Mutant Number Statistics for Spatially Structured Microbial Populations

Abstract

The evolution of microbial populations is very interesting to humans for various reasons such as the use of microbes to produce new medicines and to manufacture edible products, gut microbes play role in human health, and formulation and testing of evolutionary theories. Many population genetics models of evolution assume homogeneous environments for the populations. These models miss various features of natural populations and models with heterogeneous environments need to be developed. Recently, microbial populations growing in environments that have spatial structures have been widely studied. These growth processes are very interesting from the perspective of statistical physics. In this thesis, we are interested in understanding the role of the spatial structure of the surrounding medium in the evolution of a microbial population. We construct a stochastic model for studying the growth of a population of wild-type microbes undergoing mutations. We model the active layer of a linearly expanding microbial population as a finite square lattice. The microbes assume positions on the lattice points. We provide dynamical rules that capture the reproductive, mutational, and spatial dynamics of the microbes within the active layer. For studying the number statistics of the mutants in the population, we calculate clone size distribution for such a microbial colony. The clone size distribution has been studied experimentally as well as theoretically and some scaling laws and power laws have been obtained that describe the distribution. We derive analytically the compact form for the clone size distribution and verify it against the simulations of the model. We have been able to reproduce the results already known for such populations. Our model holds the potential to give new results and new understandings about the clone size distribution for linearly expanding populations.