For example, in 2009 I discussed a paper showing that food deprivation extends lifespan of C. elegans nematode worms by delaying their reproduction. I've seen other papers claiming to extend lifespan without reducing reproduction, but those papers have ignored possible effects on timing of reproduction. In a growing population, reproducing later reduces fitness, because your offspring are added to a larger gene pool. On the other hand, if the population is decreasing...
But a recent paper in PNAS reports that chemicals called ascorides (thought to be used as a crowding cue) increase the lifespan of C. elegans, without an apparent reproductive cost. Treated animals produced at least as many offspring as controls, at all ages. I don't understand this result. If there's no tradeoff, why haven't they evolved to turn on this response all the time, even without the crowding cue?
In humans, though, "Exceptional longevity is associated with decreased reproduction." That was the conclusion of a 2011 paper. They found that Ashkenazi Jewish centenarians (average age ~100 years) averaged 2.0 children, while a control group (parents of their children's spouses and friends, who died in their 70's) averaged 2.5 children. The centenarians also reproduced later in life (28-32 vs. 26-30). So, is it worth having 0.5 fewer children, to live 30 more years? Natural selection apparently doesn't think so.