Pigs and poultry have been the most common animals raised for millenia.
Both can forage on their own. The Polynesians brought poultry to Hawai'i; pigs came later, introduced by Captain Cook. Both are now feral as well as domestic, the pigs a problem especially on the Big Island, and the chickens live free in several areas. My point here is that both can get along without being provided with large volumes of feed and thus are preferred livestock by poorer peoples.

As SINSULL says, in populous countries like China and others in Asia and some in Latin America where both poultry and pigs are often confined close to humans and essentially living with them, the waste of the three intermix;, there is ample opportunity for evolution viruses.

No need to invoke the existence of sinister labs.