Size-Dependent Variations in Plant Growth Rates and the "¾ Power Rule"

Abstract

Size-dependent variations in morphological and physiological variables adduced to influence growth rate (e.g., cell surface area and volume, chlorophyll a concentration per cell) were determined by reevaluating published data from unicellular and multicellular plants and animals. With respect to cell volume, reduced major axis regression of the available data indicated that cell surface area decreases roughly as the 0.69-power, the concentration of Chl a decreased roughly as the 0.80-power, and cell mass decreased as the 0.77-power. Computer simulations indicated that the scaling exponent for cell surface area was the consequence of size-dependent variations in cell geometry and aspect ratio (i.e., cell length/width) rather than the result of geometric similitude among cells differing in size. The anisometric relation between cell mass and volume indicated that bulk cell density declines with increasing cell volume. Reanalyses of published data showed that growth rate and weight-specific growth rate scale as the ¾- and negative ¼-power, respectively, with respect to the body mass of unicellular and multicellular plants and animals. It is speculated that the anisometric relation between the growth rate and mass of unicellular plants is attributable to a “dilution” of metabolically active cellular constituents with increasing cell size in combination with the scaling of surface area with respect to volume (and therefore cell mass). It is further speculated that similar biological scalings may account for the ¾-power rule obtained for taxonomically and ecologically diverse multicellular plants and animals.