Predicting marine phytoplankton maximum growth rates from temperature: Improving on the Eppley curve using quantile regression

The Eppley curve describes an exponential function that defines the maximum attainable daily growth rate of marine phytoplankton as a function of temperature. The curve was originally fitted by eye as the upper envelope of a data set, and despite its wide use, the reliability of this function has not been statistically tested. Our analysis of the data using quantile regression indicates that while the curve appears to be a good estimate of the edge of the data, it may not be reliable because the data set is small (n = 162). We construct a contemporary, comprehensive data set (n = 1,501) and apply an objective approach, quantile regression, to estimate its upper edge (99th quantile). This analysis yields a new predictive equation, mu(max) = 0.81e(0.0631T), that describes the maximum specific growth rates (mu(max), d(-1)) of marine phytoplankton as a function of temperature (T, degrees C). The Liverpool phytoplankton database (LPD) curve is higher than the Eppley curve across all temperatures, and at temperatures below 19 degrees C, the Eppley curve falls below the lower 95% confidence interval of the LPD curve. However, the LPD Q(10) value (1.88) is identical to that of the Eppley curve and thus supports the use of models that incorporate this as an estimate of phytoplankton growth-rate response to temperature change. To assess the potential effect of the LPD curve on primary production, we embedded the LPD function into a one-dimensional numerical model of a temperate, pelagic ecosystem. This analysis suggests that models using the Eppley function will underestimate primary production by as much as 30%.