Shape correction function

The shape correction function is a ratio of the surface area of a growing organism and that of an isomorph as function of the volume. The shape of the isomorph is taken to be equal to that of the organism for a given reference volume, so for that particular volume the surface areas are also equal and the shape correction function has value one.

For volume $$V$$, reference volume $$V_d$$, the shape correction function $$M(V)$$ equals for
 * V0-morphs: $$M(V) = (V/V_d)^{-2/3}$$
 * V1-morphs: $$M(V) = (V/V_d)^{1/3}$$
 * isomorphs: $$M(V) = (V/V_d)^0 = 1$$
 * static mixtures between a V0- and a V1-morph: $$M(V) = w(V/V_d)^{-2/3} + (1-w)(V/V_d)^{1/3}$$ for $$0<w<1$$

The shape correction function is used in the Dynamic Energy Budget theory to convert the equations for isomorphs to that for organisms that change in shape during growth. The conversion is necessary for food (substrate) acquisition and mobilization of reserve for use by metabolism.