Ecology Ecology and Physics
Luca Giuggioli
  • LAST REVIEWED: 26 October 2023
  • LAST MODIFIED: 26 October 2023
  • DOI: 10.1093/obo/9780199830060-0249


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.

Stochastic Approaches to Ecological Problems

Since the 1970s, statistical physics approaches have started to enter the ecological arena bringing a shift in modeling techniques, in particular with the explicit representation of space and the introduction of stochastic models. Tilman and Kareiva 1997 is an example of the debates that emerged at the time on when it is relevant to account for space. The importance of stochasticity in describing spatial ecological problems can be found in Okubo and Levin 2001. There the authors look at some of the applications of the theory of diffusive processes to problems in animal and plant ecology as well as nutrient and chemical transport. Kenkre and Giuggioli 2021 is a more recent compendium of statistical physics techniques applied to spatial epidemic spread and animal ecology that also includes non-diffusive dynamics. Another work on theoretical ecology that contains techniques both from physics and applied mathematics is the edited book May and McLean 2007.

  • Kenkre, V. M., and Luca Giuggioli. 2021. Theory of the spread of epidemics and movement ecology of animals: An interdisciplinary approach using methodologies of physics and mathematics. Cambridge, UK: Cambridge Univ. Press.

    DOI: 10.1017/9781108882279

    A compendium of theoretical physics techniques to represent the movement and interaction dynamics of animals. Applications include hantavirus transmission events and spatial disease spread in an animal population, the formation dynamics of scent-marked animal territories, and the spatio-temporal dynamics of bacteria population under environmental constraints.

  • May, Robert, and Angela R. McLean. eds. 2007. Theoretical ecology: Principles and applications. Oxford: Oxford Univ. Press.

    Gives an account of the basic principles that govern the structure, function, and dynamics in space and time of populations and communities of plants and animals. Applications of these ideas and approaches to practical issues in epidemiology, food supplies, climate change, and conservation biology are also presented.

  • Okubo, Akira, and Simon A. Levin. 2001. Diffusion and ecological problems: Modern perspectives. New York: Springer.

    DOI: 10.1007/978-1-4757-4978-6

    An updated version of the original book by Akira Okubo, after his passing, edited by Simon Levin and with contributions expanded by experts in the respective areas. The underlying theme is diffusive movement across various animal taxa, plants, as well as chemicals and nutrients, when tethered to a location or when subject to a drift, and both for a single individual and for groups.

  • Tilman, David, and Peter Kareiva. 1997. Spatial ecology: The role of space in population dynamics and interspecific interactions. Princeton, NJ: Princeton Univ. Press.

    An analysis of the role of space on a series of topical subjects in ecological systems: diversity, invasions, coexistence and stability. The importance of spatial versus non-spatial models is the main thread of this edited book.

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