Birds like the rhode island red are red because of a number of genes- so there is not a dominant red gene.
In males, you have to think of them as a black bird. Then there are genes that remove the black and replace the black with red or white. The same is true for a female but it gets more complicated with them.
It takes 4 different genes to make a black-tailed red bird.
One is called wheaten- this gene adds black to the wings, tail, and breast.
gold- adds red to the pyle region- pyle region is the red area on a black breasted red bird
columbian- removes black from certain parts of the wing, breast, and from hackles and head
mahogany- makes any red a darker red color- also removes some black from wings and hackles
In the end, the only black in the bird would be in the tail and wings. The rest is red.