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# KABAM Version 1.0 User's Guide and Technical Documentation - Appendix G - Description of Equations Used to Calculate Dietary-based and Dose-based EECs, Toxicity Values, and RQs for Mammals and Birds Consuming Contaminated Aquatic Organisms

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## Appendix G. Description of Equations Used to Calculate Dietary-based and Dose-based EECs, Toxicity Values, and RQs for Mammals and Birds Consuming Contaminated Aquatic Organisms

Exposures of birds and mammals to pesticides accumulated in tissues of aquatic organisms are calculated by the KABAM tool. Relevant toxicity data are also calculated by KABAM based on input data from toxicity studies for birds and mammals. The equations used to estimate exposure and to adjust toxicity values and to calculate RQs depicted in Tables 14-15 of the KABAM tool are described below.

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• ### G.1 Food Ingestion Rates

Dry food ingestion rates (FIdry) are estimated for mammals and birds using allometric equations that relate food intake with body weight (Equations G1 and G2, respectively). FI is calculated in kg dry food/kg-bw day and BW is animal body weight in kg.

Equation G1

FIdry = (0.0687 * BW0.822) / BW      (mammals)

Equation G2

FIdry = (0.0582 * BW0.651) / BW      (birds)

Food intake (FI) values are converted from food dry weight/kg-bw day to food wet weight/day using the wet weight of the assigned diet of each mammal and bird (Equation G3). The variable Pi represents the fraction of diet of the mammal or bird containing prey item i (an aquatic organism). The variable VWBi represents the fraction of water in the body of the prey item i.

Equation G3

FIwet = FIdry / [1 - ∑(Pi * VWBi)]

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• ### G.2 Drinking Water Intake Rates

Drinking water intake rates (DW) for mammals and birds are calculated based on Equations G4 and G5 (USEPA 1993); where BW represents the body weight (in kg) of the animal for which the drinking water intake is being assessed. Resulting units of DW are L/day.

Equation G4

DW = (0.099 * BW0.90)      (mammals)

Equation G5

DW = (0.059 * BW0.67)      (birds)

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• ### G.3 Dose-based EECs

Dose-based EECs are estimated assuming that pesticide intake is a function of the amount of pesticide contained in the food and drinking water of an animal. The dose-based EEC is derived according to Equation G6. In this equation, pesticide intake through food is calculated as the sum of the products of the fraction of each prey item in the diet (Pi) and the pesticide tissue residue concentration for each prey item (CBi; µg/kg-ww). The sum of the pesticide residues ingested through food is converted into units of mg pesticide/kg food. This value is then multiplied by the intake rate for wet food (kg food/kg-bw day). The resulting value is in units of mg pesticide/kg-bw day. Pesticide intake through drinking water is calculated by multiplying the concentration of the pesticide in water (CWTO, mg/L) by the water intake (DW in units of L/d) and dividing by the bodyweight of the mammal or bird of concern. This results in units of mg pesticide/kg-bw day. The sum of pesticide intake through diet and through drinking water is the dose-based EEC.

Equation G6

Dose-based EEC = ∑(Pi * CBi) * FIwet + [(CWTO * DW) / BW]

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• ### G.4 Dietary-based EECs

Dietary-based EECs are estimated assuming that pesticide intake is a function of the amount of pesticide contained in the food of an animal. This differs from the dose-based EECs in that pesticide exposure through drinking water is not considered. In addition, the dietary-based exposure value is not adjusted for the relative amount of food consumed per day by animals of different sizes. The dietary-based EEC is derived according to Equation G7. In this equation, the pesticide intake through food is calculated as the sum of the products of the fraction of each prey item in the diet (Pi) and the pesticide tissue residue concentration for each prey item (CBi; µg/kg-ww).

Equation G7

Dietary-based EEC = ∑(Pi * CBi)

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• ### G.5 Adjusted Dose-based Toxicity Values

Available dose-based toxicity values are adjusted for the weights of the animal tested (e.g., laboratory rat, mallard duck) and of the animal for which the risks are being assessed (e.g., mink, bald eagle). These adjustments are made for mammals and birds according to Equations G8 and G9, respectively (USEPA 2006). In these equations, AT = adjusted toxicity value; LD50 or NOAEL = endpoint reported by toxicity study; TW = body weight of tested animal (350g rat; 1580g mallard, 178 g Northern bobwhite quail or weight defined by the model user for an alternative species); AW = body weight of assessed animal; x = Mineau scaling factor. Chemical specific values for x may be located in Mineau et al. 1996). If no chemical specific data are available, the default value of 1.15 should be used for this parameter. Methods for adjusting toxicity values are consistent with those used by T-REX (USEPA 2008a).

Equation G8

AT = (LD50or NOAEL) (TW / AW)0.25      (mammals)

Equation G9

AT = LD50(AW / TW)(x - 1)      (birds)

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