Multiscale Structure in Eco-Evolutionary Dynamics

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, “more is different,” and I address this from several perspectives. Spatial host–consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory. The idea of natural selection “acting at multiple levels” has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

💡 Research Summary

This dissertation develops a rigorous information‑theoretic framework for quantifying multiscale structure in complex biological systems and applies it to a wide range of eco‑evolutionary models. The core of the theory defines a system as a set of components A together with an information function H that assigns to each subset U⊂A the minimal number of bits required to describe U. H must satisfy monotonicity (information never decreases when adding components) and submodularity (the whole contains no more information than the sum of its parts minus their overlap). From these axioms the author derives a suite of structural indices—complexity profiles, redundancy, synergy, and multiscale information—that capture how information is distributed across scales.

Geometric toy examples (three‑component systems, minimal incidence geometry, the Fano plane) illustrate how higher‑order interactions generate new information that cannot be reduced to pairwise relationships. These examples build intuition for later biological applications.

The thesis then integrates the formalism with three major strands of evolutionary theory:

1. Spatial host‑consumer dynamics – Lattice‑based simulations of transmissibility, patch size, and network topology (regular grids, random graphs, scale‑free networks) reveal that the evolution of transmissibility hinges on a critical balance between local clustering and global spread. Percolation theory predicts the critical transmissibility, while the emergence of large patches demonstrates genuine multiscale organization that mean‑field approximations miss.

2. Evolutionary game theory with multiplayer interactions – By extending beyond two‑player games to multiplayer games with nonlinear payoffs, the author shows that cooperation can be stabilized at the group level rather than the pair level. This reframes the Price equation and multilevel selection (MLS‑A, MLS‑B) in terms of conditional probability updates, highlighting how ecological stochasticity reshapes replicator dynamics.

3. Stochastic adaptive dynamics – The adaptive dynamics of traits are cast as a Fokker‑Planck equation. When multiple mutations arise simultaneously and strategies are discrete, the classic Fisher Fundamental Theorem no longer holds; instead, new conserved quantities emerge that depend on the multiscale interaction structure.

A dedicated chapter dissects the literature on multilevel selection, clarifying that MLS‑A and MLS‑B embody different assumptions about interaction range and selection pressure, which explains much of the existing confusion.

Finally, the dissertation proposes speculative mathematical extensions. It suggests using category theory to formalize moment‑closure approximations, linking Doi‑operator formalism with multiscale information. It outlines how gauge‑theoretic concepts could describe evolutionary flows, and it sketches biodiversity indices derived from multiplayer game structures.

Overall, the work demonstrates that “more is different” can be made precise: multiscale information measures reveal hidden layers of organization that shape evolutionary trajectories. By unifying information theory, statistical physics, and evolutionary biology, the thesis provides both a conceptual resolution of multilevel selection debates and a toolbox for future quantitative studies of complex eco‑evolutionary systems.