Final answer:
Chagnon employed the genealogical method to collect Yanomamo genealogies, which is a systematic approach to understanding kinship and social structures through interviews or surveys, examining how kinship affects roles, statuses, and social institutions.
Step-by-step explanation:
Chagnon collected Yanomamo genealogies by engaging with the members of the community and utilizing the genealogical method, which follows a systematic approach to study kinship and social structure. Although Chagnon's specific methods are not detailed in the provided information, the genealogical method, as established by early anthropologists like W.H.R. Rivers and later expanded upon by Bronislaw Malinowski and A.R. Radcliffe-Brown, involves collecting data through interviews or surveys. This method seeks to understand sociocultural relationships within a society by examining the roles and statuses that kinship confers upon individuals. Chagnon's approach was likely influenced by Malinowski's emphasis on the function of kinship in addressing human needs and Radcliffe-Brown's focus on kinship as a social institution intertwined with other aspects of society such as inheritance and education. The end goal of using the genealogical method is the comprehensive understanding of familial bonds and their role in shaping cultural practices and social norms.