1O ppb is much but the approach via a mathematical model to simulate the
response of a colony is rather original:

http://onlinelibrary.wiley.com/doi/10.1111/ele.12188/abstract


Chronic sublethal stress causes bee colony failure
John Bryden, Richard J. Gill, Robert A. A. Mitton,Nigel E. Raine and Vincent
A. A. Jansen

Abstract
Current bee population declines and colony failures are well documented yet
poorly understood and no single
factor has been identified as a leading cause. The evidence is equivocal and
puzzling: for instance, many
pathogens and parasites can be found in both failing and surviving colonies
and field pesticide exposure is
typically sublethal. Here, we investigate how these results can be due to
sublethal stress impairing colony
function. We mathematically modelled stress on individual bees which impairs
colony function and found
how positive density dependence can cause multiple dynamic outcomes: some
colonies fail while others
thrive. We then exposed bumblebee colonies to sublethal levels of a
neonicotinoid pesticide. The dynamics
of colony failure, which we observed, were most accurately described by our
model. We argue that our
model can explain the enigmatic aspects of bee colony failures, highlighting
an important role for sublethal
stress in colony declines.

Ecology Letters, (2013) 16: 1463-1469

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