Grade Up To Elite Cow

BoardGameGeek.com describes this boardgame (which came out in 1986) as a "game of skill and chance for Dairy Farmers' made by Waddingtons of behalf of 'The British Friesian Cattle Society of Great Britain and Ireland.'"

YouTuber David Ball offers more details, describing it as a "rare cow-insemination boardgame," noting that the aim of the game is to "to collect semen, then inseminate your friesian cows & breed an 'Elite Status' herd."

It reminds me of the game Antler Island, which is about stags mating with does. The existence of these two games, taken together, means there's a genre of boardgames about animal breeding.

source: University of Reading