Final answer:
The correct term to describe Irene's connection to an ancestral general is 'lineage', which implies a direct descent or hereditary line. This term is specifically relevant in the context of Irene's European ancestry during colonial times, typically associated with patrilineal descent.
Step-by-step explanation:
The genealogical link that best represents Irene's connection to a general in the Spanish forces that colonized South America in the 1600s is d) lineage. Unlike other options such as clan, which may imply a larger group of families, or nuclear family which is too immediate to describe a connection from centuries past, lineage refers to direct descent from an ancestor. In this case, it represents the direct bloodline or hereditary line from Irene to the general, documenting her ancestral connection through several generations.
Other kinship systems mentioned are also relevant in describing family connections, such as matrilineal descent patterns, often prevalent in indigenous societies where descendance and inheritance follow the female line, ensuring a clear trace of clan affiliation especially when paternity may be uncertain. However, since the reference is about a general from European ancestry during the time of colonization, we are typically inferring a patrilineal descent, where the lineage is traced through the male ancestors.