Inferring a Species Tree from Gene Trees in the Presence of HGT

A midsole system for a running shoe or foot prosthesis have a sole spring, a heel spring and/or a forefoot spring stores energy of foot impact and releases it during the running cycle. A preferred embodiment provides bending beam sole systems for shoes or foot prostheses comprising a bending beam heel spring, a bending beam forefoot spring, a two coupled spring sole system, and a three coupled spring sole system. The sole systems of this invention maximize stability, cushioning, and walking or running economy.