Ecology and Physics
Authors: Giuggioli Luca 
Published: October 2023

Ecology and physics have borrowed ideas and techniques from each other for a long time. The archetypal example is the concept of Brownian motion, coined after the botanist Robert Brown who, in 1827, observed grains of pollen suspended in water undergoing jittering movement. It was this jittering and unpredictable movement that led Karl Pearson in 1905 to coin the name random walk which led to the first model of migration for biological organisms in his seminal contribution, A Mathematical Theory of Random Migration in 1906. The explanation of the observations by Robert Brown had to wait until Einstein’s formulation of diffusion in 1905, and its experimental validation by Perrin in 1909, which ultimately led to the acceptance in the physics community of the molecular nature of physical reality. Since then, the diffusion or random walk paradigm has been a workhorse of movement modeling in most, if not all, areas of ecology. While this example clearly shows that ecology and physics have had an illustrious entangled past, it is the second half of the 20th century that has witnessed an increasing number of collaborations between practitioners from the two fields. The interactions bridging the gaps between ecology and physics have been fruitful in multiple ways, both empirically and theoretically. While instrumentations for ecological applications have naturally profited from advances in experimental physics, e.g., biosensors, imaging technologies, and tracking devices, theoretical physics has provided modeling approaches and quantitative tools to help tackle both theoretical and applied problems in ecology. More generally, physics methodologies have instilled a way of thinking characterized by the search for spatial and temporal scales that are critical to the system, by the quest to differentiate between the deterministic and the random forces at play, by the need to relate mathematical descriptions in terms of microscopic, mesoscopic, or macroscopic perspectives, and by exploring the links between population level phenomena and the interaction events of the underlying individuals. Examples of such an approach include the study of the order/disorder phase transitions in collective animal behavior, the application of renormalization group ideas to landscape ecology, and the identification of scaling properties of transportation networks to analyze the characteristic quarter power relations in allometry. Underlying these and other examples is the belief that in living systems general or universal quantitative laws can be captured by a coarse-grained description of their most salient features. This very aspect is what has often made a physics approach to ecology controversial. While it is inevitable that simple theories have limitations, when they quantify and explain key characteristics of a process, they have much merit. They in fact provide the foundational ground from where to understand the full complexity of nature. Over the last forty years a vast literature of methodologies from theoretical physics have been applied to ecology. In some instances, they have provided a solid quantitative basis to an already developed body of literature, and in other instances they have opened up new perspectives and ideas. The sections below recount some of these ideas with citations made either to the original contributions or to review articles where research findings on a topic are synthetized and systematized, the focus being though on theoretical developments rather than empirical ones. The article also aims, predominantly, to identify distinct contributions from physics rather than the much broader applied mathematics community.