The power coefficient k decreases along evolution in an allometric relationship between the oxygen consumption rate and the body mass of animals. This theoretical study investigated the role of the power coefficient k and its behavior along evolution. The animals were organized in three groups according to the values of the power coefficient k as follows: (I) from unicellular Prokaryotes to Eukaryotes; (II) from Mytilus and Annelida to Pisces; (III) from Reptilia to Mammals and Aves. At the beginning of each animal group (stage), the value of k was close to 0.9-1.0 and at the end of the stage it was close to 0.67-0.70. Exponential sharp increase of the power coefficient k was observed during the biological transition from Protozoa to simply organized Metazoa and in the transition from Poikylothermic to Homothermic organisms (e.g. from Pisces to Reptilia). Also, when using the periodogram regression analysis, a cyclic (periodic) pattern in this increase was observed (i.e. period T approximately 8-11 units, P<0.05). It was postulated that the power coefficient k, as with the coefficient a, might represent the increase of complexity of animal organization within each group.
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