Related papers: Population growth in discrete time: a renewal equa…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
In this study, we forecast the population of the Philippines using a discrete age-structured compartmental model. We estimated the future population structure of the Philippines if the government imposes an n-child policy on top of the…
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…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
Ecologists have long argued about the strength of density dependence and population regulation, respectively defined as the short-term and long-term rates of return to equilibrium. Here, I give three arguments for the intractability of…
Many life-history traits, like the age at maturity or adult longevity, are important determinants of the generation time. For instance, semelparous species whose adults reproduce once and die have shorter generation times than iteroparous…
This paper aims to develop practical applications of the model for the highly technical measure-valued populations developed by the authors in \cite{FanEtal20}. We consider the problem of estimation of parameters in the general age and…
We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
We develop a linear one-sex dynamical model of human population reproduction through marriage. In our model, a woman may marry and divorce multiple times; however, only women who are currently married are assumed to bear children. The…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate…
Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated…
To describe the dynamics of a size-structured population and its unstructured resource, we formulate bookkeeping equations in two different ways. The first, called the PDE formulation, is rather standard. It employs a first order partial…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
We study the population size time series of a Neotropical small mammal with the intent of detecting and modelling population regulation processes generated by density-dependent factors and their possible delayed effects. The application of…