Zombie Cliché Lookout:
A power struggle is an essential part of any fictional survival situation (and probably most non-fictional survival situations, for that matter). You’re always going to have more than one person who thinks they should be calling the shots, whether that’s because they’ve got experience with leadership, they have some special insight, or they’re just egotistical enough to think they’re better than everyone else.
The leadership struggle can take place in one big dramatic moment, or slowly expand over the course of the narrative until it reaches it’s natural boiling point (after plenty of sniping and passive-aggressiveness, of course). Regardless of the way the struggle crops up, it almost always ends the same way: a clear winner takes charge, and the loser licks their wounds and starts thinking about their next coup.