Related papers: On competition through growth reduction
In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals…
We consider models of growing multi-level systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational…
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…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
We introduce a model in which city populations grow at rates proportional to the area of their "sphere of influence", where the influence of a city depends on its population (to power \alpha) and distance from city (to power -\beta) and…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e. the increase of the number of new elementary business units and…
In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
We follow up on a companion work that considered growth rates of populations growing at different sites, with different randomly varying growth rates at each site, in the limit as migration between sites goes to 0. We extend this work here…
We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to China's one-child policy. By allowing any number of births, but with an…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large…