Stochastic dynamics of biological populations in changing environments

Abstract

The focus of this thesis is the study of biological populations subject to external changing environments exploring a number of theoretical, numerical, and experimental approaches. We study different classes of environments, considering cases whose evolution over time is deterministic or stochastic. The first class of environments we consider vary deterministically. Here we focus on the study of microbial resistance in bacterial populations subject to therapies of one or two antibiotics. The environment specifies the drug concentration administered to the population, so it is determined by the type of dosing schedules. We investigate how subpopulations with higher mutation rates drive the emergence of multi-drug resistance. We approach this problem analysing experimental data (obtained by Dr. Danna Gifford), comparing their observations against stochastic simulations of a multi-type branching model we design. In separate work related to the previous one, we explore the delaying effect of competition on the emergence of single and double resistance through theoretical predictions of a similar stochastic model. We calculate the probability of having at least one resistant cell for dosing schedules with constant and time-dependent drug concentrations using a theoretical approach based on branching processes. The second class of environments we consider vary stochastically. The first system we study is a Moran-type model, describing a population subject to a switching environment that determines the type of reproduction, namely sexual or asexual. The population can exhibit several number of `mating types' (analog to male/female sexes, but not restricted to two) that depends on the rate of reproduction, as well as the mutation rate (i.e., inclusion of new types). We investigate the stationary distribution of the number of mating types for different switching regimes. We show that for slow switching regimes the distribution can become bimodal, while for fast switching the system behaves as if there was one single effective environment. Our approach exploits properties of branching processes and integer partitions in number theory. Lastly, we study and design an algorithm based on the so-called tau-leaping algorithm, focusing on systems with fast fluctuating environments. Our algorithm treats the input rates for the tau-leaping as (clipped) Gaussian random variables with first and second moments constructed from the environmental process. Several biological examples are explored, such as genetic circuits, birth-death processes, and genetic switches. We consider cases with discrete and continuous environmental spaces. The algorithm can produce results for macroscopic observables in fluctuating regimes beyond the adiabatic limit (i.e., infinitely fast switching) that are in good agreement with measurements from other simulation methods, but with a significantly reduced computing time.

Date of Award	1 Aug 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Tobias Galla (Supervisor) & Danna Gifford (Supervisor)