According to the researchers in the roundworm study, how did a calorie-restricted diet extend the roundworms’ life span?

Listen to part of a lecture in a biology class.
Professor: Aging of course is a natural part of life for all living things. Most theories of aging, of why aging occurs, fall into one of two categories. First, you have the biological clock category—theories in this category assert that all organisms have a sort of internal biological clock, that they are sort of genetically programmed to age in a certain age at a certain rate. The second category asserts that aging is the result of the gradual accumulation of damage to cells and tissues. In the second category, we have a theory called "the free radical theory," which we’ll now examine.
    According to this theory, an organism’s cells in their regular metabolic processes—by metabolic processes I mean... things like cellular respiration and reproduction... in their regular metabolic processes, cells generate oxygen molecules, some of which have an extra electron. That extra or free electron makes the whole molecule unstable. The unstable molecule is known as a free radical, okay?
    And according to this theory these free radicals cause damage to other molecules and structures within the cell, including, most significantly, to the cell’s DNA, and it’s this gradual degradation of DNA and tissues and larger structures that drives the aging process.
    You may be wondering how does this theory hold up? Well, some organisms do have some protection against free radical damage in the form of substances called antioxidants. Antioxidants through a series of chemical reactions, can help stabilized free radicals, so they can’t damage the cell. An important antioxidant is an enzyme called "superoxide dismutase" (or SOD). ln experiments with fruit flies, when researchers increased the level of SOD, there was less free radicals harm. The fruit flies had longer lifespans and stayed younger longer. So this seems to show that indeed, at least in some invertebrates, free radical damage is what causes aging.
    Ok, and there is another line of thought that at one point was used to support the free radical theory. It was discovered that when organisms, such as yeast—a fungus—were given a calorie restricted diet, they lived longer. If their diets included far fewer calories than normal but still included all the necessary nutrients, their lifespan increased. For a while researches explained this by arguing that the limited food intake leads the yeast cell’s metabolism to slow down. You’ll need to remember that according to the free radical theory, cells metabolic processes were what brought about those extra electrons that created free radicals, and, so the argument went at the time, if the cells metabolism slowed down, the rate of free radical production also slowed down, so there was less cell damage. And that’s why the yeast cells aged slower and lived longer.
    However, later research, this time on roundworms, suggested that while it was true that organisms on a calorie restricted diet live longer, it wasn’t because of a slower metabolism. In fact, the researchers in this roundworm study claimed that the special diet actually increased cell respiration, and what happened was this increased respiration activated a certain gene, a gene that has been linked to a longer lifespan. And these researchers claimed that it was actually the activation of this longevity gene, not the slowing of free radical damage, that lengthen the lifespan.