There are definitely two Alfa male cowboys in the movie Red River. Both the characters have the qualities of the Alfa male cowboys. In the beginning of the movie we see that Dunson gets away and gets separated from the wagons. He does it the way he wants to do it. He and his companion go off alone in the desert, not scared of anyone or anything. Ready to face everything that comes along in their way. He then makes his way over a period of 14 years and handles a huge cattle herd in Texas.
He leads the journey, after deciding to go to Missouri and he does each and everything the way he wants to do it. On the way he gets week and loses control of the men and he is no longer able to lead the group.
Then Matt takes the lead, Dunson was wrong in some of the decisions. He then challenges Dunson and decided to lead the trail from then onwards. He then was determined to reach Abilene. At that point of time Dunson was weal physically and he could not do anything about it.
We see the determination in Matt that he wanted to take everyone safely to Abilene. He does not rest a nit until he has reached there. He does not let a women come in his way, his priorities were set as those of a true Alfa male cowboy.
As Matheson says in the article “Only the fittest, the strongest, and the most ruthless survive in the noir frontier.” We see the ruthlessness in Matt. Dunson had taken care of Matt and brought him up as if he was his own kid, but he had no feelings for Dunson when it came to right or wrong. He did what he thought was right.