I'm working on some old data from Columbus, GA that I should have published years ago. So it goes.
This is something that has been bugging me for over a decade. If you look at the relationship below which shows how native bird diversity changes with urbanization.
Urbanization is quantified as the amount of impervious surface a km around where they were counted. The data are transformed but the whole scale goes from 0% to 100% (just take the sine of any of those numbers to transform back into a percent).
Note that the relationship is positive from 0 to 20% and negative >20% urbanization. The post 20% is easy to understand: as urbanization comes to dominate a landscape, native birds find fewer habitats.
Less than 20% there is little urbanization. That's easy to get. But what is there? In a real complex landscape, where there is not city there can be anything. It can be completely forested, agriculture, suburban, a mix of all the above. I think that explains all the noise on the low-urbanization side.
I think what's lacking - in any statistical approach that I'm aware of - is how to model with factors whose effect can vary with their values. So in this case, I bet species richness increases with urbanization at first because a little bit of urbanization adds some birds associated with urban habitats but there's still enough natural habitat to have those birds persist but as urbanization increases the natural habitat gives way and birds are lost.
So I need to invent a statistical method.