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.