Thur writes

sparrowhawks (another post)
Predators may lower the population if they recover themselves from
population losses such as the agro-chemicals combined with
gamekeeper slaughter.

Apart from raptors, and then many years ago, I haven't heard of
gamekeepers shooting birds other than some corvids.

Shooting crows/pigeons was once the only shooting allowed to
farmworkers, which kept populations down 30 years ago.

Apart from DDT, banned in the early 1970's, do you have any evidence of
significant bird losses due pesticides?

Once established though, there should be a "natural" balance between
prey and predator numbers?

Yes, but this need not be, and often is not, a stable population as in
the same every year.

--
Oz
This post is worth absolutely nothing and is probably fallacious.
DEMON address no longer in use.