My guess is nothing. While anything can change, United and Continental technically merged their program, but kept Continental's card with Mastercard, United program with Visa, both under the same "United Explorer" branded card. For these cards, both were issued by same bank, Chase. No longer renewable on Mastercard.
Similarly, I believe Alaska (Visa) and Hawaiian (Mastercard) can and will likely co-exist. Alaska's card is issued by Bank of America, while Hawaiian card is issued by Barclay. The issuer is different and while they can sell the asset to the other, I doubt this will happen. It is possible, however that one card may be closed to new applicant, as did happen to Continental version of Explorer card.
Jiburi