Related papers: On discretely structured growth models and their m…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…
Two types of population models are well known -- the continuous and the discrete types.The two have very different characteristics and methods of solutions and analysis.In this note, we point out that an iterative technique when applied to…
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…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…
A simple spatial computer simulation model was recently introduced to study the evolution of the linguistic diversity. The model considers processes of selective geographic colonization, linguistic anomalous diffusion and mutation. In the…
In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of…
In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…
We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
The growth of world population, limitation of resources, economic problems and environmental issues force engineers to develop increasingly efficient solutions for logistic systems. Pure optimization for efficiency, however, has often led…
I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical…