Can birds control the sex of the eggs they lay? If so, how?

Factual Questions
1

In the Wikipedia article on the house finch, I came across this interesting nugget:

I would have assumed that egg-laying is pretty much random, but this seems to indicate that the mother can selectively determine the sex of the eggs she is laying. How is that done?

2

Most birds use a similar genetic system to mammals for determining sex, except that it’s the female who has two different chromosomes, instead of the males like it is with us. So a mother finch (but not a father) might be able to control which chromosome is in the ovum that gets fertilized.

3

It’s not going to be something the bird has any awareness of.

I would guess it is achieved by the use of epigenetic controls, which make have an effect on which gametes are viable and which are not. This would occur as a response to environmental conditions triggered by the presence of the mites.

4

The Wikipedia article cites an article by Badyaev et al. (2006) for the egg-laying strategy of the house finch. This in turn cites the following review article:
Pike, T.W. and M. Petrie, 2003. Potential mechanisms of avian sex manipulation. Biol. Rev. 78:553-574. DOI: 10.1017/S1464793103006146

The mechanisms outlined in the article are:

  1. Asynchronous follicular development - eggs of one sex develop faster in the ovary and hence get laid before eggs of the other sex

  2. Segregation distortion - non-random segregation of sex chromosomes at meiosis has been observed in insects though not in birds

  3. Selective resorbtion - abortion and subsequent reabsorbtion of yolk deposits of post-meiotic ova prior to ovulation

  4. Selective ovulation - non-random shedding of Z- and W-bearing ova following the completion of meiosis

  5. Sex-specific fertilization - there’s a possibility that the sperm themselves (despite all bearing Z chromosomes) might prefer to fertilize Z- or W-bearing eggs

  6. Sex-specific inhibition of zygote formation - possibly a consequence of hormonal action

  7. Sex-specific post-laying embryo mortality - eggs of one sex tend to die (or are killed) more than egss of the other sex

  8. Sex-specific incubation and ‘dump laying’ - egg size is correlated with sex in some species and the mother may subsequently prefer to incubate eggs of one size over the other

There may have been additional research published in the decade+ since the above articles were published. I’ll leave that for others to find.