Does sirtuin 1 (SIRT1/SIR1) function to mediate the effects of a low calorie diet? Perhaps, but its really not clear. Is the function of SIRT1 primarily to mediate low calorie response? Absolutely not. What does that mean for SIRT2/SIR2 - its probably not more closely associated with calorie restriction signals, though it might be connected in a similar ambiguous way... but see below.
Firstly SIRT1 has also been shown to have many influences in many studies of conditions such as Alzheimers, anxiety and other neuro-functions. SIRT1 modifies p53 - a bottleneck in cellular reproduction and a key regulator in cancer prevention, but which also an important aspect as to why it is active in calorie restriction conditions.
When reading reference like the one you have here its important to remember that correlation is not causality. Very few genes in animals function only when specific behavior or conditions are experienced, especially signaling genes.
Examining the OMIM report (see link above) there has been a close examination of the possible role of SIRT1 in calorie restriction since the early 2000s in knockout mice.
SIRT1 would seem to play an important role in embryonic development for instance - cell growth is so important at that point and 80% of mice who are homozygous SIRT1 (-/-) knockouts die before they are born and even more die in the early natal period. The mice who do survive have problems generating red blood cells which is another important case of cellular reproduction.
Yet the relationship of the knockout mice to calorie restriction has been debated - its been difficult to interpret the activity and the weight loss or gain of the knockout mice compared to wild type mice since the SIRT1 knockouts are smaller. They may also have genetic traits that compensate for the absence SIRT1 in order to have survived.
More recently mice where SIRT1 expression in the brain have been produced, but the result has been anxiety or anxiousness as opposed to specific calorie restriction diet.
This reminds me of the story of leptin, in the early 90s they found that leptin deficient mice became quite fat, but despite this obvious linkage to obesity, leptin turned out to mediate a lot of other psychological factors as well - it only caused obesity when its function was blocked. It did not turn out to be an appetite signal.
SIRT2 seems to have similar roles in calorie restriction.
Rogina et al (2002) found that under 2 life-extending conditions, Rpd3 (601241) mutants fed normal food and wildtype flies fed low calorie food, Sir2 expression was increased 2-fold.
But also has similar relationships to Alzheimers. SIRT2 has not been followed up on as much as SIRT1. This correlation might not be causal or should be nuanced in a similar way.