I'm interested in what the fastest growing microalgae are under optimal conditions for photoautotrophic growth (energy from photosynthesis only). Fastest can be interpreted as either shortest doubling time, or maximum biomass yield per day per unit area.
Many of the algae investigated for biofuels are fast-growing, for example Nannochloropsis and Ankistrodesmus. There are many publications that give yields in pond culture or in outdoor photobioreactor, for example Nannochloropsis at 20g/m^2/day (dry mass). However it is not as common to see yields for lab photobioreactor (axenic, possibly with continuous illumination, and all other conditions optimized for fast growth). I'm mainly interested in what family of algae would be evolved for fast growth, and where they may be found in nature.
EDIT As one of the answers pointed out, algae can grow heterotrophically as well and that may not be a fair comparison. I changed the question to be about autotrophic growth (from photosynthesis) only.