Quantitative Branching Geometry of the Vascular System of the Blue Crab, Callinectes sapidus (Arthropoda, Crustacea): A Test of Murray's Law in an Open Circulatory System.

Murray's law predicts that there will be a radius-cubed relationship between the parent and daughter vessels of a branching system of vessels that carry the flow of a fluid, a relationship that theoretically minimizes the costs of building, maintaining, and operating the system. The vascular system of the blue crab, Callinectes sapidus, was replicated by corrosion casting at physiological pressures; vessel diameters were measured off the casts and used to calculate a junction exponent for 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 distribution, 3.020, was not significantly different from the value of 3 predicted by Murray's law. The phylogenetic distance of arthropods from the animals previously studied in this context, sponges and mammals, is evidence for three independent evolutions of this branching relationship in biological fluid transport systems.