Spaying before the first heat reduces the risk of mammary tumours by 99.5% in female dogs and by 91% in cats; spaying at a later stage — after the first, second or third heat — reduces it by a correspondingly smaller percentage.
The explanation is that these tumours are hormone-dependent: when spaying is done before the first heat, the mammary glands are still intact — not yet stimulated by the sex hormones.
Accordingly, the more heats your animal has had, or the more often hormonal products have been used to interrupt heat, the greater the risk of mammary tumours.
Spaying removes the risk of uterine and ovarian tumours, ovarian cysts and pyometra (inflammation of the uterus) by 100%, because the operation removes the ovaries and the uterus.