Bleaching as a result of coral optimization in a changing environment
Corals play an essential role in marine ecosystems by creating protective coastal structures and habitats for marine biodiversity. Their symbiotic relationship with various algal species, where corals supply nitrogen in exchange for carbon products, is vital for their survival. However, with some algal species being temperature sensitive, this vital symbiosis is increasingly threatened by global warming, causing significant symbiont losses, potentially leading to coral bleaching and fatal consequences. Here, we model the optimal regulation of algal populations by corals through nitrogen allocation. Two algal species compete for nitrogen: one is effective in carbon supply and rapid growth, and the other is resilient to temperature increases. Our testable analytical solution identifies the optimal total algal population as a function of the current temperature and symbiont composition. The model also determines the relative abundances of the two algal species based on current and historical temperatures. Our findings are consistent with numerous previous observations and experimental studies. The model clarifies how inter-species competition under varying temperature patterns shapes the composition and dynamics of algal species in coral symbiosis. It also clarifies that bleaching occurs when the relatively efficient algae fail to exchange enough carbon products at high temperatures.