Indeed Metynnis sp.. Very nice fish and having a school of 13 is sweet!
That's the problem of common names (i.e. red hook sd's or spotted sd's, or 'regular sd's'). They don't mean a thing without seeing the specimen, and even then, only to the trained eyed sd keeper.
Among 'regular' sds, you get at least 3 (our of the ~16 described taxa), sometimes one more species mixed in, and which is common at any one time changes sometime over time.
What is considered red hook is Myleus rubripinnis, a larger sd. Differences: Females have a long red hook. Males a bilobed, not as red hook. They get larger than all Metynnis (7-9"?). They have a smaller, shorter adipose fin than all Metynnis. All Metynnis have a substantially longer adipose fin (relatively), and the common species in the trade max out at 5.5-6.5" in aquariums.
Mock breeding behavior in Metynnis is relatively common.
RE- id. as hypsauchen. maybe yes, maybe not. Maybe the group has more than one species.
Without trying to steal the thread, I post two images of two of my males, which are certainly two different species, and which I consider Metynnis cf altidorsalis, and Metynnis cf maculatus, respectively. They have been in the same aquarium for ~2 years, in a group of 8 fish (3 species of Metynnis). The 4 adults fish (2 species represented), all 'mock breed' with others, but never actual breeding.
Many thanks for posting the images. Awesome fish. Well kept. There is some nipping going on.
What size tank, filtration, others?
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