When discussing the subject with the "minimal filtration crowd", I've often heard it stated that the size of nitrifying bacteria colonies in an aquarium will only equal the amount of ammonia being produced so there is no need for major amounts of filtration. There is at least some truth to this. However, I don't think it is as much of a mathematical absolute as people may otherwise think. In other words, if "x" amount of ammonia is produced, "y" populations of nitrifying bacteria will not be a constant absolute.
We know with all scientific certainty that there are many variables that determine nitrifying bacteria colony size, they are discussed (in detail) in Autotrophic Nitrifying Bacteria and Their Practical Application in a Freshwater Aquarium; temperature, pH, and O2 levels foremost amongst them. Each of these factors, in combination with the amount of ammonia being produced (bioload) will determine the nitrifying bacteria colony sizes. But I am of the opinion that there are additional variables. Let's take a real world, actual experience, and then consider their impacts to this discussion.
Aquarium "A" - 55 gallons, stocked with a single adult Oscar, filtered by a pair of cartridge type HOB filters. The Aquarium is dosed with the recommended amount of antibacterial medication. Prior to dosage, tank is registering zero ammonia, zero nitrites, with nitrate creep occurring, so it is a fully cycled established aquarium. Within three days of dosing with antibacterial medications, the tank is registering for potentially lethal levels of ammonia. The antibacterial medications have negatively impacted the nitrifying bacteria to a point where the colony size is no longer able to maintain zero ammonia and nitrite.
Aquarium "B" - 100 gallons, stocked with an adult Oscar, adult male convict, and three adult Silver Dollars. Filtered by a Penguin 350, Eheim 2217, Eheim 2215, Marineland C-360, Marineland HOT 250 (filled with Matrix), and several air driven sponge filters. The aquarium is dosed with the same medication as Aquarium "A" and subsequently dosed with a second antibacterial medication, followed by a third round of antibacterial medications. No ammonia or nitrite spike was experienced over a three week run of antibacterial medications.
Aquarium "A" does not survive a three day run of medication without reaching toxic ammonia levels. Aquarium "B" runs three weeks of the same medication without experiencing ammonia or nitrite spikes.
So we have two tanks, very similar bioloads, with vastly different filtration. The aquarium with minimal biological filtration experiences ammonia spikes soon after dosing with an antibacterial medication. The aquarium with "over the top" amounts of filtration (especially biological filtration), never experiences an ammonia or nitrite spike, even with seven times the dosage duration.
If the concept of "the bacteria colony size will only equal the amount of ammonia being produced" is a mathematical absolute, how could this be? One of two things occurred for Aquarium "B" to withstand a medicinal dosage that Aquarium "A" could not. Either the nitrifying bacteria in Aquarium "B" is stronger or there are more nitrifying bacteria in Aquarium "B" than in Aquarium "A".
I propose that bacteria colony size is not a mathematical absolute. It is a variable and one of the variables is the biofiltration capacity of a tank. There are more bacteria in Aquarium "B" than in Aquarium "A".
Of course, you are asking, how can this be? The amount of ammonia being produced will only support "so much" bacteria. This is true, but this is a very different concept than declaring a mathematical absolute. "So much" leaves open possibilities, other variables.
I'll ask you to consider this concept. In a minimally filtered aquarium, the primary limitation to autotrophic nitrifying bacterial population is a lack of surface area in the filter media, not the amount of ammonia being produced. The amount of ammonia being produced is capable of supporting larger colonies of bacteria but the bacteria do not have a sufficient room, especially considering they are sharing the limited surface area with Heterotrophic Bacteria, which are very much able to out-compete the autotrophs for limited resources on filter media certain to be rich in heterotrophic bacteria food sources (organics). Obviously, in a tank with limited filtration, as was Aquarium "A", the populations of autotrophic nitrifying bacteria are able to grow large enough to deal, under normal circumstances, with the amount of ammonia being produced. What it is not able to do is grow large enough to survive when circumstances are less than optimal, such as when you medicate, forget to turn a filter on, suffer a power outage, have a filter break down, or any number of emergencies that are common in the hobby.
So, how does a sufficiently filtered tank survive these emergencies?
The first obvious observation is that with vast amounts of biofiltration capacity, such as exists with Aquarium "B", surface area is no longer a limiting factor. Less obvious is my proposal that with extended surface area, larger bacterial populations will exist. Even with the same (or similar) amount of ammonia being produced between Aquarium "A" and Aquarium "B", the autotrophic nitrifying bacteria population in Tank "B" will be larger. It is true, that without ammonia, nitrifying bacteria will not exist. What is not considered in the "mathematical absolute" concept is the amount of ammonia consumed by each individual bacterium. In an inadequately filtered tank (as I consider Aquarium "A"), the bacteria that exists consumes more ammonia per individual bacterium than occurs in Aquarium "B". In a minimally (or marginally) filtered tank, it is almost a certainty that some level of ammonia is passing through the filter on each pass. With HOB type filters, you have two limitations that apply to this discussion. First is surface area. Filter cartridges are about worthless as biofilters due to their limited bed depth and even AquaClear filters, which try to expand upon bed depth via their design, are far inferior to even a small canister filter. Second is contact time with the filter media. Optimal contact time for biofiltration is at a flow rate of around 250gph. Most HOBs we use are far in excess of this. Combine the high flow rates with a limited bed depth and you have a very ineffective biofilter, which suggests with near certainty that ammonia is passing through the filter (hence the need for 10x turnover). So there is enough ammonia to support larger concentrations of bacteria, just not enough surface area for those bacteria to expand their colony and the flow rate is too high (with an insufficient media bed depth) for the ammonia to remain in contact with the filter media long enough to be removed on the initial pass.
In a well filtered aquarium, ammonia that passes bacteria in one section of a filter (or one filter) is utilized by bacteria in another, with each bacterium utilizing less ammonia (as a whole) than an individual bacterium in the inadequately filtered tank. This allows nitrifying bacteria populations in a well filtered aquarium to grow larger than in a minimally filtered tank.
If we take the real world examples of Aquarium “A” and Aquarium “B”, and assume that each dosage of the medication is killing off some measure of the nitrifying bacteria, we have to come to the conclusion that the bacterial populations of Aquarium “B” are not just marginally larger than Aquarium “A”, they are substantially larger. With each filter containing significant populations of nitrifying bacteria. This can only occur if the mathematical absolute concept includes “available surface area” as a larger component of the equation than the minimal filtration crowd may be willing to accept.
I can provide additional real world experiences. My 55 gallon Kissing Gourami tank was filtered by a Penguin 350, Marineland 350 (filled with Matrix), Fluval 404, and assorted sponge filters. The Fluval does what these Fluvals do, it died. Despite the fact that the Fluval would be considered the primary filter (due to flow rate and media capacity), I never experienced an ammonia or nitrite spike. Since it takes at least 24 hours for autotrophic nitrifying bacteria to divide, you would think with the removal of such a large colony of bacteria (a result of the death of the Fluval) an ammonia or nitrite spike would have occurred within that first 12-24 hours, until the bacteria populations could expand in size to deal with the ammonia previously utilized by bacteria in the Fluval. It did not. A possibility, and what I propose, is that a combination of the other filters actually possessed enough bacteria to manage the entirety of the ammonia being produced. These bacteria simply began utilizing more ammonia, because more ammonia was available to them.
In summary, what I propose is that while nitrifying bacteria populations will only grow based upon the amount of ammonia being produced, in a tank with substantial biofiltration capacity, the colony sizes will be significantly larger than in a minimally filtered tank. In a minimally filtered tank, the primary limitation of nitrifying colony size is available surface area, not the amount of ammonia. Secondly, the amount of ammonia utilized by an individual bacterium is another variable. A smaller colony of bacteria is able to consume the same amount of ammonia as a significantly larger colony of bacteria and the larger colony of bacteria is able to sustain itself on the same amount of ammonia as a smaller colony.