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RE: How to Know if it's Pure
"Pure" is often badly misused.
It means "both the shown/dominant and hidden/recessive are" but the use most people put it it is more like "I think it is pure, but I cannot prove it and it might not be". All of the examples you give are of this later case.
The "True Recessive" is, by definition, "Pure". For some traits, such as Eye Shape and Pupil Size, the True Recessive is fixed. Small Pupil Size is, by it's very definition "pure" and no further proof is needed. Fur and Eye Color, though, for example, don't have a fixed True Recessive. They have what we think if the CURRENT True Recessive; but we can never be sure, and we know it changes occasionally.
Proving "pure" is a logical process where you show the hidden/recessive for a box/cat cannot be anything other than the shown/dominant.
The common mistake it believing that simply because the parents, grand-parents, or great-grandparents, or ANY number of generations back you care to look all show the same dominant trait value, the offspring must be "pure". This is not the case! It is "probably pure" but you must always remember, this is not proof .. it's a probabilistic statement .. the odds are good, it is "pure" but it might not be.
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