Final answer:
The greater sage grouse engages in polygynous mating, where one male mates with multiple females. Monogamous mating contrasts this with pairing between one male and one female, which can last for a season or lifetime. Polyandrous mating, where one female mates with several males, is less common and seen in species like seahorses.
Step-by-step explanation:
The mating system where one male mates with many females is known as polygynous mating. In this system, the females may establish territories separating from other females and attract males to the resources they control. This behavior results in a few males being attracted to many females within each territory, which is opposite of polyandrous mating, where one female mates with many males, an example of which can be seen in seahorses and pipefish.
In contrast, monogamous mating involves one male pairing with one female for at least one breeding season, and sometimes for life. This system may be favored under conditions where males can increase reproductive success by helping to rear offspring, preventing other males from mating with the female, or through female-enforcement, ensuring the male's resources are not split between multiple offspring from different females.