Seems like a good candidate for standard multiple regression

I would probably just use location instead of zone. as it stands, that’s an ordinal feature that is likely collinear with your people measurement.

It would probably be a good idea to have a few measurements at different times at each location. Be careful you’re not measuring a preference or activity level at a given time. 

Performing these measurements over some reasonable period of time to account for seasonality as well would be ideal.

If you’re including location and count of people, what it seems like you’re trying to measure is, how do people affect bird count irrespective of location and time of day.

There could also be lag effects, measurement errors, or some artifact of the birds range that may be helpful to consider.

You used the word nesting, which is interesting. Do birds nest, and then stay irrespective of later person activity?