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Kobollians are humans who are of the House of Kobol's direct bloodline.
Most Capricans are direct descendants from settlers of Kobol, however the bloodline of the Lords of Kobol is found in Adama and his children. Troy is also of the bloodline, as are a few people in the Fleet, although he is not genetically related to Adama's family.
Those of the bloodline are capable, through mental training, able to be empathic to feelings and have a heightened danger sense (Armageddon).