Integrate-and-fire models of insolation-driven entrainment of broadcast spawning in corals

Abstract

The circa-annual cycle of gametogenesis produces mature gametes at the spawning “season” for successful mass spawning of broadcast corals. We develop a bioenergetic integrate-and-fire model that reveals how annual insolation rhythms can entrain the gametogenetic cycles in tropical hermatypic corals to the appropriate spawning season, since photosynthate is their primary source of energy. In the presence of short-term fluctuations in the energy input, a feedback regulatory mechanism is likely required to achieve coherence of spawning times to within one lunar cycle, in order for subsequent signals such as lunar and diurnal light cycles to unambiguously determine the “correct” night of spawning. The feedback mechanism can also provide robustness against population heterogeneity that may arise due to genetic and environmental effects. 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.