Interpretation of replica symmetry breaking in ecological community dynamics

Ascertain the dynamical implications of replica symmetry breaking in random generalized Lotka–Volterra models of ecological communities, specifically whether replica symmetry breaking corresponds to a finite cascade of timescales or to a hierarchical (fractal) sequence of ever-slower timescales in out‑of‑equilibrium dynamics, to clarify how glassy features manifest biologically.

Background

The notes map phases of random generalized Lotka–Volterra systems (with demographic noise) to glassy landscapes known from disordered systems. As interaction heterogeneity increases and noise decreases, the model transitions from a single fixed point (replica symmetric) to multiple equilibria (1‑RSB) and then to a marginal, fractal phase (full‑RSB), analogous to Gardner transitions in glasses.

While this theoretical structure is well-developed in physics, its concrete ecological meaning—especially how the hierarchical structure translates into dynamical timescales and observable behaviors in biological communities—remains to be clarified. Establishing the precise dynamical interpretation of RSB in ecology would link equilibrium landscape features to empirically measurable temporal phenomena such as aging, metastability, and hysteresis.