He and Annett both talk about a gene coming in 2 versions, one for right preference (R+ say), one for random preference (R-). The R- version is recessive and the R+ version is dominant.

Since our genes come in pairs we might have:

R+ and R+ - gives a right hander
R+ and R- - gives a right hander (since R+ is dominant).
R- and R- - randomly gives a right hander or a left hander.

This is not a bad theory since it explains why 2 left-handed parents are likely to have about 50% right handed children, even though all the children would be expected to be R- and R-.

Annett may now have modified her theory - but this is the theory as stated in Corballis’ book ‘The Lop-sided Ape’.