"Bleaching as a result of coral optimization in a changing environment"Cavailles, JeromeCorals provide important ecosystem services as protective coastal structures and as habitats for other coastal biodiversity. By establishing a symbiosis with algae ("zooxanthellae"), corals supply nitrogen in exchange for carbon products generated by photosynthesis. This vital relationship is under threat due to rising temperatures over the last few decades. The resulting loss of symbionts and bleaching has contributed to a dramatic decline in overall coral cover. The Adaptive Bleaching Hypothesis states that a temporary decrease in the algae population could be an opportunity for the coral to shuffle the actual maladaptive population of algae to a more thermally resilient species. We use here a simple and analytically solvable optimization model including the nitrogen quantity provided by the coral to the population of algae, while either a relatively efficient or a relatively temperature-resilient algal type competes for access to this nutritional source. We give an analytical solution of the proportional abundances of the two species of algae as a function of present and past temperatures. We also give an expression of the coral's optimal total population of algae, controlled by nutrient provision, while a decrease in the population density of algae defines bleaching severity. Results from our approach match several previous observations and experimental studies. Mainly, our model deduces the composition and dynamics of algal species in coral symbiosis - and their related features - as a direct consequence of inter-species competition at different temperatures. Also, bleaching and its associated features are elucidated by our model as a decline in resources provided to the current algae populations. This arises from the inability of the relatively efficient algal species to exchange enough carbon products when the temperature is elevated. |
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