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In this answer to a previous question of mine it was mentioned that the fermentation phase of yogurt making has 3 phases of growth - lag, logistic and plateau. This means that the growth rate follows approximatly logistic function or S-curve. My understanding is that steepening left of the curve represents maximum bacterial growth rate unconstrained by availability of lactose, and the flattening right of the curve is the lactose running out as it has all been converted to lactic acid.

Online instructions for making yogurt frequently suggest different fermentation times for different qualities, for example the top hit on google says "6-8 hours produces a mild yogurt, 8-12 hours a tart yogurt, and more than 12 hours produces a sour yogurt."

Roughly where on the S curve would these points be? Would they all be in the growth phase, such that one would expect a 12 hour yogurt to have lost far more lactose than a 6 hour yogurt but still have substantial amounts of lactose remaining? Would they all be well into the resource depletion phase, such that most of the lactose would have been used by 6 hours and by 12 hours almost none is left?

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First, to clear up one misunderstanding: The plateau of the S-curve isn't because of a lactose constraint. The colony would stabilize at some point, but it would be other factors, probably the accumulation of too much waste product, that creates the true constraint. In fact, if lactose were the limiting factor, you wouldn't have an S-curve, but an inverted-U or even a Russian-cursive-L curve.

With that out of the way, we do have an S-curve, whatever the factors leading to the plateau. And all the yogurt we eat nowadays is in the growth phase of the colony, actually quite in the beginning of it, even in places where tart yogurt is preferred. You'd need many days to stabilize the colony - and arguably, it won't even be the same thing we call "yogurt" any more, especially if made at home, where it will catch more microorganisms to grow freely.

Also, as I now notice that you have used the tag: To spell it out, there is no noticeable difference in the lactose content of long- and short-fermented yogurt (or for that matter, yogurt and milk).

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  • Never before had I worried that my ignorance of Russian cursive was holding me back as a chef….
    – Sneftel
    Feb 4 at 14:26
  • @Sneftel it's probably holding you more back as a data nerd - the average chef outside of Stack Exchange doesn't speak of S-curves either :) Admittedly, I tried to find a better-imaginable symbolic name, but came up empty. If you can come up with a better suggestion for that curve shape, please tell.
    – rumtscho
    Feb 4 at 15:07
  • @User65535 The growth curve isn't a measure of rate, it's a measure of population growth, though if you take the slope of the curve, then you can get rate, so essentially there is no increase in population at the top of the curve due to a limit on the carrying capacity of the environment. I'm pretty certain lactose isn't the limiting factor here, it's more likely to be pH or build up of metabolic by-products from the bacteria - especially as there's plenty of lactose in the yogurt after fermentation.
    – bob1
    Feb 7 at 21:06

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