Towards a statistical physics of eco-evolutionary systems

Abstract

In this thesis, we employ the principles of statistical physics to investigate the ecology and evolution of bacterial communities. By studying the collective behavior of large ensembles of molecules or components, statistical physics uncovers new phenomena and transitions between different phases . This approach, originally applied to physical systems, has been extended to complex systems like biology and social systems, leading to the emergence of the discipline of complex systems. Ecosystems, exemplifying complex systems, consist of numerous interacting species that generate emergent properties such as diversity, stability, and functionality. Given the continuous evolution of species, constructing a statistical physics framework for ecological systems is a challenging task. To tackle this, the thesis focuses on bacterial populations as a relatively accessible system. Recent technological advancements allow for easy sampling, analysis, and sequencing of bacterial communities, making them ideal for studying emergent phenomena. The thesis is divided into three parts, corresponding to ecology, evolution and non-equilibrium physics. In Chapter 1, we provide an overview of the motivations and content of this thesis, along with a general introduction to complex systems and the ecology and evolution of bacteria. Part I centers on microbial macroecology, with Chapter 2 specifically investigating interactions within bacterial ecosystems. Through extensive data analysis, we discover a universal macroecological law that relates pairwise correlations between species to their phylogenetic distance. Utilizing a statistical physics approach, we develop a stochastic model that reproduces this empirical pattern, attributing it to coupled environmental fluctuations, also known as environmental filtering. Part II focuses on bacterial eco-evolution, particularly the formulation of a new theoretical framework and its application to antibiotic tolerance evolution. In Chapter 3, we establish a general framework for trait distributions using statistical physics tools, investigating various evolutionary phenomena such as evolutionary branching. In Chapter 4, we employ this framework to study the evolution of antibiotic tolerance in bacteria through lag-time adaptation. By presenting a stochastic individual-based model that replicates experimental results, we derive analytical predictions using our framework. Finally, in Part III, we delve into the concept of irreversibility in non-equilibrium statistical physics. Chapter 5 examines the geometric properties of non-equilibrium currents in stochastic thermodynamics, extracting theoretical insights. This geometric information is then utilized to comprehend the relationship between irreversibility, dissipation, and current symmetry breaking in non-equilibrium stationary states. In Chapter 6, we analyze the irreversible properties of evolution using the general framework introduced in Chapter 3. Evolution is found to be constantly out of equilibrium due to the simultaneous presence of selection and mutations, and we explore its irreversibility in various examples, including evolutionary branching. Ultimately, in Chapter 7, we present general conclusions drawn from our findings and suggest potential avenues for future research. Also, in appendix E we include a resume and the conclusions of the thesis in English.