Models of population dynamics and their applications in genetics

摘要

The aim of these lectures is to give a survey of mathematical models and methods of population dynamics. The main subject will be structured models which describe the distribution of population with respect to some parameters such as age, size, maturity or proliferative state of cells. Some models are general, e.g. age-structured model can be applied to human population as well as to a cell population but others will concern specific populations e.g. the population of erythrocytes. We concentrate on models connected with genetics: the Penna model and models describing telomere shortening, distribution of genes in a genome, stochastic gene expression and the cell-cycle.