On the Origin of Taxa

The fundamental structure of the Biosphere how taxa resiliently survive millions of years—can be based on principles and laws of physics, particularly through analogy with relationships of classical mechanics and the Pareto alpha index matching a fractal dimension. Like physical conservation laws, these controlling elements survive intact during system change. Arguments are advanced to support the hypothesis of a quadratic origin of taxa based on symmetry breaking and mirror parity, which is extensible from bryophytes to all taxonomic groups. A minimally monophyletic group is one ancestral species with four monothetic immediate descendant species. This relationship is optimized by the Pareto ratio as a pattern constant, which is expressed as an inverse power law at ln(5)/ln(4) or fractal dimension 1.161. Actual species per genus curves are well fitted with the formula 16/x1.161, and actual species per genus numbers are modeled by integration of the same curve truncated at 7 species. New species are generated by symmetry breaking of the immediate ancestron (the set of new traits of the single ancestral species shared monothetically by all immediate descendant species). Fractal modeling leads to a quadratic model of evolution, which, because of self-similarity, is applicable to all taxonomic ranks. Models show that control of evolution at least analogically follow first and second differentials of the fitted curve.