The F in F1, F2 or so on… stands for Filial
In a scientific experiment the first generation born within the experiment is F1, second generation born within the experiment is F2, etc, etc…
In the experiment’s description it will be stated if the F2 offspring are born from F1 parents, or are the second set of offspring of the Base parents…
The we borrowed this labeling system and made up the term F0 to describe our “Base”, being wild caught. We consistently refer to F2 as offspring of F1... Not the second brood of F0 parents…
The F# system is not designed to track crossing F# generations (such as F1 x F3)… in a scientific experiment if such generations were crossed this would be a secondary experiment and these parameters would be redefined and the cross would be considered F1 of the second experiment.
Since we are a vast hobby with no governing board, naturally different people will use this short hand differently and others will bastardize it all together.
My solution to this! Give up the shorthand… If it is Wild Caught, say it is Wild Caught… if it is the offspring of Wild Caught, say it is the offspring of Wild Caught… If it takes too much typing to describe how far from wild caught it is, accept it is simply an aquarium bred fish…This “labeling” system also allows for descriptions such as “one wild parent and one parent one generation out of the wild” and similar…
Unfortunately fish are rarely advertised based on inbreeding or lack there of. So be it with fish, being inbred once isn’t that big of a deal (though it does make a difference)… but I feel excessive inbreeding happens far too often and can be a big deal…
I also feel that not using the strongest fish of a brood (mimicking “survival of the fittest”

reducing the quality of offspring drastically. We also rarely see any type of labeling suggesting this type of selective breeding…