Processing The Images Of A Typical Species Of Bi-dimensional Primary Producer

Priyadarshi Majumdar; Sandip Dey

doi:10.36948/ijfmr.2025.v07i02.38519

Processing The Images Of A Typical Species Of Bi-dimensional Primary Producer

Author(s)	Priyadarshi Majumdar, Sandip Dey
Country	India
Abstract	Experimental studies on bi-dimensional 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 two perpendicular length parameters along the directions of growth of a bi-dimensional organism. The length-biomass allometric parameters may 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. A method is proposed to determine the power index experimentally. Some mathematical expressions, relating mass, length and other parameters, have been formulated for a typical seaweed (namely Fucus vesiculosus) 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. Assuming the seaweed species follows ontogenetic growth mechanism we solve such dynamical equation and express mass as a function of time. Numerical data on mass for that typical species has been fitted on the ontogenetic solution to make the time dependence of mass precise, the temporal behavior of sample area has also been proposed. Studying the images of three samples of Fucus vesiculosus we have predicted their ages from the model itself. Modifying some important earlier works on transport mechanism through linear networks for living organisms, those uses volume filling fractal (self-similar) like network the concept of surface filling fractals has been introduced. That the kind of sea-weeds under examination obeys Von Bertalanffy model which differs from the universal inter-specific trend defined by micro algae and vascular plants, has been clearly established.
Keywords	flat organism, power law dependence, ontogenetic growth model, allometric scaling, data analysis;
Field	Mathematics > Statistics
Published In	Volume 7, Issue 2, March-April 2025
Published On	2025-03-18
DOI	https://doi.org/10.36948/ijfmr.2025.v07i02.38519
Short DOI	https://doi.org/g895j2

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Processing The Images Of A Typical Species Of Bi-dimensional Primary Producer

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