Male or female button quail

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[chicken0044]

Male or female

 

[DK newbie]

The first one is male, but I think you'll have to go by behavior with the white one. Mating and no fighting between the two would suggest female, but unless you get eggs, it's hard to be certain. Some say you can discern from the sounds they make, but personally I haven't noticed a great difference in the sounds of my male and female buttons.
I have also read that only male buttons get a white ring around their pupil, so if it has or gets (if it is young) a white ring, it's probably male, but I'm not certain that the lack of a white ring means it's female for certain, at least not in all colors(I only have wild colored ones).
You can also try giving them insects, females usually just eat as many as they can get, whereas males sometimes pick them up and start calling for their mate to come and get them.