Carbaryl, Carbofuran, and Methomyl - National Marine Fisheries ...

exposure is greater; alternatively, the spike will be small when few prey are available and/or the
exposure toxicity is low.
Below are the mathematical equations used to derive Figures 2, 3, and 4.
Figures 2A and 3A use a step function:
time < start; exposure = 0
start ≤ time ≤ end; exposure = exposure concentration(s)
time > end; exposure = 0.
Figures 2B and 3B use a sigmoid function:
y = bottom + (top – bottom)/(1 + (exposure concentration/EC50)^slope).
For 2B, y = AChE activity, top = Ac, bottom = 0.
For Figure 3B, y = prey abundance, top = Pc (in this case 1), bottom = Pf.
Figures 2D, 2E, and 4C use a linear function (the point-slope form of a line):
y = m*(x – x1) + y1.
For 2D, m = Mfa, x1 = Ac, and y1 = Fc.
For 2E, m = Mrf (computed as Rc/Fc), x1 = Fc, and y1 = Rc.
For 4C, m = Mgr, x1 = Rc, and y1 = Gc.
Figure 2C uses a series of exponential functions:
time < start; y = c
start ≤ time ≤ end; y = c – (c – i)*(1 – exp(-ke*(time – start)))
time > end; ye = c – (c – i)*(1 – exp(-ke*(end – start)))
y = ye + (c – ye)*(1 – exp(-kr*(time – end))).
For Figure 2C, c = Ac, i = Ai, ke = ln(2)/AChE effect half-life, kr = ln(2)/AChE recovery
half-life. For Figure 2C the value of ye is calculated to determine the amount of inhibition
that is reached during the exposure time, which may not be long enough to reach the
maximum level of inhibition.
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