comparison of deterministic and probabilistic calculation of ecological soil screening levels

882

Environmental Toxicology and Chemistry, Vol. 21, No. 4, pp. 882–890, 2002q 2002 SETAC

Printed in the USA0730-7268/02 $9.00 1 .00

COMPARISON OF DETERMINISTIC AND PROBABILISTIC CALCULATION OFECOLOGICAL SOIL SCREENING LEVELS

HELEN M. REGAN,*† BRAD E. SAMPLE,‡ and SCOTT FERSON††Applied Biomathematics, 100 North Country Road, Setauket, New York 11733, USA

‡CH2M HILL, 2485 Natomas Park Drive, Suite 600, Sacramento, California 95833, USA

(Received 13 December 2001; Accepted 2 October 2001)

Abstract—The U.S. Environmental Protection Agency (U.S. EPA) is sponsoring development of ecological soil screening levels(Eco-SSLs) for terrestrial wildlife. These are intended to be used to identify chemicals of potential ecological concern at Superfundsites. Ecological soil screening levels represent concentrations of contaminants in soils that are believed to be protective of ecologicalreceptors. An exposure model, based on soil- and food-ingestion rates and the relationship between the concentrations of contaminantsin soil and food, has been developed for estimation of wildlife Eco-SSLs. It is important to understand how conservative andprotective these values are, how parameterization of the model influences the resulting Eco-SSL, and how the treatment of uncertaintyimpacts results. The Eco-SSLs were calculated for meadow voles (Microtus pennsylvanicus) and northern short-tailed shrews(Blarina brevicauda) for lead and DDT using deterministic and probabilistic methods. Conclusions obtained include that use ofcentral-tendency point estimates may result in hazard quotients much larger than one; that a Monte Carlo approach also leads tohazard quotients that can be substantially larger than one; that, if no hazard quotients larger than one are allowed, any probabilisticapproach is identical to a worst-case approach; and that an improvement in the quality and amount of data is necessary to increaseconfidence that Eco-SSLs are protective at their intended levels of conservatism.

Keywords—Ecological soil screening levels Back calculation Superfund sites Probabilistic risk assessment Soilcontamination

INTRODUCTION

The U.S. Environmental Protection Agency (U.S. EPA), incooperation with various Department of Defense agencies, theDepartment of Energy, state environmental agencies, industryorganizations (e.g., the American Petroleum Institute and theAmerican Chemistry Council), and consultants, has developeddraft soil screening criteria for ecological receptors. These screen-ing criteria are collectively known as Ecological Soil ScreeningLevels or Eco-SSLs. In the Eco-SSL Guidance drafted by theU.S. EPA, it states that Eco-SSLs are concentrations of contam-inants in soils that are protective of ecological receptors thatcommonly come into contact with soil or ingest biota that livein soil. They are screening levels that should be used during step2 of the Superfund Ecological Risk Assessment (ERA) process(the screening-level risk calculation) to identify chemicals of po-tential concern that require further evaluation in the site-specificbaseline risk assessment. The Eco-SSLs are intentionally con-servative in order to provide confidence that contaminants thatcould present an unacceptable risk are not screened out early inthe ERA process. The U.S. EPA recognizes that, for many soiltypes and conditions, the Eco-SSLs may be conservative butnonetheless provide an acceptable balance of protectiveness andreasonableness (http://www.epa.gov/superfund/programs/risk/ecorisk/ecossl.htm) [1].

Exposure and effects for birds and mammals are typicallyexpressed in terms of a dosage in milligrams chemical/kilo-gram body weight/day. Wildlife Eco-SSLs are calculated bysolving a hazard quotient (HQ) model for the soil concentrationgiving a HQ of one, where HQ 5 exposure (mg/kg/d)/effects(mg/kg/d). Exposure in the wildlife HQ model is expressed as

* To whom correspondence may be sent ([email protected]).

a dose. The relationship between soil concentration and doseis a source of uncertainty in risk calculations. Section 4.3 ofthe draft guidance specifies how this exposure uncertainty isaddressed for calculating wildlife Eco-SSLs [1].

In this article, we investigate the exposure uncertainty usingMonte Carlo analysis and probability bounds analysis. TheU.S. EPA intends for Eco-SSLs to provide conservativescreening values that can be used to eliminate contaminantsclearly not associated with unacceptable risks [1, p 4-4]. Tothat end, the U.S. EPA has made decisions about what it con-siders to be reasonable and protective exposure parameter pointestimates for calculating Eco-SSLs. We will use results of ouranalysis to address whether we believe the Eco-SSLs derivedusing these point estimates are indeed conservative. We willalso compare the results of our Monte Carlo and probabilitybounds analyses to one another.

Calculation of Eco-SSLs

The U.S. EPA guidance requires that screening-level ex-posure estimates be conservative and deterministic [2; D.Charters, personal communication]. One concern about thedeterministic application of the Eco-SSL model (and otherexposure models for that matter) is that compounding con-servatism may result if values for parameters in the model areconsistently selected to be either high (or low) values fromeach respective distribution [3]. Decisions about appropriatelevels of conservatism are incorporated into the input param-eters at the outset and do not result in an explicit and quan-titative statement about the overall level of conservatism inthe result.

Probabilistic analyses, on the other hand, incorporate arange of values that represent the uncertainty in each of theparameters in calculations, and decisions about levels of con-

Probabilistic ecological soil screening levels for wildlife Environ. Toxicol. Chem. 21, 2002 883

servatism can then be applied to the output. The most commonmethod used to propagate uncertainty in calculations is theMonte Carlo method. A number of criticisms have been leveledat the application of the Monte Carlo method in risk assessmentin recent years [3–6]. The most prominent complaint is thatthe specification of accurate distributions for input parametersis near impossible when data are scarce. Hence, any singleinput distribution based on scant data is also highly uncertainand may misrepresent the parameter values. Another majorcriticism of Monte Carlo simulations concerns dependencyissues (i.e., correlations among model parameters). In manyapplications, the precise dependency structure between param-eters is not known.

Probability bounds analysis overcomes many of the criti-cisms leveled at Monte Carlo simulations [5–7]. This semian-alytical approach grew out of the theory of interval probabil-ities and Dempster–Shafer belief functions [8–10]. It allowsthe calculation of bounds on arithmetic combinations of prob-ability distributions when only bounds on the input distribu-tions are given. The approach allows an analyst to decide whatinformation is reliable and what is not. When the informationabout a distribution is very good, the bounds on the distributionwill be very tight. When the information is very poor, thebounds will tend to be much wider, representing weaker con-fidence about the specification of the distribution. This analysiscan be thought of as a sensitivity analysis that handles alluncertainties simultaneously but only produces upper and low-er bounds on the distributions of the endpoint variables withoutany indication of the relative likelihood of particular distri-butions within the range. Ignorance regarding parameter de-pendencies is represented by assigning the narrowest possiblebounds on the result for the full range of possible dependencystructures. The resultant bounds on a calculation are rigorousin that they are sure to enclose the true distribution providedthe input bounds enclose their respective distributions. Theyare also best possible bounds in that they do not overcom-pensate for the uncertainty [7]. In this article, we examine howdeterministic, Monte Carlo, and probability bounds analysescompare in dealing with the uncertainty in calculations of Eco-SSLs.

METHODS

Wildlife Eco-SSL model

Chapter 4 of the Draft Ecological Soil Screening LevelGuidance presents the derivation of the Wildlife Eco-SSL mod-el. The general form of the model is

(P 1 BAF) 3 soil 3 FIRsHQ 5 (1)TRV

where soil 5 chemical concentration of contaminant in soil(mg/kg dry wt), FIR 5 food ingestion rate (kg food (dry wt)/kg BW (wet wt)/d) (BW 5 body wt), Ps 5 soil ingestion asproportion of diet, TRV 5 toxicity reference value for con-taminant (mg (dry wt)/kg BW (wet wt)/d), and BAF 5 soil-to-biota bioaccumulation factor for contaminant for relevantbiota type.

With the assumption that HQ may not exceed one, this formof the model (also referred to as the forward equation) can besolved for the soil screening level to give the inverted equation,

TRVEcoSSL 5 (2)

FIR 3 (P 1 BAF)s

To select conservative Eco-SSL values, it is important tounderstand how the treatment of uncertainty influences resultsand the extent to which the various treatments affect the finalresult. To meet this end, a comparison was made of a deter-ministic strategy similar to that specified in the Draft Guidancebased on conservative parameter estimates, a deterministicstrategy based on central tendencies, a Monte Carlo proba-bilistic assessment, and probability bounds analysis. It shouldbe noted that, strictly speaking, the term Eco-SSL is reservedfor those values derived in the Draft Ecological Soil ScreeningLevel Guidance document [1]. For convenience of comparison,however, we are extending the use of this term to refer toquantities derived from Equations 1 and 2 regardless of themethod of dealing with uncertainty. We stress that this con-vention is merely to avoid confusion in the comparisons pre-sented in this present work and is not a rejection, recommen-dation, or endorsement of alternative Eco-SSL values.

The default method of Eco-SSL calculation set out in thedraft guidance [1] involves using conservative point estimatesfor each of the parameters in Equation 2, in this case, 90thpercentile values from the distribution of food ingestion rates,proportions of soil in diet, and bioaccumulation factors. Acorresponding conservatively low value is used for the toxicityreference value. The Eco-SSL is then calculated determinis-tically. This is the same approach taken for the deterministicEco-SSL based on central tendencies; however, median valuesare used in place of 90th percentiles. Monte Carlo simulations,on the other hand, use distributions for each parameter in thecalculation. Each distribution is sampled separately and theresultant random deviates are used in the calculation. This isperformed numerous times to arrive at a representative andsufficiently complete distribution for the Eco-SSL. Probabilitybounds analysis differs from both these calculations in thatbounds are assigned to the distributions for each parameter inthe calculation and then convolved through the model to pro-duce bounds on the resultant Eco-SSL.

For the purposes of this analysis, Eco-SSLs were calculatedfor the meadow vole (Microtus pennsylvanicus) and the north-ern short-tailed shrew (Blarina brevicauda) for an inorganiccontaminant (lead) and an organic contaminant (DDT) usingdeterministic and probabilistic methods. The two mammal spe-cies were chosen because they represent divergent foragingguilds and exposure pathways. Shrews are insectivores andingest soil-residing organisms with relatively high bioaccu-mulation factors. Meadow voles, on the other hand, are her-bivorous and ingest plants with much lower bioaccumulationfactors. The amount and type of data available for this analysisvaried with each species. The assessments for the meadowvole and the northern short-tailed shrew provide two examplesof the data typically available for this type of study and thesubsequent assumptions needed for parameter evaluation.

Parameter values

Food ingestion rate. The food ingestion rate (FIR) in Equa-tion 2 is defined as the (dry) weight of food ingested per gramof (wet) body weight per day and is calculated according toa linear regression model in [1,11,12]. Food intake rates forthe meadow vole and the shrew were calculated using bodyweight data from various sources in the literature. For themeadow vole, we used 11 data sources from [13–15], whilefor the shrew, 9 data sources were used from [15–18]. Thedata in the literature were presented in a variety of forms,

884 Environ. Toxicol. Chem. 21, 2002 H.M. Regan et al.

including means and standard deviations, ranges, and meansand ranges.

Probability bounds were assigned as normal distributionsfor data presented as means and standard deviations (as in theMonte Carlo simulations). The normal distribution was as-sumed realistic for body weight data when means and standarddeviations are available. For data in the form of ranges, prob-ability bounds were specified by the minimum and maximum.The upper and lower bounds were further constrained by themean for data in the form of means and ranges. In this way,the narrowest bounds on the cumulative probability distribu-tion, given the available data, were assigned without makingunjustified assumptions about the distribution shape. Proba-bility bounds analysis was performed by taking the envelopeof all the body weight distributions; i.e., the left bound wasassigned as the minimum value across all the distributions andthe right bound as the maximum value across all the distri-butions. The Monte Carlo and probability bounds analysis in-put parameters for the FIRs for meadow voles and shrewsappear in Tables 1 and 2, respectively, while the input for thedeterministic calculations appears in Table 3. The median and90th percentile values were selected from the Monte Carloresults. The resultant distributions for the FIRs for meadowvoles and shrews are shown in Figure 1a and b, respectively.

Proportion of soil in diet. The proportion of soil in the dietsof meadow voles and shrews was calculated using the modeland data presented in [1,19–21]. The data and distributionsfor each of the input parameters for the Monte Carlo analysisappear in Tables 1 (for meadow voles) and 2 (for shrews). Oneof the problems of incorporating uncertainty into calculationsof parameters that are constrained to take values between zeroand one (such as Ps) is that the model inputs may producebounds that lie outside the constraints. Simply truncating theresult to satisfy the constraints is ad hoc and ignores the un-derlying cause of the transgression. One reason why input datamight produce results that transgress the constraints is that thedata is incompatible across parameters. The model used for Ps

assumes that all the parameters pertain to the one animal andyet the data used for each parameter has been pooled acrossa number of individuals. Furthermore, different samples areused for each parameter estimate. In order to satisfy the con-straints for Ps, probability bounds were calculated via an it-erative process with all parameters initialized as in Tables 1and 2 and Ps initialized as the interval with a minimum valueof zero and a maximum value of one. The model for Ps wasinverted to solve for each parameter, in turn, with the updatedinputs serving as the new estimates for the subsequent cal-culations. This process was repeated until convergence wasreached. The result was a set of updated compatible parameterestimates and probability bounds for the constrained Ps. Themodel for Ps was used directly for the Monte Carlo analysis.Figure 2a and b displays the respective estimates of Ps formeadow voles and shrews using probability bounds analysisand Monte Carlo simulations.

Bioaccumulation factors for plants. Field data from [1,22]was used to construct distributions for lead uptake in plantsfor the Eco-SSL calculation for meadow voles. Probabilitybounds were assigned as Kolmogorov–Smirnov (K-S) 95%confidence intervals on the data. Figure 3a displays the re-sultant distributions for BAFPb for plants.

The bioaccumulation factor for DDT in plants was calcu-lated according to the regression model and data from [1,23].Data for log(Kow) was extracted from [24]. Monte Carlo sim-

ulations used an empirical distribution for log(Kow), whereasprobability bounds analysis used bounds constructed from K-S 95% confidence intervals. The input parameter estimatesappear in Table 1 and the resultant distributions are displayedin Figure 3b.

Bioaccumulation factors for earthworms. Field data from[25] was used to construct distributions for lead uptake inearthworms for the Eco-SSL calculation for shrews. An em-pirical distribution was constructed from the data for MonteCarlo simulations. Probability bounds were assigned as K-S95% confidence intervals on the data. Figure 3c displays theresultant distributions for BAFPb for earthworms.

Distributions for the bioaccumulation factor for DDT inearthworms was constructed using the model and data in[1,26]. The K-S 95% confidence intervals were used for theprobability bounds analysis using data from [24]. Table 2 pro-vides details of the parameter inputs for the calculation ofBAFDDT for earthworms for the Eco-SSL calculation forshrews. Figure 3d displays the resulting distributions.

Toxicity reference value. Toxicity reference values (TRVs)for lead and DDT were deterministic for all of the alternativestrategies. To be conservative, they were chosen as the min-imum of mammalian no-observed-adverse-effects levels(NOAELs) (draft data provided by U.S. EPA Eco-SSL TaskGroup on Wildlife Toxicity Reference Values and J. Burris,personal communication). The values used for the Eco-SSLcalculations appear in Tables 1 and 2.

Medians and 90th percentiles for all parameters (excludingTRVs) were selected from the Monte Carlo distributions. Thevalues for all the input parameters for meadow voles andshrews appear in Table 3. The Eco-SSL calculation was per-formed under assumptions of independence between all var-iables for the Monte Carlo simulations and under no assump-tions regarding dependencies for probability bounds analysis.Monte Carlo simulations of the inverted Equation 2 were per-formed with Crystal Ball 2000 Standard version 5.0 [27] with1,000 replicates in each simulation. All probability boundswere constructed using RAMAS Risk Calc [28]. Probabilitybounds analysis was performed by backcalculation [29–31] ofthe forward Equation 1, also using RAMAS Risk Calc.

Once the Eco-SSLs have been calculated by each method,the next question is how the various Eco-SSLs perform in thecontext of the apparent variability in all the parameters. Inother words, how sure are we that our level of conservatismof not exceeding a hazard quotient of one is satisfied giventhe prevailing uncertainty about the underlying ecological pro-cesses? To answer this question, each calculated Eco-SSL wassubstituted back into Equation 1 and probability bounds anal-yses were performed to determine the extent to which therespective Eco-SSL satisfied the hazard quotient constraint. Torepresent the true variability in each parameter, single distri-butions were selected from within the relevant probabilitybounds.

RESULTS

The Eco-SSLs for DDT and lead for meadow voles andshrews, as estimated by different methods, are summarized inTable 4; graphical presentations are displayed in Figure 4a to d.Regardless of receptor or chemical, probability bounds anal-yses consistently resulted in the lowest Eco-SSL estimates(Table 4). The Eco-SSLs based on deterministic application ofconservative parameter estimates were approximately 100times greater for meadow voles and from .200 to .1,000


Tab

le1.

Var

iabl

esfo

rth

efo

odch

ain

mod

elfo

rca

lcul

atin

gec

olog

ical

soil

scre

enin

gle

vels

(Eco

-SS

Ls)

for

wil

dlif

e.V

alue

sfo

rpa

ram

eter

sin

the

tier

1as

sess

men

tfo

rth

ew

ildl

ife

spec

ies

Mic

rotu

spe

nnsy

lvan

icus

(mea

dow

vole

)an

dth

eco

ntam

inan

tsP

ban

dD

DT.

Kow

5oc

tano

l/w

ater

part

itio

ning

coef

fici

ent

Des

crip

tion

Sym

bol

Val

ues

for

mea

dow

vole

(p-b

ound

s)V

alue

sfo

rm

eado

wvo

le(M

onte

Car

lo)

Soi

lin

gest

ion

aspr

opor

tion

ofdi

etin

endp

oint

spec

ies

Ps

y5

b5

a5

c5

y5 5

(b[1

2P

s]1

c3

Ps)

/(1

2a[

12

Ps]

)a

acid

-ins

olub

leas

hin

food

(dry

wt)

5[0

,0.

02]

dige

stib

ilit

yof

food

(dry

mas

s)5

[0.5

6,0.

96]

acid

-ins

olub

leas

hin

soil

(dry

mas

s)5

[0.9

,1]

acid

-ins

olub

leas

hin

scat

mm

m(0

.012

,0.

14,

0.08

9)

Ps

5b

5a

5c

5y

5

(b2

y1

ay)/

(ay

2c

1b)

b

acid

-ins

olub

leas

hin

food

(dry

wt)

5U

(0,

0.02

)di

gest

ibil

ity

offo

od(d

rym

ass)

5N

(0.7

6,0.

076)

acid

-ins

olub

leas

hin

soil

(dry

mas

s)5

U(0

.9,

1)ac

id-i

nsol

uble

ash

insc

at5

Tr(

0.01

2,0.

089,

0.14

)

Bod

yw

eigh

tof

endp

oint

spec

ies

BW

(g)

BW

5B

W1

5B

W2

5B

W3

5B

W4

5B

W5

5B

W6

5B

W7

5B

W8

5B

W9

5B

W10

5B

W11

5

enve

lope

(BW

i),a

i5

1,..

.,11

N(2

9.4,

4.4)

N(4

4.2,

6.3)

N(4

4.0,

10.3

)m

mm

(20.

4,48

.5,

32.5

)m

mm

(29.

2,47

.2,

35.6

)m

mm

(25.

1,62

.7,

38.2

)m

mm

(24.

4,63

.2,

38.8

)m

mm

(32.

0,71

.0,

48.8

)m

mm

(28.

0,56

.0,

36.8

)m

m(3

4.2,

46.5

)m

m(2

5.0,

45.0

)

BW

5B

W1

5B

W2

5B

W3

5B

W4

5B

W5

5B

W6

5B

W7

5B

W8

5B

W9

5B

W10

5B

W11

5

aver

age(

BW

i),b

i5

1,..

.,11

N(2

9.4,

4.4)

N(4

4.2,

6.3)

N(4

4.0,

10.3

)T

r(20

.4,

32.5

,48

.5)

Tr(

29.2

,35

.6,

47.2

)T

r(25

.1,

38.2

,62

.7)

Tr(

24.4

,38

.8,

63.2

)T

r(32

.0,

48.8

,71

.0)

Tr(

28.0

,36

.8,

56.0

)U

(34.

2,46

.5)

U(2

5.0,

45.0

)

Tot

alfo

odin

take

rate

for

endp

oint

spec

ies

FIR

(g/g

/d)

FIR

510

(a1

e)B

W(b

21)

b(b

ased

oneu

ther

ian

mam

mal

[her

bivo

re]

data

)F

IR5

10(a

1e)B

W(b

21)

b(b

ased

oneu

ther

ian

mam

mal

[her

bivo

re]

data

)a

50.

0752

,b

50.

579,

e5

N(0

,0.

28)

a5

0.07

52,

b5

0.57

9,e

5N

(0,

0.28

)

Soi

l-to

-bio

taP

bbi

oacc

umul

atio

nfa

ctor

for

plan

tsB

AF

Pb

Raw

data

used

toco

nstr

uct

dist

ribu

tion

wit

h95

%K

-Sbo

unds

for

lead

upta

kein

plan

tsD

istr

ibut

ion

cons

truc

ted

usin

gra

wda

tafo

rle

adup

take

inpl

ants

Soi

l-to

-bio

taD

DT

bioa

ccum

u-la

tion

fact

orfo

rpl

ants

BA

FD

DT

p-B

ound

sco

nstr

ucte

dvi

ath

eeq

uati

onB

AF

510

(b1

e)K

owm

b

b;

0.84

04,

m;

20.

419;

e5

N(0

,sq

rt(0

.492

2))

log(

Kow

);

raw

data

used

toco

nstr

uct

empi

rica

ldi

stri

buti

onw

ith

K-S

95%

confi

denc

ein

terv

als

Dis

trib

utio

nco

nstr

ucte

dvi

ath

eeq

uati

onB

AF

510

(b1

e)K

owm

b

b;

0.84

04;

m;

20.

419;

e5

N(0

,sq

rt(0

.492

2))

log(

Kow

);

raw

data

used

toco

nstr

uct

empi

rica

ldi

stri

buti

on

Tox

icit

yre

fere

nce

valu

efo

rP

bT

RV

Pb

(mg/

g/d)

Min

imum

50.

92M

inim

um5

0.92

Tox

icit

yre

fere

nce

valu

efo

rD

DT

TR

VD

DT

(mg/

g/d)

Min

imum

50.

8M

inim

um5

0.8

aN

ode

pend

ency

assu

mpt

ions

.b

Inde

pend

ence

assu

med

;m

mm

(x,

y,z)

5p-

boun

dsw

ith

min

imum

5x,

max

imum

5y,

and

mea

n5

z;m

m(x

,y)

5p-

boun

dsw

ith

min

imum

5x

and

max

imum

5y;

U(x

,y)

5un

ifor

mdi

stri

buti

on,

mea

n5

x,st

anda

rdde

viat

ion

5y;

N(x

,y)

5no

rmal

dist

ribu

tion

,m

ean

5x,

stan

dard

devi

atio

n5

y;T

r(x,

y,z)

5tr

iang

ular

dist

ribu

tion

,m

inim

um5

x,m

ode

5y,

max

imum

5z;

BW

5bo

dyw

eigh

t;F

IR5

food

inta

kera

te;

BA

F5

bioa

ccum

ulat

ion

fact

or.


Tab

le2.

Var

iabl

esfo

rth

efo

odch

ain

mod

elfo

rca

lcul

atin

gec

olog

ical

soil

scre

enin

gle

vels

(Eco

-SS

Ls)

for

wil

dlif

e.V

alue

son

lysp

ecifi

edfo

rpa

ram

eter

sin

the

tier

1as

sess

men

tfo

rth

ew

ildl

ife

spec

ies

Bla

rina

brev

icau

da(n

orth

ern

shor

t-ta

iled

shre

w)

and

the

cont

amin

ants

lead

and

DD

T.K

bw5

biot

a/so

ilw

ater

part

itio

ning

coef

fici

ent;

Kow

5oc

tano

l/w

ater

part

itio

ning

coef

fici

ent;

Koc

5w

ater

/soi

lor

gani

cca

rbon

part

itio

ning

coef

fici

ent;

f oc

5fr

acti

onof

orga

nic

carb

onin

soil

Des

crip

tion

Sym

bol

Val

ues

for

shor

t-ta

iled

shre

w(p

-bou

nds)

Val

ues

for

shor

t-ta

iled

shre

w(M

onte

Car

lo)

Soi

lin

gest

ion

aspr

opor

tion

ofdi

etin

endp

oint

spec

ies

Ps

y5

b5

a5

c5

y5 5

(b[1

2P

s]1

c3

Ps)

/(1

2a[

12

Ps]

)a

acid

-ins

olub

leas

hin

food

(dry

wt)

5[0

,0.

02]

dige

stib

ilit

yof

food

(dry

mas

s)5

[0.7

0,0.

94]

acid

-ins

olub

leas

hin

soil

(dry

mas

s)5

[0.9

,1]

acid

-ins

olub

leas

hin

scat

mm

m(0

.067

,0.

173,

0.10

4)

Ps

5b

5a

5c

5y

5

(b2

y1

ay)/

(ay

2c

1b)

b

acid

-ins

olub

leas

hin

food

(dry

wt)

5U

(0,

0.02

)di

gest

ibil

ity

offo

od(d

rym

ass)

5N

(0.8

2,0.

048)

acid

-ins

olub

leas

hin

soil

(dry

mas

s)5

U(0

.9,

1)ac

id-i

nsol

uble

ash

insc

at5

Tr(

0.06

7,0.

104,

0.17

3)

Bod

yw

eigh

tof

endp

oint

spec

ies

BW

(g)

BW

5B

W1

5B

W2

5B

W3

5B

W4

5B

W5

5B

W6

5B

W7

5B

W8

5B

W9

5

enve

lope

(BW

i),a

i5

1,..

.,9

N(1

6.4,

2.5)

N(1

9.8,

3.1)

N(1

5.9,

1.0)

N(2

2.2,

2.4)

mm

m(1

5.0,

29.0

,22

.0)

mm

m(1

1.0,

26.3

,17

.5)

mm

m(9

.9,

19.9

,14

.1)

mm

m(1

1.4,

24.8

,16

.3)

mm

(9.0

,18

.5)

BW

5B

W1

5B

W2

5B

W3

5B

W4

5B

W5

5B

W6

5B

W7

5B

W8

5B

W9

5

aver

age(

BW

i),b

i5

1,..

.,9

N(1

6.4,

2.5)

N(1

9.8,

3.1)

N(1

5.9,

1.0)

N(2

2.2,

2.4)

Tr(

15.0

,22

.0,

29.0

)T

r(11

.0,

17.5

,26

.3)

Tr(

9.9,

14.1

,19

.9)

Tr(

11.4

,16

.3,

24.8

)U

(9.0

,18

.5)

Tot

alfo

odin

take

rate

for

endp

oint

spec

ies

FIR

(g/g

/d)

FIR

510

(a1

e)B

W(b

21)

b(b

ased

oneu

ther

ian

mam

mal

[ins

ecti

vore

]da

ta)

FIR

510

(a1

e)B

W(b

21)

b(b

ased

oneu

ther

ian

mam

mal

[ins

ecti

vore

]da

ta)

a5

20.

5102

,b

50.

640,

e5

N(0

,0.

21)

a5

20.

5102

,b

50.

640,

e5

N(0

,0.

21)

Soi

l-to

-bio

taP

bbi

oacc

umul

atio

nfa

ctor

for

wor

ms

BA

FP

bR

awda

taus

edto

cons

truc

tdi

stri

buti

onw

ith

95%

K-S

boun

dsfo

rle

adup

take

inea

rth

wor

ms

Dis

trib

utio

nco

nstr

ucte

dus

ing

raw

data

for

lead

upta

kein

eart

hw

orm

s

Soi

l-to

-bio

taD

DT

bioa

ccum

ulat

ion

fact

orfo

rw

orm

s

BA

FD

DT

p-B

ound

sco

nstr

ucte

dvi

ath

eeq

uati

ons

Kbw

510

(b1

e)K

owm

b

b;

20.

6019

,m

;0.

9914

,e

5N

(0,

sqrt

(0.5

360)

)lo

g(K

oc)

50.

983

3lo

g(K

ow)

10.

0002

8lo

g(K

ow)

;ra

wda

taus

edto

cons

truc

t95

%K

-Sbo

unds

f oc

;m

mm

(0.0

043,

0.08

88,

0.01

69)

Ti5

Kbw

/(f o

c/K

oc)

Dis

trib

utio

nco

nstr

ucte

dvi

ath

eeq

uati

ons

Kbw

510

(b1

e)K

owm

b

b;

20.

6019

,m

;0.

9914

,e

5N

(0,

sqrt

(0.5

360)

)lo

g(K

oc)

50.

983

3lo

g(K

ow)

10.

0002

8lo

g(K

ow)

;ra

wda

taus

edto

cons

truc

tem

piri

cal

dist

ribu

tion

f oc

;T

r(0.

0043

,0.

0169

,0.

0088

8)T

i5

Kbw

/(f o

c3

Koc

)

Tox

icit

yre

fere

nce

valu

efo

rP

bT

RV

Pb

(mg/

g/d)

Min

imum

50.

92M

inim

um5

0.92

Tox

icit

yre

fere

nce

valu

efo

rD

DT

TR

VD

DT

(mg/

g/d)

Min

imum

50.

8M

inim

um5

0.8

aN

ode

pend

ency

assu

mpt

ions

.b

Inde

pend

ence

assu

med

;m

mm

(x,

y,z)

5p-

boun

dsw

ith

min

imum

5x,

max

imum

5y,

and

mea

n5

z;m

m(x

,y)

5p-

boun

dsw

ith

min

imum

5x

and

max

imum

5y;

U(x

,y)

5un

ifor

mdi

stri

buti

on,

mea

n5

x,st

anda

rdde

viat

ion

5y;

N(x

,y)

5no

rmal

dist

ribu

tion

,m

ean

5x,

stan

dard

devi

atio

n5

y;T

r(x,

y,z)

5tr

iang

ular

dist

ribu

tion

,m

inim

um5

x,m

ode

5y,

max

imum

5z;

BW

5bo

dyw

eigh

t;F

IR5

food

inta

kera

te;

BA

F5

bioa

ccum

ulat

ion

fact

or;

TR

V5

toxi

city

refe

renc

eva

lue.


Table 3. Values for each of the parameters and results for the ecological soil screening level (Eco-SSL)calculation from Monte Carlo simulations and probability bounds analysis. Probability bounds are

specified as a range onlya

Parameter

Monte Carlo simulations

Minimum Maximum Median90th

percentile

p-Bounds

Minimum Maximum

Meadow voleFIRPs

BAFPb

BAFDDT

TRVPb

TRVDDT

0.030.001.13 3 1024

1.52 3 1024

0.920.8

2.430.06

10.601.91

0.250.0130.110.018

0.560.0300.550.17

0.0360.001.13 3 1024

1.25 3 1024

0.920.8

2.630.08

10.604.77

ShrewFIRPs

BAFPb

BAFDDT

TRVPb

TRVDDT

0.020.003.81 3 1024

0.040.920.8

0.510.06

228.262,178.9

0.100.020.209.09

0.200.032.09

95.97

0.0260.003.81 3 1024

0.00150.920.8

0.490.07

228.26136,271

a See Table 2 for explanation of abbreviations.

Fig. 1. Food intake rate (FIR) for (a) meadow voles and (b) shrews.Regression coefficients and body weight data for FIR appear in Tables1 (for meadow voles) and 2 (for shrews). Estimates for FIR appearas p-bounds, distributions from Monte Carlo analyses, and 50th and90th percentiles of the Monte Carlo distributions.

Fig. 2. Proportion of soil in diet (Ps) for (a) meadow voles and (b)shrews. Probability bounds are calculated using an iterative updatingtechnique; Monte Carlo distributions are calculated directly from theequation in [1]. Estimates for Ps appear as p-bounds, distributionsfrom Monte Carlo analyses, and 50th and 90th percentiles of theMonte Carlo distributions.

times greater for shrews (Table 4). Deterministic calculationswith median values for all variables resulted in Eco-SSL es-timates that were approximately 10-fold greater than conser-vative deterministic Eco-SSLs. Finally, Eco-SSLs based on theinverted Monte Carlo simulation (the simulation according toEqn. 2) generally fell between the conservative and median-based deterministic estimates, depending on how the outputdistributions for the Monte Carlo-generated Eco-SSLs are in-terpreted (i.e., 10th percentile or minimum values; Table 4).

Comparison of the estimated Eco-SSL values to the dis-

tribution of background lead concentrations indicates that leadoccurs naturally at higher concentrations (;80–3,000 timeshigher) than the strictest screening value generated by prob-ability bounds analysis (Fig. 4b). Ninetieth percentile and me-dian deterministic Eco-SSLs fall at approximately the mini-mum and 95th percentiles of background, whereas the MonteCarlo-based Eco-SSLs generally exceed background. Thismeans that the uncertainty about the ecological effects fromlead on voles or shrews is too great to justify a practically


Fig. 3. Bioaccumulation factors (BAF) for (a) lead in plants, (b) DDTin plants, (c) lead in earthworms, and (d) DDT in earthworms. Theplant BAFs are used in the ecological soil screening level (Eco-SSL)calculations for meadow voles, while the earthworm BAFs are usedin the Eco-SSL calculations for shrews. The BAFs for lead in bothplants and worms were derived directly from field data (from [22] forplants and [25] for earthworms), whereas BAFs for DDT in plantsand earthworms were calculated according to equations in [1]. Esti-mates for the BAFs appear as p-bounds, distributions from MonteCarlo analyses, and 50th and 90th percentiles of the Monte Carlodistributions.

Fig. 4. Ecological soil screening levels (Eco-SSLs) for (a) DDT andmeadow voles, (b) lead and meadow voles, (c) DDT and shrews, and(d) lead and shrews. The Eco-SSLs corresponding to the probabilitybounds data were calculated via backcalculation of Equation 1, where-as the Monte Carlo analyses were performed on the inverted Equation2. Figure 4b also includes background distributions for lead from [25].Results for the Eco-SSL estimates result from calculations using p-bounds, Monte Carlo analyses, conservative point estimates (i.e., 90thpercentiles for food intake rate [FIR], Ps, and bioaccumulation factor[BAF] and a minimum for toxicity reference values [TRV]), and me-dians.

Table 4. Lead and DDT ecological soil screening level (Eco-SSL) values for meadow voles and shrewscalculated using each of the four methods; p-bounds analysis, deterministic using 90th percentiles and

minimums (for toxicity reference values [TRVs]), medians, and Monte Carlo simulation

Meadow vole

LeadEco-SSL(mg/kg)

DDTEco-SSL(mg/kg)

Shrew

LeadEco-SSL(mg/kg)

DDTEco-SSL(mg/kg)

p-BoundsDeterministic, 90th percentilesDeterministic, mediansMonte Carlo 10th percentile

(min)

0.0332.82

30.726.60

(0.34)

0.0637.17

102.916.95(0.83)

0.00822.17

42.7311.5(0.32)

1.2 3 1025

0.0420.880.07

(0.0)

useful screening level. This uncertainty is the likely result ofassumptions concerning chemical bioavailability and site usethat are incorporated into the Eco-SSL model. Section 6.3 ofthe Draft Guidance acknowledges that acquisition and com-parison of natural background levels is an important step to-ward evaluating whether observed concentrations are naturallyoccurring or released. The U.S. EPA is currently developingguidance on how to determine background conditions and onhow to use background levels in the assessment process.

Figures 5 and 6 display the results of substituting eachcalculated Eco-SSL back into Equation 1 to determine theresultant levels of conservatism with a comprehensive treat-ment of uncertainty. Results based on input distributions thatspan the entire range of plausible values for each parameterare presented in Figure 5. Results based on selecting conser-vative distributions from within the probability bounds (i.e.,distributions toward the right side of the plausible ranges iden-tified in Figs. 1 to 3) are presented in Figure 6. Thus, Figure5 describes entirely plausible sets of outcomes, whereas Figure6 represents worst-case assessments.

In Figure 5, the curves represent complementary cumula-tive distribution functions of the variation in hazard quotientsimplied by typical scenarios selected for the input distributionsand assuming independence among all variables. For the Eco-

SSL for DDT and shrews based on medians, there is an 80%chance that sites found to have acceptable contamination levels(and therefore exempted from further assessment or remedi-ation) exhibit HQs above one when assuming absolute con-servatism (Fig. 5a). In some cases, the values could be as largeas 100 or more. The Eco-SSL based on 90th percentiles ismore conservative than that based on medians, but even itallows HQs larger than unity under our level of conservatismwith a probability of about 40%, even under entirely plausiblescenarios about natural variability. The Eco-SSL resultingfrom probability bounds analysis never produces hazard quo-tients above one. There is a much lower chance (;15%) ofexceeding the HQ criterion for lead Eco-SSLs for meadowvoles based on 90th percentiles under typical scenarios andabout a 60% of exceedance with medians (Fig. 5b).

The curves in Figure 6 were also estimated using proba-bility bounds analysis. Each calculated Eco-SSL for DDT inshrews and lead in meadow voles was substituted into Equation1 along with the most conservative or right-most probabilitybound for each of the input parameters. No assumptions aboutdependencies were made. The results suggest that the viola-tions of the criterion of HQ , 1 could be quite severe. Thecurves represent the best possible upper bounds on the poten-tial exceedance risks. They should not be interpreted as pos-


Fig. 5. Magnitudes of realized hazard quotients for (a) DDT andshrews and (b) lead and meadow voles using plausible distributionsfor food intake rate (FIR), Ps, and bioaccumulation factors (BAFs)that span the p-bounds range. Realized hazard quotient distributionswere calculated according to Equation 1 using the ecological soilscreening levels (Eco-SSLs) obtained from probability bounds anal-ysis and Monte Carlo analysis and from conservative and medianestimates.

Fig. 6. Magnitudes of realized hazard quotients for (a) DDT andshrews and (b) lead and meadow voles using conservative distribu-tions for food intake rate (FIR) and Ps and bioaccumulation factors(BAFs) from the right-most bound of the p-bounds range. Realizedhazard quotient distributions were calculated according to Equation1 using the ecological soil screening levels (Eco-SSLs) obtained fromprobability bounds analysis and Monte Carlo analysis and from con-servative and median estimates.

sible distributions themselves. For instance, they should notbe taken to imply that HQ under any particular scenario willsurely be larger than one. They do tell us, however, how likelyit is that any HQ threshold could be exceeded. For instance,for Eco-SSLs for DDT (in shrews, Fig. 6a) and lead (in mead-ow voles, Fig. 6b) based on median values, there is an almost30 and 10% chance, respectively, that soil concentrations iden-tified as presenting no risk may actually exceed the HQ con-straint by a factor of 100.

DISCUSSION

Although the inverted equation (Eqn. 2) may be used tocalculate deterministic Eco-SSLs, for probabilistic analyses,the forward equation must be untangled (or the Eco-SSL mustbe backcalculated) in such a way that respects the criterionthat the HQ not be larger than one [29–31]. If median oraverage point values are used to represent variables such asfood ingestion rate, proportion of soil ingested, or bioaccu-mulation factors, the resulting Eco-SSL is likely to be unac-ceptably nonconservative. When this Eco-SSL is validated bysubstitution into Equation 1 along with modest estimates ofdistributions for the other variables, HQs much greater thanone can be obtained (e.g., Fig. 5). When the realized hazardquotient is greater than one, the defining criterion for the soilscreening level calculation is violated. Using a Monte Carloprobabilistic approach in which entire distributions, rather thanpoint estimates, are used in the calculation does not escapethe problem. Even with assumptions that ensure the distri-butions are representative of their respective ranges of uncer-tainty (i.e., they span the range of possible values and are not

extreme in any way), the Eco-SSL resulting from Monte Carlosimulations may also yield HQ values larger than one (e.g.,Fig. 5). In fact, for lead and meadow voles, there is a 60%chance the HQ value will be larger than one. There is a 5%chance that the HQ will be larger than 100. In general, theexceedance may actually be much worse. Figure 6 shows thebest possible upper bound on how bad they might be. It showsthere is at most a 40% chance the HQ value is larger than 100for Eco-SSLs for DDT and shrews and potentially a 5% chancethat it is larger than 10,000 for Monte Carlo simulations. Suchoutcomes may arise if the distributions used in the Eco-SSLcalculation are not in the middle of their possible ranges or ifthere are nonlinear dependencies among the variables.

We recognize that the method proposed in the Draft Guid-ance for calculating deterministic Eco-SSLs has built-in levelsof conservatism based on conservative model parameter es-timates. Our analysis demonstrates how much larger these Eco-SSLs are than those derived probabilistically via backcalcu-lation and with absolute conservatism. The differences hereare largely due to the uncertainty in the input parameters ratherthan discrepancies in levels of conservatism; however, ourresults show how the combination of both the uncertainty andthe chosen level of conservatism compare with the worst-casescenario under a more comprehensive treatment of uncertainty.For the Monte Carlo analysis, where the underlying level ofconservatism is identical to that of the probability bounds anal-ysis, the substantial difference is induced by uncertain distri-butions and by not backcalculating. Probabilistic methods doallow the regulatory criterion to be specified in a differentway, however. For instance, we might ask what the soil screen-


ing level would be that ensures at least a 90% chance that theHQ is less than one. This 10% window would relax the con-straint and allow a probabilistic approach to yield an answerthat is different from that produced by a strict worst-case ap-proach. It would also make the imposed level of conservatismquantitatively explicit. We believe that probability boundsanalysis is most useful as a tool for identifying the extent ofuncertainty in model application and can assist in reducingthis uncertainty. For instance, it is clear from Figure 3 thatbioaccumulation factors contribute a great deal to the overalluncertainty. Improving the quality and amount of data for theseparameters would be a start in reducing the uncertainty in Eco-SSL calculations.

CONCLUSIONS

A number of conclusions can be made from the resultsobtained in this exploration. Although the inverted Equation2 may be used to calculate deterministic Eco-SSLs, it shouldnot be used to compute probabilistic Eco-SSLs. Instead, theforward Equation 1 must be backcalculated. Even using dis-tributions in a Monte Carlo approach may lead to hazard quo-tients that can be substantially larger than one under reasonablelevels of conservatism. This is due to a combination of as-sumptions about dependencies, the representation of all un-certainty in the input parameters as single, precise probabilitydistributions, and the failure to backcalculate Equation 1. Ifno hazard quotients larger than one are allowed, any proba-bilistic approach is identical to a strict worst-case approach.Quantitatively explicit levels of conservatism can be imposedusing probabilistic methods that allow this constraint to berelaxed.

Acknowledgement—We are grateful for the assistance of the U.S. EPAEco-SSL Task Groups on Wildlife Toxicity Reference Values andExposure Models for Wildlife Species and Janet Burris. We also thankLev Ginzburg and David Myers for valuable discussion and com-ments. This work was supported in part by the U.S. EPA and theAmerican Chemistry Council as well as by a National Cancer Institutegrant to Applied Biomathematics (9R44CA81741). Any opinions,findings, conclusions, or recommendations expressed in this publi-cation are those of the authors and do not necessarily reflect the viewsof the National Cancer Institute. Helen Regan completed part of thiswork while a postdoctoral associate at the National Center for Eco-logical Analysis and Synthesis, a center funded by the National Sci-ence Foundation (grant DEB-0072909), the University of California,and the Santa Barbara campus.

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