The fermentation reaction only involves two steps.  Pyruvate is converted to acetaldehyde by Pdc and then acetaldehyde is converted to ethanol by alcohol dehydrogenase (Adh).  There is no significant increase in the number of Pdc genes in Crabtree-positive compared to Crabtree-negative species and no correlation between number of Pdc genes and efficiency of fermentation.  There are five Adh genes in S. cerevisiae.  Adh1 is the major enzyme responsible for catalyzing the fermentation step from acetaldehyde to ethanol.  Adh2 catalyzes the reverse reaction, consuming ethanol and converting it to acetaldehyde.  The ancestral, or original, Adh had a similar function as Adh1 and after a duplication in this gene, Adh2 evolved a lower K for ethanol.  Adh2 is believed to have increased yeast species tolerance for ethanol and allowed Crabtree-positive species to consume the ethanol they produced after depleting sugars.  However, Adh2 and consumption of ethanol is not essential for aerobic fermentation.  Sch. pombe and other Crabtree positive species do not have the ADH2'  gene and consumes ethanol very poorly.