Matthew McConaughey: Devoted Dog Dad!

For their June wedding, and his bride Camila Alves included their two children: Levi, who turns 4 in July, and Vida, 2½. But McConaughey is also a doting father to his other kids, two dogs that are frequently spotted living the good life with their easygoing dad.

Asked his favorite tune, McConaughey told a PEOPLE reader in 2009, “Right now it’s a rhyming song that goes along with ‘Levi Alves McConaughey,’ and I go through the things he has in his life, and it always ends up with ‘and a dog BJ’ ‘cause our dog’s name is BJ.”

McConaughey’s onetime trainer, Gunnar Peterson, told PEOPLE the actor finds a run with his dogs to be “rewarding. You deepen the bond you have with the dog.”

Given the frequency of their workouts, the bond must run very deep.

“Over the weekend he refers to six things as ‘nectar,’” writes Tom Chiarella in a 2011 Esquire profile of McConaughey. “A steak, the wine, the company of his older dog … Broadly speaking, nectar is good.”

McConaughey takes a day off from walking the dogs, and Alves is there to pick up the leashes on a 2011 outing with Levi and a barefoot Vida.

McConaughey doesn’t just advise his fans to just keep livin’, he also encourages them to just keep breathin’, as he likes to do on the beach with BJ.

BJ listens closely as McConaughey instructs him on the finer points of dealing with paparazzi.

There’s no doubt who the alpha is in this family. Wherever the big dog goes, everybody follows.

The apple doesn’t fall far from the tree! Little Levi, seen here at age 2, takes after his old man in more ways than one.

“We’re a tribe now,” McConaughey told PEOPLE of his family, and the four-legged ones are proud members of the clan.