Final answer:
Polyandry is rare due to its role in controlling population growth and resource allocation in societies with limited resources, while polygyny is common as it maximizes family labor force, and shared resources, and creates wide kinship connections, often associated with higher social status.
Step-by-step explanation:
Polyandry is a mating system where one female mates with many males and is quite rare. It can help manage population growth and resource allocation in societies where these are pressing concerns. For instance, fraternal polyandry allows brothers to share land and resources that might otherwise be divided and diminish in utility.
In contrast, polygyny is a mating system where one male mates with many females and is much more common. It often occurs in societies where larger families have higher social status and can create advantageous political and economic alliances. Benefits of polygyny include maximizing the labor force and shared resources within a family, creating wide kinship connections, and attributing economic success to a male head of household.
Polygyny can also refer to various mating systems observed in other species. For example, in resource-based polygyny in the animal kingdom, males may control territories with valuable resources to attract mating opportunities with females. Examples include the yellow-rumped honeyguide and elephant seals.