The maximum growth rate hypothesis is correct for eukaryotic photosynthetic organisms, but not cyanobacteria

The (maximum) growth rate (µmax) hypothesis predicts that cellular and tissue phosphorus (P) concentrations should increase with increasing growth rate, and RNA should also increase as most of the P is required to make ribosomes.
Using published data, we show that though there is a strong positive relationship between the µmax of all photosynthetic organisms and their P content (% dry weight), leading to a relatively constant P productivity, the relationship with RNA content is more complex.
In eukaryotes there is a strong positive relationship between µmax and RNA content expressed as % dry weight, and RNA constitutes a relatively constant 25% of total P. In prokaryotes the rRNA operon copy number is the important determinant of the amount of RNA present in the cell. The amount of phospholipid expressed as % dry weight increases with increasing µmax in microalgae. The relative proportions of each of the five major P-containing constituents is remarkably constant, except that the proportion of RNA is greater and phospholipids smaller in prokaryotic than eukaryotic photosynthetic organisms. The effect of temperature differences between studies was minor.
The evidence for and against P-containing constituents other than RNA being involved with ribosome synthesis and functioning is discussed.