A Hamiltonian framework for predicting ecological functioning capacity of coral reefs under climate change.

Abstract

Coral reef condition is commonly assessed using structural indicators such as coral cover, although the persistence of reef ecosystems depends on the interactions among multiple ecological processes. Here, we develop a Hamiltonian framework for representing reef functioning as a coupled dynamical system of three functional capacities: production and reef building, consumer-mediated energy transfer, and recycling and reef turnover. These components integrate the major ecosystem processes that collectively sustain energy and matter cycling within coral reef ecosystems and are represented as interacting functional state variables within a tri-trophic model. We formulate an ecological Hamiltonian to describe their coupled dynamics and incorporate sea-surface temperature (SST) as an external climate forcing that modifies the functional capacities of the system over time. Numerical simulations show that the autonomous system generates persistent cycling among the three functional components. Under climate forcing, increasing thermal stress progressively alters these dynamics: low and moderate warming maintain relatively broad functional trajectories, whereas stronger warming progressively dampens functional oscillations and constrains the range of functional states explored by the system. This contraction indicates a reduction in the dynamic range of energy and matter transfer among functional components under sustained thermal stress. The framework therefore provides a theoretical basis for evaluating reef condition beyond structural metrics such as coral cover and for exploring how ecosystem functioning may change under future climate conditions. Changes in the amplitude and range of functional trajectories may also provide candidate indicators of declining functional capacity, although this requires validation against empirical observations.