This debate may be elucidated by first clarifying some issues about yeast metabolism.
When the starter is first innoculated, you will also typically aerate it. So the yeast begin with a source of oxygen and a wort rich in saccharides. The first task of the yeast will be to synthesize sterols for the cell membrane via oxidation. This will use up a certain percentage of the oxygen in solution. Different yeast strains have extremely different oxygen requirements for the synthesis of sterols, with some strains requiring only 4ppm and others requiring greater than 19ppm. Therefore, a great deal of the initial oxygen will be utilized just for the synthesis of the cell membrane. Internal glycogen reserves that the cell has already built up, not the saccharides in solution, are used to to fuel this process of cell membrane synthesis.
Once the cell membrane has been synthesized, the yeast will focus on growth and division. It is NOT the case that cell division only occurs via respiration in an aerobic environment, as some posters have stated. In fact, because the solution at this point will contain greater than 0.4% glucose, aerobic metabolism will initially be inhibited. Only after the glucose content of the solution has been reduced below 0.4% will the catabolic repression of the Crabtree Effect be removed. At that point, if there is still oxygen left in solution, then the yeast WILL employ aerobic respiration and will reproduce quite efficiently until the oxygen is used up. However, once this source of oxygen is used up, they do not cease division. They will just transition to fermentation. Fermentation is the process of cell growth and division via anerobic metabolism.
So, IF a stir plate DOES continuously add oxygen to the solution, this WILL keep the yeast in a state of aerobic metabolism (after the initial glucose is consumed and the sterols are synthesized) and will therefore increase the efficiency of yeast metabolism by 14 times that of anerobic metabolism. However, the total amount of yeast growth will be limited, of course, by the total fermentable sugars in the wort. The stirring activity will also increase the efficiency of growth by keeping the yeast in suspension.
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Edit: I was wrong on one point here. The Crabtree Effect applies not just to glucose levels, but to other hexose sugars that can be converted to glucose intracellularly, i.e. glucose, fructose, and maltose, but not sucrose. Since at least one of these sugars exists during the full course of the fermentation, and the fermentation is aneraobic after the first hour or two, aerobic metabolism (respiration) never occurs in a brewery fermentation. Also, in a typical fermentation, sterols levels are typically the limitation of growth, not sugars, though it is possible, given a large enough pitching rate and sufficient oxygenation, for some nutrient besides sterols to become limiting. But typically nitrogen will become limiting before carbohydrates.