Adding fish today, which type and how many should I add first?

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The formula I have always used is one fish inch (excluding tail) per four liters or one gallon of water. I have been criticized for this method repeatedly on this site.
 
When you asked how many fish, I understood you to mean the actual number of fish which is why I was struggling to explain. Now you've said 1 inch per gallon, I see what you meant.
That is actually a good starting point for newcomers to the hobby, but it does need to be explained that the one inch is adult size not the size of the fish in the shop tank. While an experienced fish keeper does not necessarily need to stick with that rule, it can stop newcomers overstocking their tank in their enthusiasm. Most members do discuss their plans for the tank so they can be warned if they are planning too many fish - and if their planned stocking is inappropriate, such as 2 of this fish, 2 of that for shoaling fish.
 
Full stocking is more than just bio-load. The species chosen may have numerical requirements. Since FW fish can come from water with almost no hardness and a pH of 4.0 or lower to very hard water with a pH in the 9.0 range, no rule is simple. Then there are considertions for diet. Vegertatian fish make more poop than canrivores. Most active fish create more ammonia than their more sedentary tankmates. As for how to know what to keep as a newbie, you need to work with somebody or bodies who have decent experience. And of course there is the consideration of what fish might eat tankmattes etc.

You then can create a stocking plan which, hopefully, will have taken into account species and numbers of fish that would make the tank fully stocked and that will live together in a reasonably peaceful way. As a rule, it is always better to understock a tank the to over stock it.

One key to a full stocking is that the fish all come from the same source. That way they will likely have all been exposed to any possible problem rather than from multiple sources where there may be different potential nasties.

If you can not do a full stock all at onece, you have two options. One os to reduce the amount of ammonia used to cycle which will mean it takes less time to complete. You will add fish more slowly in such a tank. The other option is to stock as many as possible even though it will be some number fewer than full stocking. But them you should plan tio have Q. tank and to add more fish based on what you have in the tank at the time. You should never add new fish if you have ammonia, nitrite or high nitrate.

Next.

No. Part of the bacteria do not go dormant. It is an all or none situation. If ammonia drops in half, ultimately the colony will do likewise. But when either ammonia, oxygen or inorganic carbon become unavailable, they all go dormant.

Every day some number of individuals die a natural death. However, at the same time some are dividing and this keeps the total size of the colony reasonably stable. It is when ammonia changes up or down by more than a little that the reproductive rate changes to accommodate this. When there is less ammonia the reproductive rate slows so the number of new bacteria are way fewer than those dying. When the balance between the ammonia available and the size of the colony are in basic balance, then, in oversimplified terms, one dies and one divides and the total colony is the same.

I have tried to simplify the explanation but it is more complex than I have laid out. However, for most situations regarding the nitrifying bacteria in our tanks it is pretty much on the money.

For those who are nuts about the science involved:

Joke Geets, Nico Boon, Willy Verstraete, Strategies of aerobic ammonia-oxidizing bacteria for coping with nutrient and oxygen fluctuations, FEMS Microbiology Ecology, Volume 58, Issue 1, October 2006, Pages 1–13, https://doi.org/10.1111/j.1574-6941.2006.00170.x

Bollmann A, Schmidt I, Saunders AM, Nicolaisen MH. Influence of starvation on potential ammonia-oxidizing activity and amoA mRNA levels of Nitrosospira briensis. Appl Environ Microbiol. 2005;71(3):1276-1282. doi:10.1128/AEM.71.3.1276-1282.2005
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1065156/

Salem S, Moussa MS, van Loosdrecht MC. Determination of the decay rate of nitrifying bacteria. Biotechnology and Bioengineering. 2006;94:252-62.
https://onlinelibrary.wiley.com/doi/10.1002/bit.20822 (Only the Abstract is available)

 
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