If you're not familiar with the work of Kai Troester at Braukaiser.com, I suggest you catch up and keep up. His pursuit of brewing knowledge is academically rigorous, and he doesn't give free passes to conventional wisdom. I don't think his experiments are perfect, but he's currently doing more than anyone I can think of to explore new territory in brewing science in ways that are relevant to home and craft brewers.
A month and a half ago, he wrote an article about yeast growth (here) that destroyed the credibility of my calculations for stir plate starters (based on predictions of the Wyeast Pitch Rate Calculator, I had simply taken the growth rates of non-stir plate starters and multiplied them by 2). His experimental results were all over the map, though, so I didn't feel comfortable adopting his conclusions (which are presented here) or drawing my own conclusions from his data (which I did with his mash pH experiments).
While digging into the typical growth rates of large-scale commercial yeast propagators, I came across the following two articles in the MBAA Technical Quarterly that either discuss a pair of overlapping experiments or refer to the same experiment:
-"Yeast Management Under High-Gravity Brewing Conditions" by Mike Cholerton (2003).
-"Control of the Yeast Propagation Process - How To Optimize Oxygen Supply and Minimize Stress" by Olau Nielsen (2005).
The articles deal with batch-fed propagations where oxygen is continuously added via mixing, which are essentially large-scale versions of yeast starters on stir plates. Both articles mention that big commercial operations typically limit their propagations to final cell concentrations of 100 million cells per mL to maximize yeast vitality, which most homebrewers lack the means to do, and imply that letting their experimental propagations continue beyond that point resulted in final cell concentrations around 170 million cells per mL. The Cholerton article also stated that his experiments were carried out with 12 Plato wort, which means that the final cell counts of the non-arrested propagations were around 1.35 billion cells per gram of original extract.
It could be the case that Kai is mistakenly focusing on new cells created per gram of extract instead of final cell count per gram of extract, but I suspect that both considerations - and countless others - contribute to how life actually behaves. I also feel that if the experimental data represents reality, i.e. sample sizes are significant and measurement errors are minimal, mathematical analysis will take both approaches to the same endpoint. With that in mind, I like the simplicity of "if I want X billion cells, I need X/1.35 grams of extract in my starter" and I'm currently using that calculation in my brewing spreadsheets.
However, the assumption is invalid for high pitch rates (i.e. lots of yeast in a small volume of starter wort). According to Yeast by Chris White and Jamil Zainasheff, which I very much trust (it's Jamil's leap from the book's data to his stir plate calculations that Kai doesn't trust, and I agree), pitching 100 billion viable cells into a 500-mL starter with an OG of 1.036 - which contains 47 g of extract - will result in a final cell count of 112 billion cells. To achieve the same cell count with a stir plate, I'd predict an extract requirement of 112 / 1.35 = 83 g. Knowing that adding a stir plate should never increase the required size of a starter, and acknowledging that Chris White's left foot knows more about yeast than I do, the band-aid I applied to my stir plate calculations was to simply defer to the book's predictions in those instances. I'm fine with that because oxygen is probably not a growth limiter when there's so little extract.
In the long-term, I hope to perform a series of experiments in the Ale Asylum lab that will complement Kai's work and hopefully make us all smarter. It's not going to happen until our bottling line is operational and production settles into a comfortable routine, though, so I may have to wait a while.