For instance, if an animal's first offspring is male, then all subsequent offsprings will be male too (the sex of first offspring could be determined randomly). Does it happen in any species?
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$\begingroup$ Are you interested in processes operating both pre- and post zygotic formation, and both pre- and post ovulation? In other words, are you asking only about primary sex (primary sex ratio) or offspring sex at birth. It is also possible to have a situation where parents adjust sex ratio of offspring at the egg stage (e.g. birds) or when offspring are very young (e.g. by adjusting feeding rates), and this could theoretically be influenced by the sex of previous offspring. $\endgroup$– fileunderwaterCommented Nov 18, 2015 at 9:15
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$\begingroup$ I mean sex ratio at birth. $\endgroup$– Misha MonahovCommented Nov 19, 2015 at 10:39
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$\begingroup$ fileunderwater, what you mention would be tertiary sex ratio. It's adjustment is also an interesting question, but I wonder if there are any physiological mechanisms that can adjust secondary sex ratio depending on the sex of preceding sibling. We don't know if such mechanisms exist in humans, but perhaps there are animals with a known effect... $\endgroup$– Misha MonahovCommented Nov 19, 2015 at 10:45
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I can think of one (perhaps trivial) case where this happens. In insects with haplodiploid sex determination (like Hymenoptera) then almost all of a male's offspring will be female, as they will be diploid.
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$\begingroup$ Another case you might think about is female-only, clonal animals, e.g. nytimes.com/2018/02/05/science/… $\endgroup$ Commented Feb 6, 2018 at 14:05
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$\begingroup$ Also I'm not sure this answers the question, as the sex of offspring 2...n doesn't depend at all on the sex of offspring 1. $\endgroup$ Commented Feb 7, 2018 at 11:57
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1$\begingroup$ Regarding "almost all," in bees, for example, sex detemination occurs at a single genetic locus. The usual rule is hemi- or homo-zygous for the sex determination locus, you're male, heterozygous, you're female. So in inbred populations diploid males are somewhat common, in outbred populations they're very rare. $\endgroup$ Commented Feb 7, 2018 at 13:35
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$\begingroup$ And I agree, neither of these cases is as weird as the OP asks about, where the sex of first offspring might not be predetermined, but has a large effect on the sex of subsequent offspring. I am sure if you look long enough you'll find a story that matches it; I thought it might be helpful to share some more common stories that might be food for thought. $\endgroup$ Commented Feb 7, 2018 at 13:38