[S. cerevisiae]

yeast cells are continually growing and dividing throughout the whole fermentation cycle.

That assumption is incorrect.   High krausen is the demarcation point where the culture shifts from biomass growth to replacement only reproduction.  High krausen occurs as a result of maximum cell density being reached.

While I do not have a fully formed blog entry for the topic, I partially addressed what is going on in the following post: https://www.homebrewersassociation.org/forum/index.php?topic=24447.msg314704#msg314704

[charles1968]

yeast cells are continually growing and dividing throughout the whole fermentation cycle.

That assumption is incorrect.   High krausen is the demarcation point where the culture shifts from biomass growth to replacement only reproduction.  High krausen occurs as a result of maximum cell density being reached.

While I do not have a fully formed blog entry for the topic, I partially addressed what is going on in the following post: https://www.homebrewersassociation.org/forum/index.php?topic=24447.msg314704#msg314704

Thanks. I think we're using the word growth in two different ways here - growth of individual cells, which continues as long as the yeast have access to nutrients, and growth in cell numbers, which may well peak at high krausen. Yeast cells don't stop growing at high krausen - the rate of reproduction falls below replacement level, but new daughter cells continue to form and grow and produce more daughters, albeit at a declining rate. The metabolites associated with cell growth continue to be produced. A common misconception on homebrew websites is that yeast do all their growing early in fermentation and then, once they've formed a healthy population, simply chug along fermenting without any further cell growth.

[S. cerevisiae]

Thanks. I think we're using the word growth in two different ways here - growth of individual cells, which continues as long as the yeast have access to nutrients, and growth in cell numbers, which may well peak at high krausen. Yeast cells don't stop growing at high krausen - the rate of reproduction falls below replacement level, but new daughter cells continue to form and grow and produce more daughters, albeit at a declining rate. The metabolites associated with cell growth continue to be produced. A common misconception on homebrew websites is that yeast do all their growing early in fermentation and then, once they've formed a healthy population, simply chug along fermenting without any further cell growth.

Yes, but the majority of growth still occurs at the beginning of fermentation due to the exponential nature of that growth.  Given everything else equal, a underpitched culture will tend to produce higher ester levels than a conservatively pitched culture due to increased higher alcohol production.  Acetate-based esters rise on the other end of the U due to elevated levels of acetyl-CoA.   

[charles1968]

Can you explain a bit further why underpitching raises ester levels? Is the cause stress due to limited O2, for instance, or greater production of esters during exponential growth? If the latter, pitching supernatant from a starter will pitch the esters too and produce beer no different from underpitched beer.

[charles1968]

Given everything else equal, a underpitched culture will tend to produce higher ester levels than a conservatively pitched culture.

My suspicion is that this is only true in poorly aerated wort under an airlock. An inadequate starter pitched into poorly aerated wort results in a yeast population deprived of sufficient oxygen and ergosterol to grow normally. I think people are blaming pitching rate when oxygen level is the real culprit. I note that Kai Toestler's pitching rate experiment produced no significant difference in flavour in the beers, and the three pitching rate experiments on the brulosophy website all failed to find any conclusive evidence of an affect on flavour (which I suspect is because the starters and/or worts were well oxygenated in each test).

I think the influence of pitching rate is hugely exaggerated. As you've pointed out very clearly, a small population of yeast grows exponentially and very quickly becomes a large population of yeast. Whether that happens in a starter vessel or in the main FV probably doesn't matter, provided you keep bacteria at bay. But what does matter is that the yeast in the main FV have enough oxygen and ergosterol to ferment normally if they don't get enough biomass from the starter. The exponential growth is not itself a cause of high ester levels - just look how many conflicting reports there are on whether rapid growth raises or lowers ester levels if you want evidence of that.