CHICAGO—Michigan dairy farmer Doug Chapin has been unable to buy bottles of veterinary penicillin for his cows for more than a month. In Minnesota, pig farmer Randy Spronk reformulated feed rations due to a shortage of the widely used ingredient lysine, an amino acid that helps livestock grow. Supply-chain disruptions are hitting America’s meat producers and sending them scrambling for alternatives as they seek to care for farm animals and keep down costs. Shortages of some medications like penicillin reflect in part a competition for raw materials between people and animals, as the COVID-19 pandemic shifts demand and disrupts global trade through shipping logjams and port bottlenecks. Supply issues, in turn, have veterinarians questioning long-standing farm practices and are forcing changes within the food sector. WH Group’s Smithfield Foods, the world’s biggest pork producer, told Reuters it has seen shortages and substituted products and manufacturers when necessary to maintain animal …