English: The natural log of species richness (SR) displays a non-linear relationship as a function of contemporary surface thermal energy, which is derived from mean annual sea surface temperature (SST, in Kelvin) and Boltzmann’s constant (k). The dashed lines illustrate the global linear relationship predicted from the slopes expected from the MTE. The solid curves illustrate the 3rd degree polynomial fit that best explains the global variations of log(SR) as a function of mean annual available thermal energy. The colored isopleths illustrate the density of ocean grid cells, based on two dimensional kernel density estimates, and were used to highlight the parts of the gradients driving the observed non-linear relationships. The vertical dotted lines indicate the range of SST prevailing in the tropical band (i.e., latitudes < 30°) for the end-of-century period, according to the ensemble of earth system models forced by a RCP8.5 greenhouse gas emission scenario.