Yes, but not necessarily in the way you intend to claim.
Studies also clearly show that dinos outperform competitors (diatoms) in some low nutrient situations. It's a complex dance between various competitors and various types of nutrients.
https://hero.epa.gov/reference/742154/
Competition of three bloom-forming marine phytoplankton (diatom Skeletonema costatum, and dinoflagellates Prorocentrum minimum and Alexandrium tamarense) was studied through a series of multispecies cultures with different nitrate (NaNO3) and phosphate (NaH2PO4) levels and excess silicate to interpret red tide algae succession.
S. costatum outgrew the other two dinoflagellates in nitrate and phosphate replete cultures with 10 mu mol/L Na2SiO3. Under nitrate limited (8.82 mu mol/L NaNO3) conditions, the growth of S. costatum was also dominant when phosphate concentrations were from 3.6 to 108 mu mol/L. Cell density of the two dinoflagellates only increased slightly, to less than 400 and 600 cells/mL, respectively. Cell density of S. costatum decreased with time before day 12, and then increased to 4000 cells/mL (1.5 mg/L dry biomass) at NaNO3 concentrations between 88.2 and 882 mu mol/L with limited phosphate (0.36 mu mol/L NaH2PO4) levels. In addition, P minimum grew well with a maximal cell density of 1690-2100 cells/mL (0.5-0.6 mg/L dry biomass). Although S. costatum initially grew fast, its cell density decreased quickly with time later in the growth phase and the two dinoflagellates were dominant under the nitrate-limited and high nitrate conditions with limited phosphate.
These results indicated that the diatom was a poor competitor compared to the two dinoflagellates under limited phosphate; however, it grew well under limited nitrate when growth of the dinoflagellates was near detection limits.
