About 3/4 of orange cats are male. If my cat is orange, what is the probability that his mother was orange?To answer this question, you have to know a little about the genes that affect coat color in cats:
- The sex-linked red gene, O, determines whether there will be red variations to fur color. This gene is located on the X chromosome...
- Males have only one X chromosome, so only have one allele of this gene. O results in orange variations, and o results in non-orange fur.
- Since females have two X chromosomes, they have two alleles of this gene. OO results in orange toned fur, oo results in non-orange fur, and Oo results in a tortoiseshell cat, in which some parts of the fur are orange variants and others areas non-orange.
If the population genetics for the red gene are in equilibrium, we can use the Hardy-Weinberg principle. If the prevalence of the red allele is p and the prevalence of the non-red allele is q=1-p:
1) The fraction of male cats that are orange is p and the fraction that are non-orange is q.
2) The fractions of female cats that are OO, Oo, and oo are p², 2pq, and q², respectively.
Finally, if we know the genetics of a mating pair, we can compute the probability of each genetic combination in their offspring.
1) If the offspring is male, he got a Y chromosome from his father. Whether he is orange or not depends on which allele he got from his mother:
2) If the offspring is female, her coat depends on both parents: