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Heredity (the adjective is hereditary) is the transfer of characters from parent to offspring, either through their genes or through the social institution called inheritance (for example, a title of nobility is passed from individual to individual according to relevant customs and/or laws).
One's bloodline is one's familial ancestry.
In biology, heredity is effectively a pseudonym for genetics, since biological information is passed on as genes. Alternative mechanisms of heredity were proposed but falsified, see Lysenkoism.