If you are doing HST properly you won't be able to just increase your volume at will. If you are doing HST properly you should already be using as much volume as you can reasonably handle and still feel healthy (no injuries etc).
HST builds strength sure enough, however, the actual manifestation of that strength depends on the recovery of the CNS (and other neuromuscular factors) from workout to workout. Sometimes a person will gain a little ground on their CNS recovery and their strength output will go up. Those who zigzag are more likely to experience significant "strength" gains mid cycle.
The size gains are dependant on what's happening to the tissue. This of course is dependant on the absolute load as well as the relative condition of the tissue at the time.
So, should you increase, maintain or decrease "volume" as the cycle progresses? It depends! I know how many people hate to hear that...but its true. Here is how you decide. Keep in mind that these factors are to considered “collectively”, meaning each factor must be weighted, not taken as an absolute indicator.
Increase volume if:
You are never sore
You are never tired
You are not growing
Maintain volume if:
You are slightly sore most of the time
You are tired enough to sleep well, but not so tired you lose motivation to train.
You are noticeably “fuller”
Decrease volume if:
You are experiencing over use pain, and strain symptoms in joints and/or muscles.
You are tired and irritable all the time, yet don’t sleep well.
Strength levels are significantly decreasing.
I said, “The number of Sets is determined by the minimum effective volume (this changes over time according to current load and Conditioning.)" You said, “I thought … that the expression of the hypertrophic genes was increased in proportion to time under tension, i.e. 'more is better' up to a rational point.”
If I understand correctly, you are concerned about the “minimum” effective volume part. Why should a person adjust the # of sets according to the minimum effective volume if “more is better”? Answer, because other factors such as Training Load and Training Frequency are inversely related to training volume. In other words, the higher the volume of exercise, the lower the Load and Frequency that can be effectively maintained over time. Likewise, the lower the training volume, the higher the Training Load and Training Frequency that can be effectively maintained.
It is just a matter of defining “minimum”. In this case, “minimum” means as many sets as you can do without having to reduce the Load from set to set and the without having to reduce the frequency beyond 48 hours.