Sleep is often viewed as a vulnerable state that is incompatible with behaviours that nourish and propagate species. This has led to the hypothesis that sleep has survived because it fulfills some universal, but as yet unknown, vital function. I propose that sleep is best understood as a variant of dormant states seen throughout the plant and animal kingdoms and that it is itself highly adaptive because it optimizes the timing and duration of behaviour. Current evidence indicates that ecological variables are the main determinants of sleep duration and intensity across species.
Siegel goes on to argue that sleep helps animals conserve on energy at times when expending energy is wasteful. By sticking to sleeping habits, an animal transfers its use of energy to more effective times. Viewed in this light, it's not surprising that developing a regular sleeping habit is a survival trait. More energy at the right time means more successful hunting, which in turn, means more energy. And for animals, more energy is the key to survival.
In my mind, sleeping in low productivity hours is more than just an evolved trait in animals. It is also a good tip for humans. People who develop good sleeping habits (i.e., napping when productivity falls) tend to make the best use of their time. I have used this strategy for survival in graduate school, and I stand by it.
When my productivity sags around 2 pm, I take a mid-afternoon nap (provided that I am not in class). I wake up refreshed and eager to tackle the next problem. If you find that your productivity sags in the afternoon, try a nap. It might be the best thing for you.