It is from the loosing tribes of the inter-tribe dome wars that the recruits of the Blood Eagles are drawn. Those young males who have lost the right to life through their father's failures, are marked for execution via death matches. Within the arena they are pitted against their own tribal brothers; else their female relatives be put to the sword. If they win their mothers and sisters (and occasionally daughters) are spared and taken into the winning tribes families.
All Blood Eagles start their journey to become a marine with the blood of their kin staining their hands, and the execution of the women folk of their fallen brothers seared into the minds. All Blood Eagles are filled with a deep self loathing and hatred born of this loss.
In time those who survive the arena may become all powerful marines, yet they do not take revenge on the winning tribes. Instead their spite is tempered by the veterans marines into ruthlessness of action, and when they are elevated to full battle brother they join the others and become the guardians of the system and enforce the draconian rules. They also stop all further building and artificially limit the tribes environment (this is to stop any contamination via potent biological agents thawing out from the ice). They also keep an eye on their female relatives and ensure they are treated well.
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The Chapter is non-codex and divided into two houses: the low house and the high house. The high house is basically analogous to the first company, consisting of all command and specialist marines. The low house is all the regular marines, divided into war bands led by a sergeant of the high house. The war bands are in a constant state of flux and change almost on a daily basis according to the results of the daily fights of morning practice. The marines fight all the time, both playful sparing and full on murderous rage (Bionics are common, though considered a sign of weakness and failure), but scores can only be settled during morning practice. Any killing outside morning practice is considered 'traitorous'.
In time of war, sergeants pick marines from those who are combat ready, and often pick whole 'gangs'. Gangs are marines who stick together and are doing well in the daily fights.
It is entirely possible that a marine can be killed by other marines in the daily fights, though often strong marines are not killed but join the winning gang. Powerful gang leaders become sergeants in time, and appoint a 'second' to run their gang (Killing/ beating a 'second' makes you a second).
Though psychotic, they understand that being part of a gang increases their chance of getting into the high house, therefore the keep those they need alive.