heritability of Z-linked trait

[Tweedy]

In birds, with WZ (males) / ZZ (females) sex chromosomes, I want calculate the following heritabilities by means of both these regressions:

1. Paternal grandfather- male grandoffspring regression
2. Maternal grandfather- male grandoffspring regression

For traits codified by genes located in the autosomes, I know that I would have to multiply the regression coefficients by 4 in each one of both regressions.

But, were the traits I am interested be located in the Z chromosome, What would be the coefficients to apply to the regression coefficients (b) obtained in each case?...Males always have one of the maternal grandfather Z chromosomes but the likelihood of having a Z chromosome derived from the paternal grandfather is 0.5.

Thanks!

[Darby]

Aren't the unmatched chromosomes female in birds?

[Tweedy]

Aren't the unmatched chromosomes female in birds?

In birds, and lepidoptera, among others, females are the heterogametic sex (assuming "unmatched" means XY or ZW)