It depends on how you play the game. There's a commonly enforced rule called the Dupes Clause that allows you to catch another Pokemon if you've already caught the same species in a previous area. It's used to have more variety between team members. It, like many other Nuzlocke rules, is entirely optional, and you can play with or without it.
Source: I play Nuzlockes quite a bit, using the Dupes Clause every single time.
Hope I helped!