Male variability

Males are more variable than females. This observation has been observed across many species for hundreds of years. Males are also more heavily parasitized than females, which adds to their variability.

This leads to the question of why males are more variable. A simple explanation is that males have greater variability of outcome - some males have many kids and some have none. Their variability of outcome exceeds that of females. Variability of outcome leads to trait variability - as males take gambles of various kinds in the hope of becoming members of the set of super-males that have lots of offspring.

Why do makes have greater variability of outcome in the first place? This is ultimately down to gamete anisogamy - the primary defining characteristic of maleness. Females have fewer eggs and invest more in each one. Males specialize more in distribution, produce more sperm and invest less in each one. This leads directly to variability of outcome - as some males have many more offspring than females can manage.

This theory also explains increased greater male variability as a result of female choice and male combat. These phenomena result in greater male outcome variability, and so greater trait variability. I don't think these phenomena need separate theories to explain them.

The idea of males gambling also suggests that male averages can be expected to be worse than female averages, as the majority of male gambles fail. This is, I think, an observed phenomenon, although I know less about it.