Irrelevent question here...
But what is the limiting condition? Is it the availabilty of nitrogen compound? I mean given unlimited resources a hetrotrophic bacteria like E Coli will double in just 20 minutes (this despite the fact the DNA takes an hour to replicate; the daughter cells have already started to produce the grandaughter DNA before their own DNA is completed replicating)
If this the case... I would expect a fish in cycle to grow the bacteria much slower because of the necessity to starve them of energy in the form of nitrogen.
These numbers so far as I recall came from the scientific studies a few years ago that looked into the bacteria responsible for ammonia and nitrite oxidation in water. I will post links to the two primary papers below, this work was led by Dr. Tim Hovanec. Each species of bacteria can have different reproducing times, as I understand it [subject to correction], and yes, temperature and pH can affect the reproduction too. The waste control bacteria which causes a bacterial bloom can reproduce in 20 minutes for example. You might find my summary article on bacteria of interest, it is on Mike's blog here:
Paul C. Burrell, Carol M. Phalen, and Timothy A. Hovanec, “Identification of Bacteria Responsible for Ammonia Oxidation in Freshwater Aquaria,”
Applied and Environmental Microbiology, December 2001, pp. 5791-5800.
Culture enrichments and culture-independent molecular methods were employed to identify and confirm the presence of novel ammonia-oxidizing bacteria (AOB) in nitrifying freshwater aquaria. Reactors were seeded with biomass from freshwater nitrifying systems ...
www.ncbi.nlm.nih.gov
Hovanec, T. A., L. T. Taylor, A. Blakis and E. F. DeLong, “Nitrospira- Like Bacteria Associated with Nitrite Oxidation in Freshwater Aquaria,”
Applied and Environmental Microbiology, Vol. 64, No. 1, pp. 258-264.
Oxidation of nitrite to nitrate in aquaria is typically attributed to bacteria belonging to the genus Nitrobacter which are members of the α subdivision of the class Proteobacteria. In order to identify bacteria responsible for nitrite oxidation ...
www.ncbi.nlm.nih.gov