Just in case you can’t see the pics clearly:
Goldflake: “Singly, in pairs, or small groups.”
Flagfin: Same as above.
Regal: “Although adults are observed singly or in pairs, the typical social unit is a single male and one or more females (usually 2-4).”
Blue Line: “Adults are found singly, in pairs, or OCCASIONALLY in trios.”
From Kuiter and Tanaka:
1. Flagfin: “Swims singly, in pairs, or OCCASIONALLY in small groups.”
2. Goldflake: “Occurs USUALLY solitary, in pairs, or OCCASIONALLY in small groups.”
3. Regal: “Adults in pairs and OCCASIONALLY in small groups.”
4. Blue Line: “They occur in pairs or form a small harem.”
This is from a Taiwanese study about captive breeding Blue Lines (from 12 years ago): “A single male dominates a harem of two females.”
ntour.ntou.edu.tw:8080/ir/handle/987654321/50212
There’s another Taiwanese study that confirms this species shows hermaphroditism and goes a bit into the spawning patterns but doesn’t really mention social structure.
Maybe it’s just an issue of semantics with the books I have.