There seem to be a couple different questions around this phenomenon. Part of this is pointed out in the paper I talked about yesterday by Plumpton & Lutz (1996), in which the females were heavier, but the males were larger on every measure of body size. The authors suggested that it could have been sampling error because of the breeding season, but maybe it's something else.
Swaddle and colleagues (2000) list a bunch of different birds who display RSD (e.g., hawks and vultures (Accipitridae), falcons (Falconidae), sandpipers and snipe (Scolopacidae), phalaropes (Charadriidae), jacanas (Jacanidae), skuas (Stercorariidae), boobies (Sulidae), frigate birds (Fregatidae), owls (Strigiformes), cuckoos (Cuculidae), hummingbirds (Trochilidae), manakins (Pipridae), and some ratites (Struthioniformes)). These birds show (what I'm going to naively call) complete RSD. That is, the females are larger than the males on all traits.
Swaddle and colleagues look at the fairy wren, where the story is far less clear.
Some species of Fairy wren (Maluridae) demonstrate complete RSD, whereas others demonstrate independence between body parts. That is, the males might have longer tarsus length whereas the females have longer tails. This suggests independence of features for RSD (and maybe sexual dimorphism in general?).
Most theories of sexual dimorphism (in primates, at least) suggest that males are larger in order to protect access to mates, and by extension access to resources. What might it mean for a species to have sexual selection working independently on different traits? Swaddle and colleagues (2000) state that such a generalist theory won't work with the (elegant) evidence they found. They found that RSD occurs in tail length during the breeding season, suggesting that the shorter tails of the males might be selected for by females (and are used extensively in the males' mating displays).
What might this mean if we look at RSD (or SD generally) and the traits as independently selected for, rather than generally selected for. Instead of all over size differences = sexual dimorphism for mate/territory defence or attraction, perhaps different traits are selected for for different reasons. In some species this happens consistently that one sex is larger, in other species, maybe it happens independently?
Of course, I'm now going to see what folks say about burrowing owls and RSD.....
And you really should read this paper -- they do a beautiful job incorporating behavioural evidence, morphology, and phylogenetic modelling.
Swaddle, J.P., Karubian, J., & Pruett-Jones, S. (2000). A novel evolutionary pattern of reversed sexual dimorphism in fairy wrens: implications for sexual selection. Behavioural Ecology, 11(3), 345-349.
