Scaling of energy metabolism in unicellular organisms: a re-analysis

The database used by Hemmingsen (1960) to compute energy metabolism in unicellular organisms was reassembled and submitted to linear (log-log) analysis. As Hemmingsen noted, this data set includes marine zygotes, which are not unicellular organisms. If no temperature correction factors are applied to the data the best-fit regression line has a slope of 0.698 +/- 0.024. Application of the temperature correction factors assumed to have been used by Hemmingsen gave a slope of 0.756 +/- 0.021, identical to the value he reported. The correlation coefficient is 0.97. The mean scatter about the regression line exceeds 100%. A revised set of temperature correction factors gave a slope of 0.730 +/- 0.021, suggesting that the value of almost exactly three-quarters obtained by Hemmingsen was probably fortuitous. The slope of the best-fit regression line is very sensitive to the inclusion of bacteria and flagellates. When the data points for these organisms are omitted from the calculation the slope decreases to 0.645 +/- 0.045. When the data points for bacteria, flagellates and marine zygotes are omitted, the slope drops to 0.608 +/- 0.025. The correlation coefficient (0.97), compared to the best-fit line reported by Hemmingsen, is unaffected; the mean deviation about the regression line drops to 40% and the points are evenly distributed about the regression line. Because of the small number of species for which measurements have been made, the existing database relating energy metabolism to cell size is not representative of unicellular organisms generally. It is concluded that the case for a three-quarters power rule expressing energy metabolism as a function of size in unicellular organisms generally is not at all persuasive.