What size is the tank.... and what else do you have in there.

Puntius tetrazona aka "Tigar Barb" - The Tiger Barb may become aggressive and start to peck at the fins of other fish such as Angelfish or anything with longer/flowing fins. This behavior can be avoided if you keep them in groups of 6 or more so they so they spend more time chasing and nipping each other. Lonely tiger barbs, on the other hand, seem to feel bored or insecure and start fin nipping as some sort of defensive instinct. I would increace the school by at least by 4. You may have ended up with two males, but usually jaw locking is fighting.

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Gold Coast Aquarium Society South Florida
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