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The objective of this article is to create a framework to study asymptotic equilibria in human populations with a special focus on immigration. We present a new model, based on Resource Dependent Branching Processes, which is now broad…
Plant-frugivore interactions play a central role for plant persistence and spatial distribution by promoting the long-range dispersal of seeds by frugivores. However, plant-frugivore interactions are increasingly being threatened by…
In this work, the influence of inertial effects on the formation and evolution of vegetation patterns on sloped arid terrains is investigated from the onset of instability to far-from-equilibrium. Analyses are carried out in a hyperbolic…
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady state formulation amounts to recasting the nonlinear problem as…
Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other…
Aquaculture has been the fastest growing food production sector globally due to its potential to improve food security, stimulate economic growth, and reduce poverty. Its rapid development has been linked to sustainability challenges, many…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
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 FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
Does bearing children shorten a woman's life expectancy? Several demographic studies, historic and current, have found no such effect. But the Caerphilly cohort study is far the most prominent and frequently-cited, and it answers in the…
Conservation measures are implemented to support biodiversity in areas that are degraded or under anthropogenic pressure. Over the past decade, numerous projects aimed at rehabilitating a fish nursery function in ports, through the…
Understanding how an extinction event affects ecosystem is fundamental to biodiversity conservation. For this reason, food web response to species loss has been investigated in several ways in the last years. Several studies focused on…
We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $\mathbb {Z}^d$. In each of the four models studied, an individual in a local population can reproduce, die or…
We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…
The evolutionary balance between innate and learned behaviors is highly intricate, and different organisms have found different solutions to this problem. We hypothesize that the emergence and exact form of learning behaviors is naturally…