Related papers: Kinetic theory for structured populations: applica…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
A ubiquitous feature of living cells is their growth over time followed by division into daughter cells. How isogenic cell populations maintain size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental…
Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or…
We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by…
There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in…
In this paper, by resorting to classical methods of statistical mechanics, we build a kinetic model able to reproduce the observed statistical weight distribution of many diverse species. The kinetic description of the time variations of…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation functions and, at odds with modeling based on…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
In this paper we present a new modelling framework combining replicator dynamics (which is the standard model of frequency dependent selection) with the model of an age-structured population. The new framework allows for the modelling of…
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…
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…
Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were…
It is well known that the different cell-division models, such as Timer, Sizer, and Adder, can be distinguished based on the correlations between different single-cell-level quantities such as birth-size, division-time, division-size, and…
We study a size-structured population model in which individual cells grow at a rate determined by a fluctuating internal variable (e.g., gene expression levels). Many previous models of phenotypically heterogeneous populations can be…