I do not have any data information to support their relationship.  Hence, I cannot answer your question.  My research area is in statistics.  Without data information, I cannot answer any question.

Hi Ming, my PhD dealt with something similar, in the Brazilian savanna aka Cerrado. Basically you have there 3 "types" of birds: Forest dependent, forest semi dependent and forest independent, something like that. See Silva, J. M. C. 1995. Birds of the Cerrado Region, South America. Steenstrupia 21:69-92.

Glad to discuss further this. Unfortunately I never got to publish my thesis and its currently in Portuguese.

cheers

 Hi Ming, maybe our work can help with your research question

https://www.researchgate.net/publication/270161397_Natural_grasslands_in_the_Chaco._A_neglected_ecosystem_under_threat_by_agriculture_expansion_and_forest-oriented_conservation_policies

Article Natural grasslands in the Chaco. A neglected ecosystem under...

Hi Ming,  Yours is a really broad question, the answer to which depends upon which kinds of birds (woodland, grassland, specialist, generalist, etc), the specific types of agricultural lands, the biogeographic region in which you are interested, and a host of other factors.   See Faaborg et al. Eco Apps 2010 pp 398-418, Robinson et al. 1995 Science pp 1987-1990, and Benson et al. Eco Apps 2013 pp 879-887 for a broad background on some of what you're interested in, but if you focus your question further you'll find it easier to get a clearer answer.

There have been, of course,  many many studies on the effects of habitat loss, degradation and fragmentation upon species, of which the consequences for 'farmland' birds of the intensification of agriculture, and recent agri-environment schemes aimed at reversing biodiversity loss is one. I would say the study of the effects of anthropogenic activities upon the functioning of ecosystems and interactions of species is the eye-of-the-storm from which all modern ecology research emanates. The theory of biogeography and its wide-ranging research suggests heterogeneous, connected landscapes are most rich and abundant in species, and this usually decreases as habitats become more homogenous, fragmented, and isolated. Sorry if this answer is overly general, but I agree with the above answers that parameters need to be established and variables eliminated to be able to either conduct an effective study or answer more specifically the question. However the following papers on farmland birds may be of interest:

Glemnitz et al. (2015) Regionalizing land use impacts on farmland birds. Environmental Monitoring and Assessment, 187 (336), 1-21

Kleijn et al. (2011) Does conservation on farmland contribute to halting the biodiversity decline?  Trends in Ecology & Evolution, 26 (9), 474-481

Gregory  et al. (2004) The state of play of farmland birds: population trends and conservation status of lowland farmland birds in the United Kingdom. Ibis, 146 (Suppl. 2), 1–13

Good luck!

You could have a look at this paper which presents a synthesis about habitat heterogenity and farmland birds:

http://www.cb.iee.unibe.ch/content/publications/2012/index_eng.html

Look for Vickery and Arlettaz

I'm definitely not an expert but , I worked with hummingbirds in three types of habitat suffering different disturbances at the same altitude (Andean montane forest). I evaluated how hummingbirds change their food preferences (specialist or generalist) when the resources decrease in richness and abundance. I observed directly 60 parcels in each habitat and placed mist nets. I also collect pollen from the bill, throat an head from the birds to compare it with the pollen I collected from the flowers. I haven't published this work yet.

Best regards.

You have some excellent suggestions among those presented.  I'll add only this which strikes me as a general principle:  Consider the native species that evolved in your ecoregion/area of interest, especially ecological specialists.  Those specialists will likely be the least compatible with stressors such as urbanization or high-intensity row-cropping. Once you identify those most sensitive species, try to summarize the general habitat on which they depend.  (Not all will use the same habitat, but likely many will.) Now consider this question about the landscape: does the matrix of that landscape include the habitat on which those most sensitive species depend?  If so, then the landscape is likely to provide suitable habitat for those species.  If not, then it is likely that those sensitive species are declining in that landscape. 

This is the general approach I pursue in developing indicators of ecological condition/biotic integrity using landbirds. 

Article Bird Guilds as Indicators of Ecological Condition in the Cen...

Thanks you all for your excellent suggestion!