Are there any plausible hypotheses about the evolutionary psychology of pedophilia?

We know that, up to a point, youthfulness is often an attribute non-pedophiles look for in a mate. For a long-term relationship, assuming the partners do not live in an industrialized society in which having a high school education is an advantage for a mate, it makes sense to mate with someone as close to pubescence as possible, since they have more years of fertility ahead of them. This would explain the fetish behind magazines such as Barely Legal and websites that advertise models who have just turned 18 and look younger than 18.

So maybe pedophilic attractions developed because it was more adaptive to err on the side of too young rather than too old. In pubescence, fertile young women still have many characteristics of children, and therefore it might be maladaptive for a man to be strongly repelled by childlike traits.

Maybe there were situations, in caveman eras, in which someone started a sexual relationship with a prepubescent, and that relationship continued into pubescence and produced offspring. Maybe those who did this had an advantage over rivals, by being the first to form an emotional bond with the child, and to claim the child as their long-term partner. Maybe this emotional bond was promoted by their providing the child with food and other resources; thus it also served to protect the child's well-being.

Who knows what complicated social purposes pedophilia might have served? Maybe, in a variant of the super-uncles theory, pedophiles served as caregivers for young family members, since they would tend to volunteer for roles that would put them in close contact with those kids. A counter-argument would be that their engaging in child sexual abuse would cause enough harm to those children to outweigh the value of the care they provided.

Maybe in caveman days, though, the resources they provided would have meant the difference between life and death for the child, so that back then, the pedophilia was adaptive.