Coral bleaching is a cellular breakdown of the coral–algae mutualism, not just fading color. Each coral polyp hosts zooxanthellae (photosynthetic dinoflagellates) at density N. Above each polyp's thermal optimum Topt,i, the algae's photosystem II can no longer safely dissipate absorbed light energy, and reactive oxygen species (ROS) accumulate:
dROS/dt = k₁·I·max(0, T − T_opt,i)² − k₂·ROS
dN/dt = −k₃·max(0, ROS − ROS_thresh)·N + k₄·N·(1 − N/N₀)
The first term is light-driven photoinhibitory ROS production — it scales with irradiance I and with the square of how far seawater temperature T sits above each polyp's own optimum, so a small overshoot is tolerated but a large one runs away quickly. The second term is antioxidant clearance (SOD/catalase pathways). Once ROS crosses a threshold, the coral host actively expels or digests its damaged symbionts (the −k₃ term) to limit self-damage; below threshold, symbionts slowly regrow toward the carrying capacity N₀ (logistic recovery).
- Genetic variance: every polyp is seeded with its own Topt,i (~26.5–28.5 °C), so a heatwave bleaches the colony patchily rather than all at once — matching real reef observations of mosaic bleaching.
- Sea temperature is the primary driver; even 1–2 °C above the long-term summer maximum, sustained for days, is enough to trigger mass bleaching (the basis of NOAA's Degree Heating Week metric).
- Light irradiance multiplies the damage term — the same heatwave bleaches shallow, sun-exposed coral faster than shaded coral, which is why bleaching is often worse on reef flats than in deeper water.
- Cool to 26 °C tests recovery: if enough symbionts survived, N regrows via the logistic term and color returns; if density fell too low for too long, the polyp's energy budget collapses and recovery stalls (modeled here as slower regrowth once N is near zero).