How (not) to quantify aurochs-likeness in cattle

I have been trying to quantify aurochs-likeness in extant cattle multiple times and it turned out to be very difficult. It starts with the question of what is a “trait”. For example, is coat colour a trait or is it rather a complex of many traits (what types of melanin are expressed, where they are expressed et cetera)? Some traits also interfere with each other. As an example, leg length (i.e. proportions) influences height and other parameters. If a short-legged bull is only 150 cm tall, it is shorter in height than the European aurochs. If it had the right leg length it might be 20 cm taller, meeting the height of some European aurochs. Is, considering that, both the body size of the animal and the leg length deficient, or is only the leg length deficient? Even more problematic is the thought that not all traits are regulated by the same number of genes. Colour is regulated only by a handful of genes, perhaps roughly a dozen, while the bodily morphology is much more complex and influenced by many genes (I assume so because endocrinology influences the body morphology quite dramatically, and the hormone system is influenced by a very large number of genes). So which cattle individual is more aurochs-like, i.e. closer to the aurochs, one that has the right colour but a totally domestic morphology, or one that has the right morphology but deviant colours? If every defined “trait” (what is a trait?) is assigned an equal value, both individuals would be equally aurochs-like. This neglects the fact that in one individual a lot of genes are “right” and only a handful “wrong” while in the other a lot of genes are “wrong” and only a handful “right”. Therefore, the most objective and useful way to compare the phenotypic aurochs-likeness would be to compare every single gene that has an influence on the phenotype. This is practically near impossible as mammals have between 20.000 and 30.000 genes and we do not know the phenotypic impact of every single allele on every single gene. Therefore, an attempt to quantify even the solely phenotypic similarity to the aurochs necessarily has to be somewhat simplistic. I made lists of aurochs-like traits and scored a number of cattle breeds for those traits, each time a slightly different approach and the result always was that Sayaguesa and Lidia were among the two most aurochs-like breeds, “breeding-back” results were not included. It is very difficult to score “breeding-back” results as they are not as homogeneous as traditional breeds. For example, the horn size of Heck cattle varies greatly between individuals, herds and lineages. Averaging the traits found in the “breeding-back” results each would not account for the variability found within them. What can be done is scoring single individuals of “breeding-back” breeds/populations, but that leaves a lot of room for bias. One can take the best or the worst individual, or trying to figure out which individual might be representative of what is average for the breed, but that is very difficult and would, again, not account for the variability in the populations. 

All in all, I think trying to systematically objectively quantify the aurochs-likeness of cattle can only provide a very rough impression that is not any more useful than just looking at the cattle and comparing them.