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 ...
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 in ...
www.ncbi.nlm.nih.gov