For numerous shelly invertebrates, Cope’s rule is shown in this paper to merely describe the particular case where volume increase is strictly coupled with diameter or length. Allometries, which are frequently observed in the evolution of the shells’ geometry, mean that their size, volume and surface can vary independently. The consequences of this can be summarized as follows : 1) volume increase not coupled with an increase of diameter or length of the organisms generates increasing involution and/or lateral width in the shell of cephalopods, foraminifera and radiolarians ; 2) an increase of the biomineralizing surface, not coupled with volume increase, generates increasing apparent complexity in the sutures and growth lines in ammonites, and an increase in the complexity and number of chambers in foraminifera.

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