Mayr then describes how a function shift works as follows:

Parade, Cusco, Peru, 27. 8. 1989
Parade, Cusco, Peru, 27. 8. 1989

During this kind of functional shift, a structure always goes through a phase in which it can simultaneously perform two functions, such as Daphnia’s antennas, which are both a sensory organ and a floating rudder. This functional duality is possible because the genotype is a highly complex system that always produces certain aspects of the phenotype that are not directly promoted by selection but are simply “by-products” of the genotype favoured by selection.

Such by-products are then available for the acquisition of new functions. They are the ones that allow the front limbs (with a flying membrane) of a tetrapod to act as wings, or the lungs of a fish, as a swim bladder. In the phenotype of every organism there are numerous “neutral aspects” that are “admitted” by natural selection i.e. not eliminated but which have also not been specifically favoured by it.

These kinds of components of the phenotype are available for the transfer of new functions. Functional shifts are also known in macromolecules and behavioural patterns, for example, when plumage cleaning becomes part of advertising behaviour in certain ducks.
(Mayr 2002, p. 491)

Mayr continues on the intensification of the function of an existing organ:

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