QUANTITATIVE BRANCHING GEOMETRY OF THE VASCULAR SYSTEM OF THE BLUE-CRAB, CALLINECTES-SAPIDUS (ARTHROPODA, CRUSTACEA) - A TEST OF MURRAYS LAW IN AN OPEN CIRCULATORY-SYSTEM

Murray's law predicts that there will be a radius-cubed relationship b etween the parent and daughter vessels of a branching system of vessel s that carry the now of a fluid, a relationship that theoretically min imizes the costs of building, maintaining, and operating the system. T he vascular system of the blue crab, Callinectes sapidus was replicate d by corrosion casting at physiological pressures; vessel diameters we re measured off the casts and used to calculate a junction exponent fo r each branch point. This study is the first quantitative description of the vascular branching geometry in an open circulatory system. The mean value derived from the arctan-transformed junction exponent distr ibution, 3.020, was not significantly different from the value of 3 pr edicted by Murray's law. The phylogenetic distance of arthropods from the animals previously studied in this context, sponges and mammals, i s evidence for three independent evolutions of this branching relation ship in biological fluid transport systems.