From Dr. Clayton Cone of Lallemand:
Yeast need a trace amount of oxygen in an anaerobic fermentation such as meadmaking, winemaking and brewing to produce lipids in the cell wall. With out O2 the cell cannot metabolize the squalene to the next step which is a lipid. The lipids make the cell wall elastic and fluid. This allows the mother cell to produce babies, buds, in the early part of the fermentation and keeps the cell wall fluid as the alcohol level increases. With out lipids the cell wall becomes leathery and prevents bud from being formed at the beginning of the fermentation and slows down the sugar from transporting into the cell and prevents the alcohol from transporting out of the cell near the end of the fermentation. The alcohol level builds up inside the cell and becomes toxic then deadly. Lallemand packs the maximum amount of lipids into the cell wall that is possible during the aerobic production of the yeast at the factory. When you inoculate this yeast into your must, the yeast can double about three time before it runs out of lipids and the growth will stop. There is about 5% lipids in the dry yeast.
In a very general view:
At each doubling it will split the lipids with out making more lipids (no O2). The first split leaves 2.5% for each daughter cell. The second split leaves 1.25% for each daughter cell. The next split leaves 0.63%. This is the low level that stops yeast multiplication. Unless you add O2 the reproduction will stop. When you produce 3-5% alcohol beverage this is no problem. It is when you produce higher alcohol beverage or inoculate at a lower rate, that you need to add O2 to produce more yeast and for alcohol tolerance near the end of fermentation. You definitely need added O2 when you reuse the yeast for the next inoculum.
Dr. Clayton Cone