Evidence from archeology suggests that Neanderthals had limited social exchange, and lived in small, scattered groups. They would need some mechanism for avoiding inbreeding, and might also have evolved some specific adaptations.
Modern human’s primarily pairbond in age-matched pairs. They seek partners in distant groups when possible. Living in age-matched pairs optimizes survivial chances for offspring, but can lead to inbreeding, especially in small, isolated groups.
It is necesary to consider current (hybrid) traits in order to construct a viable hypothesis for Neanderthal reproduction. One of the most promising traits is non-aged matched pairbonds. These exist both between adults, and between adults and teenagers / children. The latter is sometimes called pedophila / hebephilia when it includes sexual activities.
The model
Middle-aged male and teenage female bonds and reproduction solve the problem of inbreeding. Under this scenario, siblings will not reproduce, and fathers will not reproduce with daughters, because when the children are grown-up, the father is old age. It also offers another advantage for females. In age-matched pairbonding, females need to guess work their partners abilities to provide for them and their children. A middle-aged male has already shown his ability to provide for the community, and therefore give females better opportunity to select the best genes. Another problem, the father dying before the offspring is mature, can be avoided by having a group of more than just one pair. If females are promiscous within the group, this will glue the group together and somehow compensate for the risks of older fathers. More genetic variation can also be achieved if different males in the group father offspring.
This model does not need any gender to disperse. A possible mechanism for increasing genetic diversity is group fission / fusion. For instance, the mother and all children could switch group as the children reach (or approach) maturity. Individual males or females could also switch groups upon maturity (or just before).
Male roles
When males are young they need to establish themselves as dependable and creative. Some might live alone, while others could be part of groups. As they reach middle-age, they need to form bonds with young females. They will not expect to become grandparents.
Female roles
In all species, females need to reproduce when young. They will select mates that can impress them with intelligence and creative abilities, and that has a long history of dependability. They will not bother with strangers or males with a bad reputation. When they get past reproductive age, they will get a new role as grandmothers and finding good homes for their children.
Supporting traits
Pedophilia
Pedophilia is a sexual attraction to pre-pubertal children. In its current context it is difficult to explain as an evolutionary adaptation. However, in the context of Neanderthal reproduction, heterosexual pedophilia can be explained. Since the male has to show the group his abilities before he can participate in reproduction, it is not far-fetched if he tries to bond with females before they are mature. He will then have several years at his disposal to show his quality, and to be accepted for reproduction. If he was to bond with already mature females, he would waste years of possible reproduction showing his quality. In other words, this trait has evolutionary value in the Neanderthal context.
Incest
People adapted to age-matched pairbonding have incest avoidance traits as these are essential for successful reproduction. When males with pedophilic traits enter age-matched relationships instead of non-age-matched, there probably is an increased risk of incest. This is because in the natural setting, this is not an opportunity when the father would be old age as daughters become mature, and thus these males might lack incest avoidance traits.
Aspies keeping together
Aspies often have a dislike to socialize with strangers, and it is not uncommon for them to stay with their families longer than is usual, if this is possible. This especially seems to be true for males. The lack of dispersals is compatible with this.
Aspie special interests
Aspie special interests are directly related to male gender roles. They need to impress on females with their creative talents, and special interests can be viewed as just this.
Predictions
Age preferences will increase
It is predicted that age-preference for heterosexual pedophilic males will increase as they age. This is a consequence of limited time to show quality as the male gets older, and that he is at a higher risk of dying before the children are mature.
Most people with pedophilic traits will have a preference for bonding over sex
Since the short-term goal of the middle-age male is to show-off and bond, and not to reproduce, it is anticipated that most males with pedophilic traits have a preference to bond (which will look like friendships) with children over having sex with them.
Heterosexual and homosexual pedophila have different causes
Homosexual pedophilia does not fit into the picture presented here. It is probable that homosexual pedophila is related to neurotypical traits, and to power struggles. It is also probable that much of the abused – abuser spiral is related to homosexual pedophilia. It is anticipated that hetereosexual pedophilia has a weak link to being Aspie.
Supporting evidence
The validity of the concept of older males reproducing with young females
In Gorillas, male Silverbacks, which usually are 15-20 years before they can reproduce, regularily reproduce with females aged 10 years or older. This shows that this kind of reproduction occur in closely related primate species. Link: http://www.seaworld.org/animal-info/info-books/gorilla/reproduction.htm.
Relationship distribution in Aspie-quiz
There are considerable gender differences as to when Aspies get children. Female Aspies tend to get children at about the same time as neurotypicals, while male Aspies lag considerably behind their neurotypical peers.
Disclaimer
The author does not endorse sexual activities with minors, neither the witch-hunt against people that have inborn sexual attraction to children. The author also believes that a huge majority of people with inborn sexual attraction to children are not practising pedophiles, and thus do not act on their sexual orientation.