Related papers: On population resilience to external perturbations
This paper investigates the dynamics and optimal harvesting of age-structured populations governed by McKendrick--von Foerster equations, contrasting two distinct harvesting mechanisms: rate-control and effort-control. For the rate-control…
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and,…
This work, Part II, together with its companion Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past states.…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness…
We establish upper bounds for the expected excess risk of models trained by proper iterative algorithms which approximate the local minima. Unlike the results built upon the strong globally strongly convexity or global growth conditions…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
Recently we have introduced a simplified model of ecosystem assembly (Capitan et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
We design a stochastic individual-based model structured in energy, for single species consuming an external resource, where populations are characterized by a typical energy at birth in $\mathbb{R}^{*}_{+}$. The resource is maintained at a…
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…
Climate change impacts population distributions, forcing some species to migrate poleward if they are to survive and keep up with the suitable habitat that is shifting with the temperature isoclines. Previous studies have analyzed whether…
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…
We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. We show that the interplay between turbulent dynamics and population growth and saturation leads to…