Hi from yak-land here in the Himalayas. Yaks don't like it in the balmy lowlands down here at 11,000 feet high. Some years one or two will come nosing around our school in the winter when everything is totally frozen, but in Ladakh they really prefer it up above 14,000 feet.
Yep, they really produce very little milk, though very rich. A friend's parents keep yaks (up on a high pass near a convenient highway, at 14 - 16,000 feet), and he's making cheese. His mom sends a 15 liter container down to him every morning all summer, and it seems that their 15 - 20 female yaks produce 15 liters of milk max. The advantage is that they don't have to be fed anything extra in this biome where pasturage and fodder are scarce, and they fend for themselves. Their meat is delicious, and their fluffy underwool makes a lovely, soft and exceptionally warm but heavy yarn. Their coarse long hair used to be spun for ropes and tents but those aren't needed much now.
The dzo (
Bos taurus [cattle] x
B grunniens [yak]) is happy down here at 11,000 alongside cows. Male dzos are infertile, and females produce calves that almost never survive. The males are used for draft animals here (whereas neither bulls nor yaks are), and the females are considered hardier than cows but lower producing. I suspect the
local breed of cows might share more genes with yaks than non-local breeds like Jerseys do, because a cross of a yak with a local cow produces a strong dzo, whereas a cross with a Jersey cow produces a weak dzo, even though the Jersey mother is like twice the size of the little local cow.