I know the habitat specialization of each species individually, but I am not sure how to calculate this index for bird community. Anyone know any index or bibliography about it?
I think you can get that data with the help of multitrophic network analysis (bipartite package in R). This package has functions that allow you to explore details of specialization with two approaches: 1) for each species in the interaction network and 2) the specialization of the entire network.
Are you studying terrestrial or aquatic birds? I have published several papers on dietary and habitat specialization that are available in my files on Research Gate, but these all deal with the genus Larus. When you discuss specialization do you mean habitat use, nesting habitat, diet or all of the above? These can be very different among species and among habitat categories.
There is several studies that used this indices of specialization of entire community and by species:
Ramos-Robles M, Andresen E, Díaz-Castelazo C. 2016. Temporal changes in the structure of a plant-frugivore network are influenced by bird migration and fruit availability. PeerJ 4:e2048 https://doi.org/10.7717/peerj.2048 (entire community)
Blüthgen N, Menzel F, Blüthgen N. 2006. Measuring specialization in species interaction networks. BMC Ecology 6:9 (entire community)
Martínez-Adriano CA, Díaz-Castelazo C, Aguirre-Jaimes A. 2018. Flower-mediated plant-butterfly interactions in an heterogeneous tropical coastal ecosystem. PeerJ 6:e5493https://doi.org/10.7717/peerj.5493 (at species level)