IF traits of NS included the invention religion...?

The two main schools of thought hold that either religion evolved due to natural selection and has selective advantage, this side includes the God Gene theorists, or that religion is an evolutionary by-product of other mental adaptation. Me, I lean towards the second school, which includes, Stephen Jay Gould, who believed that religion was an exaptation or a spandrel, in other words that religion evolved as by product of psychological mechanisms that evolved for other reasons.

These mechanisms include, the ability to infer the presence of organisms or entities that might do harm (agent detection), the ability to create causal narratives for natural events (etiology), and the ability to recognize that other people have minds of their own with their own beliefs, desires and intentions (theory of mind). These three adaptations (among others) allow human beings to imagine purposeful agents, behind many observations that could not readily be explained otherwise, e.g. thunder, lightning, movement of planets, complexity of life, etc.

Psychologist Matt J. Rossano argues that religion emerged after morality and built upon morality by expanding the social scrutiny of individual behaviour to include supernatural agents. By including ever-watchful ancestors, spirits and gods in the social realm, humans discovered an effective strategy for restraining selfishness and building more cooperative groups. The adaptive value of religion would have enhanced group survival prospects.