Table 2.

Summary of Empirical Metal Bioavailability Models

Metal/Species	Endpoint	Modela	N	Adj. R2	Reference
Aluminum
Ceriodaphnia dubia	Chronic	ln(EC20) = −41.026 + (0.525 × ln[DOC]) + (2.201 × ln[Hard]) + (11.282 × pH) – (0.663 × pH2) – (0.262[ln(Hard) × pH])	23	0.73	DeForest et al. 2018, USEPA 2017
Pimephales promelas	Chronic	ln(EC20) = −14.029 + (0.503 × ln[DOC]) + (3.443 × ln[Hard]) + (3.131 × pH) – (0.494[ln(Hard) × pH])	22	0.87	DeForest et al. 2018, USEPA 2017
Pseudokirchneriella subcapitata	Chronic	ln(EC20) = −61.952 + (1.678 × ln[DOC]) + (4.007 × ln[Hard]) + (17.019 × pH) – (1.020 × pH2) – (2.04[ln(DOC) × pH]) – (0.556[ln(Hard) × pH])	27	0.96	DeForest et al. 2018, USEPA 2017
Copper
Pimephales promelas	Acute	log(LC50) = −0.308 + (0.192 × pH) + (0.136[pH × log DOC])	21	0.92 b	Welsh et al. 1993, 1996
Pimephales promelas	Acute	log(LC50) = −0.856 + (0.166 × pH) + (0.095[pH × log DOC]) + (0.237 × Ca)	18	0.82 b	Welsh et al. 1993, 1996
Pimephales promelas	Acute	log(LC50) = −1.003 + (0.195 × pH) + (0.104[pH × log(DOC)]) + (0.211 × Ca)	17	0.82 b	Welsh et al. 1993, 1996
Pimephales promelas	Acute	log(LC50) = −1.003 + (0.195 × pH) + (0.104[pH × log(DOC)]) + (0.211 × Ca)	18	0.79 b	Welsh et al. 1993, 1996
Pimephales promelas	Acute	log(LC50) = −0.426 +( 0.061 × pH) + (0.005[pH × log(colour)]) + (0.116 × Hard)	17	0.89 b	Welsh et al. 1993, 1996
Daphnia magna	Acute	EC50[Cu2+] (nM) = 308 + (42.6 × Ca [mM]) – (41.3 × pH)	25	0.53 b	De Schamphelaere et al. 2002
Daphnia magna	Chronic	NOEC = −160.5 + (7.652 × DOC [mg/L]) + (25.50 × pH)	35	0.75 b	De Schamphelaere and Janssen 2004
Daphnia magna	Chronic	EC50 (μg/L) = −212.4 + (10.41 × DOC [mg/L]) + (34.36 × pH)	35	0.76 b	De Schamphelaere and Janssen 2004
Pomacea paludosa	Acute	log(LC50) = 0.540 + (0.008 × Age [d]) + (0.024 × DOC) + (0.120 × pH)	14	0.92 b	Rogevich et al. 2008
Ceriodaphnia dubia	Acute	ln(LC50) = −9.535 + (6.703 × ln[DOC]) + (0.144 × ln[Hard]) + (1.511 × pH) – (0.776[ln(DOC) × pH])	87	0.78	Brix et al. 2017
Daphnia magna	Acute	ln(LC50) = −4.005 + (0.947 × ln[DOC]) – (0.254 × ln[Hard]) + (0.628 × pH) + (0.101[ln(Hard) × pH])	307	0.87	Brix et al. 2017
Daphnia obtusa	Acute	ln(LC50) = −6.245 + (4.224 × ln[DOC]) + (0.139 × ln[Hard]) + (1.131 × pH) – (0.353[ln(DOC) × pH]) – (0.171[ln(DOC) × ln(Hard)])	53	0.89	Brix et al. 2017
Daphnia pulex	Acute	ln(LC50) = −9.932 + (0.6931 × ln[DOC]) + (0.172 × ln[Hard]) + (1.502 × pH) – (0.782[ln(DOC) × pH])	35	0.92	Brix et al. 2017
Pimephales promelas	Acute	ln(LC50) = −6.744 + (1.620 × ln[DOC]) + (1.065 × ln[Hard]) + (0.925 × pH) – (0.241[ln(DOC) × ln(Hard)])	206	0.80	Brix et al. 2017
Daphnia magna	Chronic	ln(EC20) = 0.200 + (0.848 × ln[DOC]) + (0.235 × ln[Hard]) + (0.172 × pH)	77	0.87	Brix et al. 2017
Pooled Model	Acute	ln(LC50) = InterceptSpeciesi + (0.786 × ln[DOC]) + (0.582 × ln[Hard]) + (0.966 × pH)	688	0.81	Brix et al. 2017
Lead
Ceriodaphnia dubia	Acute	ln(LC50) = −6.994 + (0.589 × ln[Ca]) + (0.992 × ln[DOC]) + (0.745 × pH)	23	0.82	Esbaugh et al. 2011
Pimephales promelas	Acute	ln(LC50) = 0.932 + (0.784 × ln[DOC]) + (0.443 × ln[ionic strength (mM)])	25	0.63	Esbaugh et al. 2011
Ceriodaphnia dubia	Chronic	ln(EC50) = −5.168 + (1.001 × ln[DOC] (μM)) + (0.322 × ln[TCO2] (μM) ) + (0.371 × ln[Na] (μM) )	22	0.55	Esbaugh et al. 2012
Lymnaea stagnalis	Chronic	ln(EC50) = −2.919 + (1.089 × ln[DOC] (μM))	7	0.82	Esbaugh et al. 2012
Philodina rapida	Chronic	ln(EC50) = 19.376 - (3.018 × pH) + (1.503 × ln[Ca] (μM))	6	0.92	Esbaugh et al. 2012
Zinc
Daphnia pulex	Acute	ln(LC50) = 3.196 + (0.284 × ln[DOC]) + (0.845 × ln[Hard])	25	0.58	CCME 2016
Daphnia magna	Acute	ln(LC50) = 3.083 + (0.191 × ln[DOC]) + (0.865 × ln[Hard])	7	0.97	CCME 2016
Daphnia spp. Pooled	Acute	ln(EC50) = 3.224 + (0.240 × ln[DOC]) + (0.833 × ln[Hard])	32	0.81	CCME 2016
Oncorhynchus mykiss	Chronic	ln(LC10) = 7.041 + (0.999 × ln[DOC]) + (0.886 × ln[Hard]) – (0.937 × pH)	14	0.79	CCME 2016

Models based only on hardness or with adjusted R² <0.50 are excluded.

^aUnless otherwise noted, units for metals are μg l⁻¹ and units for DOC, hardness, and calcium are mg l⁻¹.

^bAdjusted R² was calculated from the R² based on sample size (n) and the number of parameters (k) included in the model:

$\text{Adj. }{\mathrm{R}}^2\text{= 1-}\left(\frac{\left(\text{1-}{\text{R}}^{\text{2}}\right)\left(\text{n-1}\right)}{\text{n-k-1}}\right)$