Final answer:
Dominant female red deer are most likely to use display behavior to assert dominance by aggressively vocalizing to intimidate rivals. This action reflects their role in a polygynous mating system where control over resources attracts males and is more energy-efficient than physical combat.
Step-by-step explanation:
The dominant female red deer likely engage in behavior that asserts their dominance over other females. This does not involve displaying submissive postures as that would contradict their dominant status. Competing for territories could be part of their behavior, but it is more about defending an existing territory rather than seeking out new territories. Forming cooperative alliances could be a strategy, but it is predominantly seen in species with complex social structures.
Given the biology of red deer and similar animals, the dominant females are more likely to use display behavior to communicate their dominance and control over resources in their territory. This is aligned with the concept of polygynous mating systems, where females control resources to attract multiple males. Display behavior for dominance can be seen across many animal species and is generally safer and uses less energy than engaging in actual combat. Therefore, the most plausible option is that dominant female red deer engage in aggressively vocalizing to intimidate rivals, which is a form of display behavior.