Is it true or false homozygous organisms are true-breeding for a particular trait?

Answer 1

True for the most part, if you breed two homozygous animals then it's a 50/50 chance of the offspring breeding true to one parent. If you breed a Homozygous animal and a heterozygous animal then the homozygous animal will breed true at least 90% of the time.

Answer 2

If the gene for which they are homozygous is a dominant gene then yes, they will breed true for that trait. An example would be black pigment in horses. Black is dominant so a horse that is homozygous for black will always pass a black gene and the resulting foal will always have a black based color for its coat. If HZ black is bred to HZ black then the foal is HZ black as well. However, if HZ black is bred to red (HZ recessive) the foal will be black in appearance but will carry a recessive red gene and be heterozygous itself...and not breed true to color 100% of the time in the second generation.

If the gene for which the animal is homozygous is a recessive gene then no, they will not breed true for that trait. An example would be red pigment in horses. Red is recessive...in order for it to show there must be two genes for it. A red horse (homozygous with recessive red) bred to a horse with a black based color, will not always produce a red foal....the black based mate would have to be heterozygous for black (having one black and one red) giving a 50% chance of matching the red gene from the HZ red horse of the pair. Only if bred to another HZ recessive would this breed true 100% of the time.