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Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the…
A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition.…
Existing theories for the evolution of aging and death treat senescence as a side-effect of strong selection for fertility. These theories are well-developed mathematically, but fit poorly with emerging experimental data. The data suggest…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
A rapid decline in mortality and fertility has become major issues in many developed countries over the past few decades. A precise model for forecasting demographic movements is important for decision making in social welfare policies and…
We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the…
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 propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection…
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…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…
The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
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…
Low total fertility rates throughout the world have lead to concerns about economic growth, military security, international political power, environment impacts, and quality of life. Overall total fertility rates of today's societies are…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
In this kind of model, the main characteristic that determines population viability in the long term is the stochastic growth rate (SGR) denoted $\lambda_S$. When $\lambda_S$ is larger than one, the population grows exponentially with…
We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an…