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It is impossible to breed a blue rose or a cat with a bulldog shape. This is because breeding is limited by gene variations in the population.

What do breeders call this effect?

UPDATE

I guess this term is from medieval and/or handicraft breeders, not modern and hi-tech.

UPDATE 2

I am speaking not about principal impossibility but just about observable or tangible barrier. We can be sure that it is possible to turn dog into cat in billion years, but it is much harder than turn German Shepherd to Yorkshire Terrier, which is possible for hundreds of years.

So, there are are two main types of changes, ones take hundreds of years, others take hundreds of millions of years. Former require genetic recombination while latter require genetic mutation.

This barrier was felt by breeders in practice and caused some versions of anti-evolution beliefs.

I need to know how this barrier is named.

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2 Answers

There must be a point where a desired trait cannot be obtained by selective breeding or by evolution at all! Why can't there be viruses the size of houses or elephants as small as a flea?

Those may seem like absurd examples, but that's just to point out that not all traits can be obtained in less than infinite number of adaptive steps. Jerry Fodor pointed this out (among other things) in his essay "Why Pigs Don't Have Wings".

Exactly what you can get and what you can't get is open to effort. For instance I suppose you could turn a pig into a pigeon if you had a few million generations to do it - something similar to the evolutionary time back to the time they diverged. That would be difficult, but you could basically run evolution for another billion years to get small hollow boned pigs with bats wings on their forearms. you probably wouldn't recognize it as a pig, but then again youd be dead of old age several times over too.

Could you breed a human where bullets bounce off and they can fly? not so sure of that.

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I'm honestly not sure if one exists. They simply lack the gene/allele - the only specific term I can think of when it comes to lacking a gene is referencing Knockout variations where a researcher purposefully removes a gene from a subject in order to observe the effect.

However, "Knockout Mice/etc." imply intent on behalf of the researcher, not a result of breeding or natural lack of an allele. Perhaps "Genetically Incapable" would be a phrase meaning the same thing - but I'm not aware of any 'official' shorthand for 'Cannot because it's not in their genes.'

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