sorry, but you're fundamentally wrong and right there. i will try to illustrate with the next small example.
this is fictive, and only to illustrate the general theory behind the thoughts, it doesn't represent the correct genotype of the cattle.
i will use Angus(P1) and Hereford(P2) as a silly example. both are homozigous for colour(angus is B, herford b) and for hornes (Angus is h, hereford is H)
100% of AngusXhereford is HhBb, therefore black and horned = F1
F1XF1 Black, horned = 9 = 57% red, polled = 1 = 6% Black, polled = 3 = 18.5% Red, Horned = 3 = 18.5% (please allow for rounding off of the decimals) this is also what is understood to be an F2 by most relevant litterature.
if i do a backcross with angus: F1 (BbHh)X BBhh i get the following:
Black, polled = 2 = 50% Black, horned = 2 = 50%
If i do a backcross with the hereford (bbHH), we get:
Red, horned = 2 = 50% Black, Horned = 2 = 50%
hence my statement that it is used to generate or retain recessive qualities from a cross with dominancy over that trait, without loosing all of the heterosis (relative to P1xP2) generated from crossbreeding
Back Cross is absolutely not equal to F1XF1.
i said backcrossing was equal to inbreeding because of the fact that to get a real (ie complete) backcross you must use a genotypically equal parent, ie the orriginal parent.
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