Background/Question/Methods Colonies of spawning corals reproduce in mass-spawning events, in which polyps within each colony release sperm and eggs for fertilization in the water column, with fertilization occurring only between gametes from different colonies.  Participating colonies synchronize their gamete release to a window of a few hours once a year (for the species Acropora digitifera we study experimentally). This remarkable synchrony is essential for successful coral reproduction and thus, maintenance of the coral reef ecosystem that is currently under threat from local and global environmental effects such as pollution, global warming and ocean acidification.  The mechanisms determining this tight synchrony in reproduction are not well understood, although several influences have been hypothesized and studied including lunar phase, solar insolation, and influences of temperature and tides. Moreover, most corals are in a symbiotic relationship with photosynthetic algae (Symbiodinium spp.) that live within the host tissue.  Experiments supported by detailed bioenergetic modeling of the coral-algae symbiosis have shown that corals receive >90% of their energy needs from these symbionts. We develop a bioenergetic integrate-and-fire model in order to investigate whether annual insolation rhythms can entrain the gametogenetic cycles that produce mature gametes to the appropriate spawning season, since photosynthate is their primary source of energy.  We solve the integrate-and-fire bioenergetic model numerically using the Fokker-Planck equation and use analytical tools such as rotation number to study entrainment.

Results/Conclusions In the presence of short-term fluctuations in the energy input, our model shows that a feedback regulatory mechanism is required to achieve coherence of spawning times to within one lunar cycle, in order for subsequent cues such as lunar and diurnal light cycles to unambiguously determine the “correct” night of spawning.  Entrainment to the annual insolation cycle is by itself not sufficient to produce the observed coherence in spawning. The feedback mechanism can also provide robustness against population heterogeneity due to genetic and environmental effects. We also discuss how such bioenergetic, stochastic, integrate-and-fire models are also more generally applicable: for example to aquatic insect emergence, synchrony in cell division and masting in trees.