For my Nuzlocke, I didn't catch it if I already had one, but if it was something that I'd had at one point but ended up having to release because it had died, it was a valid replacement. Ended up catching one Rattata on Route 1, losing it in the Route 22 Rival Battle, and catching another one on Route 3.
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(this space for rent...okay, not really.)
[NO BARKLEY NO PEACE]