presence/absence of an innovation. There have been fewer studies…

We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same…

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…