Symbioses: A mathematical theory of 'living together'

Symbioses between microorganisms and their macroscopic hosts are universal and dynamic. These relationships influence every aspect of our lives --from who we are, to our health and nutrition, to the functioning of ecosystems and the well-being of our planet. Yet we still lack a general theoretical framework for understanding the principles governing this dynamic, interconnected, and resource-recycling view of life and its processes. A relational view of life is not new. Many knowledge traditions have long emphasized the interdependence of humans, other organisms, and their environment. Classic biology, however, has often approached organisms as relatively distinct entities interacting within an external environment, with a strong emphasis on competitive interactions. Symbiosis challenges this picture. The environment is not simply a pool of resources from which organisms take; organisms also modify their environments and, through their interactions with partners, become part of the conditions shaping one another's evolution. Yet we still lack a theory that can guide our intuition and provide null expectations for these symbiotic dynamics.

Symbioses raise fundamental questions for ecological and evolutionary theory. What maintains diversity within symbioses? Do symbiotic systems exhibit coexistence mechanisms that differ from those of free-living communities, when the host itself becomes a dynamic resource shaped by its microbial partners? How do competition, facilitation, and antagonism combine to determine the outcome of these relationships? In particular, microbial interactions are often non-additive and context-dependent: the effect of one symbiont may depend on the presence, abundance, or phenotype of other community members, as well as on the host and its environment. How, then, does host productivity change with microbial community composition? And how do these interactions alter processes such as community assembly and biological invasion, opening up new ecological scenarios?

Mathematics has the power to strengthen a symbiotic narrative of life, formalize feedbacks, and build intuition around the processes and mechanisms that are otherwise difficult to untangle. My research aims to lay the foundations for a "theory of living together", which could transform not only ecology and medicine, but also our broader understanding of the origin of biological organization itself. Beyond scientific progress, a mathematical theory of symbioses invites a different philosophy of life: one in which living systems are defined not by isolated individuals competing for success, but by networks of interactions, where cooperation, context, and relationships are as important as individual traits in shaping the fate of organisms.

Selected publications

An eco-evolutionary consumer-resource theory of host-microbe symbioses
M. M. Martignoni, S. Bordenstein, C. Karakoç, R. C. Tyson, S. P. Brown, J. Garnier · EcoEvoRxiv · 2026

Theory of host-microbe symbioses: Challenges and opportunities
P. Ferretti*, M. M. Martignoni*, L. McManus*, A. Liaghat, B. Stevens, T. Sakal, K. Dahlin, L. Souza, Z. Carton, C. Silveira, S. Bordenstein, J. Roughgarden · Cell Host & Microbe, 33(7), 1052–1056 · 2025
Shared co-first authorship

Parasitism within mutualist guilds explains the maintenance of diversity in multi-species mutualism
M. M. Martignoni, M. M. Hart, R. C. Tyson · Theoretical Ecology, 1–13 · 2020