Related papers: Long-term analysis of phenotypically structured mo…
We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational…
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
In this paper we consider a microscopic model of a simple ecosystem. The basic ingredients of this model are individuals, and both the phenotypic and genotypic levels are taken in account. The model is based on a long range cellular…
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…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
Species sharing a habitat will co-evolve to make use of the available resources, as consumption is modulated by competition and negative feedback loops between consumers and resources. The dietary range of a given species determines the…
This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. This population is facing an {\it environmental gradient}: to survive at location $x$, an…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…
The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of its constituent individuals. Of particular importance is the interplay between reproduction and the dynamics of starvation and recovery. To…
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…