A theoretical interpretation of length–biomass allometry of predominantly bidimensional seaweeds

Abstract

Experimental studies on bidimensional seaweeds revealed a scaling exponent of 0.472 for their length–biomass allometry. This was significantly higher than the value 0.25, which was proposed earlier as universal for all primary producers, based on the data for unicellular microalgae and vascular plants. Later, an exponent of 0.5 was theoretically derived, which agreed, to some extent, with experimental findings. Here, it is shown that there exists a power–law relation between the two perpendicular length parameters along the directions of growth of a bidimensional organism. The length–biomass allometric parameters can be expressed in terms of this power index. A relation between the allometric scaling exponent and allometric constant, involving the mass per unit area, has been obtained analytically. A method is proposed to determine the power index experimentally. Some mathematical expressions, relating mass, length and other parameters, have been formulated and these would be useful for experimental purposes in allometric studies. Analyzing images from an experimental study, a lot of parameters, regarding flat seaweeds, have been determined by analytical and numerical techniques.