> [Calculus 101]
> d(C)/d(t) = kC
> Expecting C to get to zero is not science.

"Zero" is not what was promised by the manufacturer.
What was promised was "complete degradation", meaning "below the limit of
detection".
Detection falsifies the assurances made.

If this were a debate, the equation would get a laugh from the audience, but
no points for the debater.
Such an over-simplified one-factor model seems a deliberate attempt at
misrepresentation.
There are many factors simultaneously in play, and most of them are designed
into the pesticide from the get-go.

First, tweaking water solubility and adsorption to soil will limit runoff.
You want low water solubility and good soil adsorption to keep the pesticide
from wandering off. The problem is that plants run on water, like all living
things, so you can't have too low a water solubility for systemics.  Of
course, if runoff results in soil erosion, the pesticide then moves with the
eroded soil, but I think it should be clear that water moves faster and
further than soil can.

The other common breakdown scenarios are (just off the top of my head): 

a) reactions with oxygen or free radicals
b) catalyzed by sunlight (indirect photolysis). 
c) photolysis (direct)
d) hydrolysis
e) pH
f) microorganisms

So, in this case, we have Time, Distance, and the accelerated breakdown of
at least both sunlight and water, as the pesticides are transported in
surface water from the agricultural site(s) to the very non-agricultural
detection sites, so the pesticides are both in enough water to transport
them, and exposed to sunlight during all daylight hours, as they are
transported at the surface.

Regardless, the claims of "complete breakdown" made by the manufacturers
would seem to have already baked in the expectation that the pesticide would
soon degrade to INDETECTABLE levels, even at the site of use, let alone far
away from the site of use.   For this reason the EPA publishes long and
thoughtful musings on the "Fate In The Environment" of pesticides.

Breakdown characteristics are designed into the pesticide products, so any
product that fails to meet the claims made by the manufacturer is simply a
defective product.  Pesticide apologists will feign a scoffing sound and
intone "nothing ever goes to zero", but that is not what was claimed. The
manufacturer claimed in its representations to the EPA that the pesticide
would degrade below the limit of detection, which is clearly a non-zero
value. 

Bottom line here, if the stuff can accumulate in a ditch, all those
"pollinator conservation agricultural set-asides" become taxpayer-funded
pollinator poisoning stations.  Talk about unintended consequences!  If the
persistence is sufficient to allow detection far away, even at trace levels,
the equation "d(C)/d(t) = kC" tends to say that the pesticides are more and
more concentrated as one moves from the initial detection site back towards
the use site.

Now this is (mostly) linear, not square law at all, so the degradation rate
is not so much the issue as the transport.  It is reasonable to say that the
transport will run out before the degradation process completes in every
scenario except a large river or pond.  But note well that these samples
were taken from wetlands, so water was not  lacking to break down the
pesticides.

So, the simple question remains - why were the pesticides still detectable
at all in all four seasons if this stuff is supposed to break down in water?
As a beekeeper, I don't really care "why" or "how", the detections alone
prompt me to call the pesticide product defective.

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