Popular food said to be from a limited gene pool (6)

I believe the answer is:

inbred

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'from a limited gene pool' is the definition.
I can't judge whether this defines the answer.

'popular food said to be' is the wordplay.
'popular' becomes 'in'.
'food' becomes 'b' (B is an example).
'said to be' becomes 'red' (I can't justify this - if you can you should believe this answer much more).
'in'+'b'+'red'='INBRED'

Can you help me to learn more?

(Other definitions for inbred that I've seen before include "Inherent" , "Was deep in thought" , "Born of closely related people" , "from a restricted gene pool?" , "Present by nature" .)

I've seen this clue in The Guardian.

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