1

Appendix E Additional Details for the Derivation of USGS Trophic Transfer Factor for 

Corbula amurensis1

The original text concerning the derivation of a trophic transfer factor (TTF) for Corbula 

amurensis (C. amurensis) from field data for the San Francisco Bay and Delta estuary is given on 

pages 21–23 of USGS (2010). That original text is reproduced here and annotated with notes 

(Note 1 through Note 4) which refer to additional explanatory materials presented at the end of 

the discussion. The notes: a) clarify the text; and b) refer to a spreadsheet (also presented at 

the end of the discussion) that shows the actual calculations, validation, and checks of the 

entries used in the derivation. See especially Note 4 that addresses specific questions 

concerning the calculations of TTFC. amurensis one decision or assumption at a time. The derived 

TTFC. amurensis is used in subsequent modeling of the selenium concentrations for C. amurensis as 

predicated from selenium concentrations for suspended particulate material for the estuary. 

Tables 13, 14 and 15 and Figure 2.2a in USGS (2010) provide additional illustrations of the 

agreement between model predictions and field observations. 

Trophic Transfer Factors (TTFs) Clam (C. amurensis) 

The choice of food web is critical to modeling success because the particulate material 

to prey kinetics of bioaccumulation differs widely among invertebrates (Presser and Luoma, 

2010). TTFC. amurensis derived from laboratory experiments averaged 6.25 over a range of 

assimilation efficiencies, ingestion rates, and efflux rate constants (Presser and Luoma, 2010). 

This average is within a range of 0.6 to 23 for invertebrate species, with TTFs for species of 

bivalves being the highest (Presser and Luoma, 2010). 

Experimental physiological biodynamic parameters and rates are derived under 

idealized conditions in the laboratory. These biodynamic equations can be adjusted for a 

specific ecosystem by incorporating data from that system (Presser and Luoma, 2010) (see 

Note 1). TTFC. amurensis is developed here for the estuary from a mechanistic equation for 

quantifying the biodynamics of C. amurensis and estuary-specific data for suspended 

particulate material (i.e., the food for clams). Selenium bioaccumulated at steady state by C. 

amurensis is calculated using a site-specific modification of equation (3) 

CC. amurensis = [(AE) (IR) (Csuspended particulate material] ÷ (ke) (14) 

where (AE) (IR)/ke is defined as TTFC. amurensis and Cfood is defined as the Se concentration in 

estuary suspended particulate material (Csuspended particulate material). Among field data available to 

quantify site-specific biodynamics of C. amurensis are spatially and temporally matched 

datasets (see Note 2) from estuary transects (Doblin et al., 2006) for:

 suspended particulate material Se concentration;

 suspended particulate material C concentration;

 percentage of C in suspended particulate material; and 

 

1 Also known as Potamocorbula amurensis or P. amurensis. 
2

 percentages of suspended particulate elemental Se, adsorbed Se, and organo-Se. (See Note 

3)

Our site-specific approach here differs from broader approaches where 1) laboratory 

data for biodynamic parameters such as AE and IR of particulate material may be generalized; 

2) particulate Se concentrations may be an average of several phases of material (i.e., 

particulate Setotal); or 3) field data may be sparse and thus applied across an entire watershed 

(Presser and Luoma, 2009). 

In general, for the purposes of a Bay-Delta location and estuarine processes, the 

suspended particulate material Se concentration carries with it assumptions about Se being 

associated primarily with organic material (detritus and living organisms). This allows us to 

determine IR on the same organic material basis (assuming clams seek organic material in the 

suspended particulate material) and to refine AE to account for suspended particulate material 

speciation (i.e., divide AE into three components of Se in suspended particulate material and 

their individual bioavailabilities). These assumptions are all rooted in well-established biological 

understanding of bivalve feeding (Cammen, 1980; Lopez and Levinton, 1987). We ignore the 

possibility of uptake directly from water by the clams because that has been shown in a large 

body of work to be trivial (Luoma and Rainbow, 2005). 

Justifications for values used in each parameter of the equation for a site-specific 

approach are (see Note 4): 

1. We can either assume that Se is associated with carbonaceous materials or Se is spread 

across all suspended particulate material. For the former, the concentration of Se is 

expressed as μg Se/g C. We obtain μg Se/g C by dividing the suspended particulate material 

Se concentration (μg Se/g suspended particulate material) by mg C/mg suspended 

particulate material. For the present calculations we employ suspended particulate material 

Se concentrations as justified below. 

2. IR is determined by filtration rate (125 L/g clam/d, Cole et al., 1992) multiplied by C (median 

= 0.4 mg C/L) to achieve the units (g C/g clam/d) in the suspended particulate material at 

each sampling. In the average condition in the estuary, clams ingest 5% of their body weight 

per day in C across all days for which data is available. At an average of 2% C in suspended 

particulate material (again, the average across all data) they ingest 2.5 times their body 

weight per day in total suspended particulate material. If IR is calculated at each of three 

low river discharge months where data is available, the average is 1.7 g suspended 

particulate material/g clam/d. Experience has indicated that the ingestion model is more 

accurate when actual outcomes are used (or averaged) for the generic situation (i.e., 1.7 g 

suspended particulate material/g clam/d) as compared to taking the average of each 

component of the outcome and calculating a generic average. Therefore, we recommend 

using 1.7 g suspended particulate material/g clam/d for modeling. 
3

3. The derivation of a refined site-specific AE based on individualized bioavailabilities of Se in 

suspended particulate material uses observed fractions of particulate organo-Se, adsorbed 

Se, or elemental Se found in the estuary (Doblin et al., 2006) combined with individual AEs 

for those particulate Se species from the literature (living phytoplankton, AE = 60%; 

adsorbed on seston, AE = 40%; elemental, AE = 0%; Schlekat et al., 2004; Wang et al., 1996). 

The equation is: 

AE = (fraction organic particulate Se) (AE organic particulate Se) + (fraction adsorbed 

particulate Se) (AEadsorbed particulate Se) + (fraction elemental particulate Se) 

(AEelemental particulate Se) (15)

For example, if a site-specific sample of suspended particulate material collected in the 

estuary contains 45% Se in phytoplankton at an assumed AE of 60%; 30% Se adsorbed on 

seston at an assumed AE of 40%; and 25% elemental Se in sediment at an assumed AE of 0%, 

then the composite AE = (0.45 x 0.6) + (0.30 x 0.40) + (0.25 x 0) = 0.39 or 39% AE. 

4. We apply the efflux rate constant derived experimentally (Lee et al., 2006): ke = 0.03/d. 

5. When we model for times when all data are available from the estuary, we use all data from 

that sampling date. When we model generically we employ mean parameters. 

Given the above protocol and assumptions, we can directly calculate C. amurensis Se 

concentrations for comparison to observed Se concentrations to validate predictions or 

calculate a TTFC. amurensis for use in modeling. If the data and assumptions given above are 

used in a site-specific modification of equation (4) 

(IR) (AE) ÷ ke = TTFclam (16) 

then 

TTFclam = (1.7 g suspended particulate material/g clam/d) (0.39) ÷ 0.03 = 22.1

Or, in terms of a C. amurensis Se concentration, if a 0.84 μg/g dw suspended particulate 

material Se concentration is assumed, then 

CC. amurensis = (0.84 μg Se/g) (1.7 g/g/d) (0.39) ÷ 0.03/d = 18.6 μg Se/g 

Salinity-specific or transect specific Se concentrations and TTFs for C. amurensis can be 

calculated using the same protocol as above, but with percentages of C and suspended 

particulate material Se species observed in that transect. Thus, an individual C. amurensis Se 

concentration and TTFC. amurensis can be calculated from each matched set of data from the five 

suspended particulate material transects for the estuary (Doblin et al., 2006), making the 

predictions and derivations as detailed as the data permit. This data-intensive approach yields a 

mean TTFC. amurensis of 17.1 excluding April, 1999 transects data as out of the norm (i.e., El Niño 

condition in the estuary) or 18.1 using the focused approach for Suisun Bay-Carquinez Strait. 
4

We assume a TTFC.amurensis of 17 in modeling scenarios here. The range of TTFs across all 

estuarine conditions was 14-26. These values are higher than laboratory-derived values 

primarily because ingestion rates are higher in these field systems than in experiments. This is 

the first calculation of a field-derived TTF for a marine bivalve species.

Notes:

Note 1: Why use Bay data to modify coefficients? The basic biodynamic model calculates Se 

bioaccumulation at steady state using the solution to the differential equation described 

earlier: 

Css clam = (CSPM * AE * IR) / Ke.

Coefficients for the model can be (and have been) directly derived in the laboratory (Ke, AE and 

IR) under controlled conditions for specific species. In nature, however, the value for each 

coefficient varies to some degree with environmental conditions. In many cases there is not 

enough data from the ecosystem of interest to estimate the influences of environmental 

conditions. But that is not the case for San Francisco Bay. The model in this report 

incorporated specific influences on each coefficient using experimental studies of 

environmental influences; environmental data from two different transects in the Bay and basic 

principles of bivalve biology. Then TTFs were derived (or an average TTF was derived) based 

upon variations in those conditions in the Bay. 

Uncertainty. The environment-derived TTFs add multiple factors to the equation. In pure 

statistical terms, each factor comes with an uncertainty. The overall uncertainty is the sum of 

the uncertainties in each factor. On the other hand, the laboratory estimates of TTF carry an 

inherent uncertainty that cannot be quantified, stemming from the unknown (unincorporated) 

influence of environmental factors. Ultimately we can test the net influence of the uncertainty 

by evaluating how well the model predictions fit independently determined Se concentrations 

in clams.

Note 2: Se and environmental data are used to derive one TTF for the Bay. Water-column data 

and clam data were collected during the same cruise. Clams were not available from all 

stations. For the Bay-wide TTF, we calculated a predicted composite TTF from all stations in the 

transect. To validate that prediction, we compared the predicted TTF to an observed TTF based 

upon clams collected from the cruise. The field data on clam concentrations were direct 

observations, completely independent of any data from the water-column. 

Note 3: Water-column data sufficient to model concentrations in clams were collected by 

Doblin et al. (2006) at 18 locations in the November 1999 transect (see data below in the

spreadsheet). At each location we calculated Se concentrations in clams at steady state, then 

determined the TTF at that location from the ratio of predicted clam/observed SeSPM at each 
5

site. The variation among the 18 locations is indicative of the degree of variability driven by 

both natural variability in the estuary and the summed uncertainty of the model. Using all 

values from the transect to determine a mean gives the final value more statistical power than 

would any individual value. This assumes the TTF is a constant, an assumption in which there 

may be some small uncertainty. The very close fit between the observed Se concentrations in 

the clams and the predicted concentrations (or TTFs) suggests the uncertainties do not distort 

the final answer. 

Note 4: The following table goes through the calculations for the TTF one decision or 

assumption at a time. A spreadsheet follows showing data and calculations from the transect

of Nov 1999. This is a low flow period. All the data necessary for the calculations and their 

alternatives are shown in the spreadsheet.

Question Decision or Assumption

How should Se concentrations

in suspended particulate

material (SPM) be expressed?

One way to express Se concentrations in SPM is as a function 

of the organic material in particulate materials, because 

anthropogenic Se is primarily biogenically concentrated onto 

particles and mostly concentrated in the organic fraction of 

the SPM. The organic fraction can be represented by the 

carbon content of the SPM. The proportion of the SPM that is 

inorganic varies widely in SF Bay, changing with changes in 

processes like river inflows and wind-derived resuspenion. If 

the fraction of inorganic material in an SPM sample increases 

and the organic fraction stays the same, the total Se 

concentration in the sample could artificially decrease, due to 

the dilution effect of inorganics (adding more weight than Se). 

Vice versa is true if the inorganic fraction decreases. To 

eliminate this potential uncertainty we did a set of 

calculations assuming that all Se is associated with the organic 

fraction of the sediment represented by carbon. Se was 

expressed as μg Se per g carbon per liter. As stated in the text: 

“We obtain μg Se/g C by dividing the suspended particulate 

material Se concentration (μg Se/g suspended particulate 

material) by mg C/mg suspended particulate material.” 

Column K of the spreadsheet shows the outcome of this 

calculation for each site in the transect. The uncertainty 

associated with this estimate (and the systematic estuarine 

variability) is expressed as the variability from one site to 

another. This is also represented in the first term in the 

equation in column J of the Nov 1999 spreadsheet calculation 

of TTF. See also point 1 in the justification paragraph in the 
6

text. 

How should the ingestion rate

(IR) be determined? 

Cole et al. (1992) conducted the most comprehensive study of 

ingestion rate in C. amurensis. This was a flume study in 

which IR was determined for a large number of animals under 

a variety of conditions (including different flow rates, feeding 

condition) typical of the estuary. The inclusion of different 

flow rates makes this study far superior to other studies of 

this issue. From those studies we assumed 125 L water was

ingested per g clam per day. To determine how much carbon 

would be ingested at each site in the transect we multiplied 

this by either the mg C/L that was determined at each site to 

obtain ingestion rate of C per day; or the mg SPM to express 

ingestion in terms of total mass of suspended material. 

Column L of the spreadsheet shows the outcome of this 

calculation; variability is indicative of uncertainty + estuarine 

variability, as described above. IR is represented in the 

second term in the equation in column J of the Nov 1999 

transect. 

How should Se concentrations 

be expressed in the general 

modeling, where such data is 

not available?

If we use the C-based determination of SPM we must use the 

C-based determination of IR. If we use the mg SPM basis for 

Se concentration, we must use the mg SPM basis for IR. To 

determine the influence of using either we predicted Se in 

clams using both approaches and compared them. The 

outcome, of course, was exactly the same because the C term, 

or the mg SPM term arithmetically cancel (see columns S and 

T of the spreadsheet). The calculation does also illustrate that 

the data and the assumptions were internally consistent and 

that either approach is equally valid to determining C and IR.

 

What is the best bay-wide 

ingestion rate for the general 

modeling?

One way to address the uncertainty in any individual 

determination of IR from the field data is to do the calculation 

under a variety of conditions and gain statistical power by 

averaging the results. The resultant IR from a transect such as 

that in Nov 1999 would then be representative of the Bay as a 

whole. Point 2 explains that. To collect even more statistical 

power we also determined IR from additional transects and 

from the TSM data collected with the monthly suspended 

sediment determinations by Doblin et al. (2006). The average 

IR from Nov 1999 was 2.5 g/g clam/day. The average from 

Doblin et al. (2006) collections during low flows (Sep – midNov, 1996-2002) was 1.7 g/g clam/d. Other low flow transects 

also showed IR in this range. We recommend that the 1.7 g/g 
7

clam/d value be employed in further modeling because it is at 

the low end of this range and came from only stations directly 

connected to the clam sampling. 

How should assimilation 

efficiency (AE) be determined? 

AE is determined in the laboratory with pure food sources. 

Data are available for pure algal cultures; field-collected 

detritus and elemental Se, as cited in the text. Doblin et al. 

(2006) determined the distribution of Se between elemental 

Se, organic Se and what they called “adsorbed Se” at every 

site in the Nov 1999 transect. We assumed the detrital AE 

determined by Wang et al. (1996) represented “adsorbed” Se; 

consistent with the biogenic processes that concentrate Se in 

the water-column. Instead of using one AE determined from 

pure cultures, which is often the case when data is limited, we 

partitioned the AE into three parts based upon the AE of each 

and the relative abundance of each fraction of Se in the SPM 

as determined at each site by Doblin et al. (2006). Outcomes 

are in column O in the spreadsheet. Variability across the 

transect shows effects of uncertainty + systematic estuarine 

variability.

Determination of 

concentrations in clams.

The water-column data used above is completely independent 

of clam data collected in the transects. The assumptions and 

uncertainties of the model are tested by the difference 

between the predicted clam concentrations and observed 

clam concentrations. These are independently determined 

values and there is no a priori reason they should agree if the 

model does not work. The fact that the model predictions 

are in the same general range as the observations speaks to 

the veracity of the model assumptions. As noted above 

averaging predictions from the entire transect has more 

power than any one determination. The extremely close fit 

between the mean predicted clam concentration and the 

mean observed clam concentrations shows that the model, 

despite its assumptions and uncertainties, gives a reasonable 

representation of what is actually happening in nature. The 

report shows details on the validation calculations. 

How did we reach the 

conclusion about the TTF?

As the spreadsheet for Nov 1999 shows, the mean TTF across 

all stations in Nov 1999 was 18.9, the standard deviation was 

47% of the mean and the 95% confidence limits were ± 3.9. 

So from this one transect a defensible TTF would range from 

15.9 – 22.8. We did a similar calculation for a transect from 

Oct. 1998 for which all data were available (employing an IR of 
8

1.7 g/g clam/d). The mean TTF was 17.6, the standard 

deviation was 28% of the mean and the 95% CI was ± 2.2. A 

defensible TTF would range from 15.4 – 19.8. These values 

give a sense of the uncertainty in the calculations. 

Independent transects result in a coherent set of TTFs with a 

relatively small confidence interval, especially for field data. 

The mean across all transects, as stated in the text, was 17.1. 
9

References

Cammen, 1980: L.M. Cammen. 1980. Ingestion rate: An empirical model for aquatic deposit 

feeders and detritivores. Oecologia, v. 44, no. 3, p. 303-310.

Cole et al., 1992: B.E. Cole, Thompson, J.K., and Cloern, J.E. 1992. Measurement of filtration 

rates by infaunal bivalves in a recirculating flume. Marine Biology, v. 113, p. 219 – 225.

Doblin et al., 2006: M.A. Doblin, Baines, S.B., Cutter, L.S., and Cutter, G.A. 2006. Sources and 

biogeochemical cycling of particulate selenium in the San Francisco Bay estuary. Estuarine, 

Coastal, and Shelf Science, v. 67, no. 4, p. 681-694. 

Lopez and Levinton, 1987: G.R. Lopez and J.S. Levinton. 1987. Ecology of Deposit-Feeding 

Animals in Marine Sediments. Quarterly Review of Biology, Vol. 62(3): 235-260. 

Luoma and Rainbow, 2005: S.N. Luoma and P.S. Rainbow. 2005. Why is metal bioaccumulation 

so variable? Biodynamics as a unifying concept. Environmental Science and Technology, v. 39, 

no. 7, p. 1921-1931. 

Presser and Luoma, 2009: T.S. Presser and S.N. Luoma. 2009. Modeling of selenium for the San 

Diego Creek watershed and Newport Bay, California. U.S. Geological Survey Open-File Report 

2009-1114, 48 p. At: http://pubs.usgs.gov/of/2009/1114/ .

Presser and Luoma, 2010: T.S. Presser and S.N. Luoma. 2010. A Methodology for Ecosystem 

Scale Modeling of Selenium. Integrated Environmental Assessment and Management, v. 6, no 

4, p. 685-710 (plus Supporting Information). At: 

http://wwwrcamnl.wr.usgs.gov/Selenium/Library_articles/Presser_Luoma_2010_IEAMv6no4_6

85_710p.pdf .

Schlekat et al., 2004: C.E. Schlekat, D.G. Purkerson and S.N. Luoma. Modeling selenium 

bioaccumulation through arthropod food webs in San Francisco Bay, California, USA. 

Environmental Toxicology and Chemistry, v. 23, no. 12, p. 3003-3010. 

Wang et al., 1996: W.-X Wang, N.S. Fisher and S.N. Luoma. 1996. Kinetic determinations of 

trace element bioaccumulation on the mussel Mytilus edulis. Marine Ecology Progress Series, v. 

140, p. 91-113. 
Cutter/Doblin transect Nov, 1999 w/equation

equations original check

TTFclam = (AE) (IR)/ke calculated calculated calculated calculated calculated calculated assigned calculated calculated calculated calculated TTFclam

Cclam Se = [(AE) (IR) (Cparticulate)]/ke salinity TSM carbon particulate Se particulate Se particulate inorganic Se particulate elemental Se particulate organic Se clam ppm dw ug Se/g C IR C in SPM IR AE ke TTF Carbon TTF SPM clam ppm dw clam ppm dw calc clam/particulate

Station # mg/L mg/L nmol/g ug/g fraction fraction fraction based on C fraction based on SPM based on C based on SPM

1 32.17 13.32 0.50 10.81 0.84 0.167 0.076 0.757 20.55 22.69 0.062 0.037 1.665 0.44 0.03 0.906 24.38 20.55 20.55 24.4

2 29.71 9.75 0.53 9.95 0.78 0.196 0.268 0.536 9.78 14.38 0.066 0.054 1.219 0.31 0.03 0.680 12.61 9.78 9.78 12.6

3 28.50 4.15 20.97 1.64 0.368 0.402 0.230 0.47 0.03

4 27.21 12.04 0.45 11.04 0.86 0.105 0.489 0.406 10.64 23.26 0.056 0.037 1.505 0.25 0.03 0.457 12.35 10.64 10.64 12.4

5 26.90 14.60 0.24 9.18 0.72 0.000 0.000 1.000 18.70 43.79 0.030 0.016 1.825 0.43 0.03 0.427 26.13 18.70 18.70 26.1

6 23.14 13.51 0.29 6.88 0.54 0.280 0.548 0.172 3.49 24.93 0.036 0.022 1.689 0.12 0.03 0.140 6.50 3.49 3.49 6.5

7 22.22 11.54 0.15 10.23 0.80 0.441 0.331 0.229 9.59 63.34 0.018 0.013 1.442 0.25 0.03 0.151 12.03 9.59 9.59 12.0

8 21.53 19.38 0.25 5.42 0.42 0.648 0.829 0.000 3.74 32.29 0.032 0.013 2.422 0.11 0.03 0.116 8.84 3.74 3.74 8.8

9 17.76 12.89 0.21 13.02 1.02 0.131 0.393 0.476 18.70 62.92 0.026 0.016 1.611 0.34 0.03 0.297 18.42 18.70 18.70 18.4

10 15.58 14.31 0.69 8.46 0.66 0.545 0.256 0.198 8.75 13.74 0.086 0.048 1.788 0.22 0.03 0.637 13.26 8.75 8.75 13.3

11 15.19 13.35 0.25 12.21 0.95 0.031 0.331 0.638 19.93 51.06 0.031 0.019 1.669 0.38 0.03 0.390 20.93 19.93 19.93 20.9

24 13.81 38.10 0.37 7.43 0.58 0.152 0.519 0.329 13.75 58.88 0.047 0.010 4.762 0.15 0.03 0.233 23.73 13.75 13.75 23.7

25 11.18 27.80 0.30 8.16 0.64 0.471 0.335 0.194 14.32 59.62 0.037 0.011 3.475 0.19 0.03 0.240 22.49 14.32 14.32 22.5

12 13.10 12.82 0.27 10.99 0.86 0.383 0.546 0.071 7.69 40.58 0.034 0.021 1.603 0.17 0.03 0.190 8.97 7.69 7.69 9.0

13 11.36 32.52 0.47 7.78 0.61 0.209 0.225 0.565 21.10 41.81 0.059 0.015 4.066 0.26 0.03 0.505 34.78 21.10 21.10 34.8

14 9.10 37.03 0.47 7.35 0.57 0.154 0.162 0.684 23.91 45.43 0.058 0.013 4.628 0.27 0.03 0.526 41.73 23.91 23.91 41.7

15 8.26 27.89 6.85 0.53 0.366 0.251 0.382 0.20 0.03

16 6.32 21.62 0.54 9.80 0.76 0.297 0.373 0.330 16.70 30.51 0.068 0.025 2.703 0.24 0.03 0.547 21.84 16.70 16.70 21.8

17 4.65 27.75 0.25 6.42 0.50 0.399 0.404 0.197 8.03 55.31 0.031 0.009 3.468 0.14 0.03 0.145 16.06 8.03 8.03 16.1

18 2.39 20.16 0.75 7.24 0.56 0.212 0.055 0.733 14.06 15.14 0.094 0.037 2.520 0.30 0.03 0.929 24.90 14.06 14.06 24.9

19 0.00 22.02 1.18 7.22 0.56 0.516 0.491 0.000 6.00 10.49 0.148 0.054 2.752 0.12 0.03 0.572 10.66 6.00 6.00 10.7

20 0.00 14.48 0.18 9.46 0.74 0.000 0.343 0.657 12.95 60.61 0.022 0.012 1.811 0.29 0.03 0.214 17.55 12.95 12.95 17.6

21 0.00 24.81 0.49 7.09 0.55 27.79 0.062 0.020 3.101 0.03

13.12 0.415 18.91 13.12 13.12 18.9

8.983943136 Stdev

3.937314331

Appendix E Additional Details for the Derivation of USGS Trophic Transfer Factor for Potamocorbula amurensis Page 10