In Red River, Tom and Matthew are both alpha male cowboys who are constantly dueling for control over the herd. They both share the common duty of delivering the cattle to Missouri, so the people of Texas can get their money. Matheson says that the alpha male cowboy must be detectives who are damaged and isolated from society. Tom and Matthew both seem to be isolated and damaged. Tom is the typical pack leader who is distanced from society and willing to start his own cattle ranch by himself. Matthew was forced to distance himself at a young age, when his convoy was attacked by Indians and he followed his only cow to safety.
The law of the gun is another alpha male quality that both Tom and Matthew live by. Tom believes that he is teh ultimate law of the group since he made all the members sign a contract saying that they won't quit anytime throughout the cattle drive. Tom uses his contract as a supplement to his gun. He binds everyone to their duteis that are outline in the contract then uses his gun to enforce it. Matthew, on the other hand uses his gun to help bring lawfullness to the group. When Tom was about to kill one of the members for causing a stampede, Matthew shot the man just to injure him. Matthew knew Tom would kill him, but Matthew had a sense of duty towards his people and used his gun to enforce it. Matthew also uses his gun when he takes control of the group to head to a different destination.
According to Tompkins', both Tom and Matthew are men of the land; the land is everything to them. They both rarely go into town and prefer to reside in the land. The share in common many of the harsh conditons that the land imposes on them. They are both products of their environment. The desert shows them pain and death, and they show both of these qualities and are readily willing to impose them on anyone. Tom and Matthew both have several instances where they readily killed or injured someone when the believed it was neccesarry. In the end, Tom and Matthew both were able to live together and Tom somewhat granted Matthew the title of alpha male cowboy.