This is quoted from: http://www.hastingsreserve.org/Resident%20Web%20Pages/Koenig%20Web%20Pages/AWIntroPoster/AWposter.html

"Acorn Woodpeckers have one of the most bizarre mating systems of any bird in the world. They are COOPERATIVE BREEDERS and live in groups composed of up to 6 COBREEDER MALES, 3 JOINT-NESTING FEMALES, and NONBREEDING HELPERS of both sexes.

COBREEDER MALES are brothers and/or fathers and their sons competing for matings with the JOINT-NESTING FEMALES, who are sisters or a mother and her daughter who lay their eggs in the same nest cavity. Offspring produced from this communal nest may remain in their natal group for several years as NONBREEDING HELPERS, during which time they help feed younger siblings at subsequent nests.

This kind of mating system is known as POLYGYNANDRY. All individuals within the group are close relatives except that cobreeder males are not related to joint-nesting females. INCEST AVOIDANCE is maintained because helpers only inherit and become cobreeders following REPRODUCTIVE VACANCIES when the breeders of the OPPOSITE sex die and are replaced by unrelated birds from elsewhere. Reproductive vacancies are often filled by a unisexual set of siblings who compete against other sibling groups in spectacular events called POWER STRUGGLES. Winners of power struggles become cobreeders in the new group; losers return home and resume nonbreeding helper status."

The two fighting on the post, falling to the ground, and continuing to fight on the ground, are females. This is presumably a power struggle.