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Full Idea
An objection to the prototype view concerns compositionality. A complex concept often has emergent properties, as when it seems that 'pet fish' encodes for brightly coloured, which has no basis in the prototypes for 'pet' or 'fish'.
Clarification
'Compositionality' is assembling the whole from components
Gist of Idea
Complex concepts have emergent properties not in the ingredient prototypes
Source
E Margolis/S Laurence (Concepts [2009], 2.2)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8
A Reaction
I would take 'pet fish' to work like a database query. 'Fish' has a very vague prototype, and then 'pet fish' narrows the search to fish which are appropriate to be pets. We might say that the prototype is refined, or the Mk 2 prototype appears.