Throughout the world, there is a male-bias in the sex ratio at birth (SRB). It is not known whether this phenomenon has a genetic basis, though there is tentative evidence from genealogical and genomic studies that it may have. It has been proposed that the higher rate of male childhood mortality in humans is linked to the male-bias in SRB through parental investment, but this may only apply to facultative not genetic sex ratio adjustment. In previous population genetic models, elevated mortality in one sex (prior to breeding) has been shown not to affect the SRB, but these models did not consider the role of replacement births (i.e. births that only occur because a sibling died prematurely). In a set of population genetic modelling simulations, in which sex ratio is controlled by an autosomal gene expressed in the male line, this study shows that when there is replacement of dead offspring, this leads to a sustained bias in the SRB in the direction of the sex suffering the highest mortality. In the example of higher male mortality, this occurs, because replacement offspring are disproportionately drawn from fathers who were genetically predisposed to have initially had sons (because sons were more likely to die prematurely), and more likely to pass on male-biasing alleles to replacement offspring. To test the empirical basis for replacement births, an analysis of birth data from the Demographic and Health Survey program was conducted, which shows that parents do indeed tend to replace children who die prematurely.