Related papers: Density-dependent feedback in age-structured popul…
This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations…
As a result of climate change, many populations have to modify their range to follow the suitable areas - their "climate envelope" - often risking extinction. During this migration process, they may face absolute boundaries to dispersal,…
In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of initial distributions for the population such that for small…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability…
This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic…
The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important…
We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying…
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…
We model sex-structured population dynamics to analyze pairwise competition between groups differing both genetically and culturally. A sex-ratio allele is expressed in the heterogametic sex only, so that assumptions of Fisher's analysis do…
For the Ramsey model of economic growth, which describes the optimal allocation of consumption and saving over time, we assume the population dynamics to follow the Allee effect. The so-called Allee threshold separates two regimes from each…
This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative…
Environmental fluctuations can create population-depleted areas and even extinct areas for the population. This effect is more severe in the presence of the Allee effect (decreasing growth rate at low population densities). Dispersal inside…
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…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
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…
Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes…