Table 1 Log-transformedtoxicity data information for three metals.

Metals / Parameters / All Species / Plants / Vertebratesf / Fish / Amphibians / Invertebratesg / Crustaceans / Other Invertebrates
Zn / Na / 139 / 35 / 63 / 60 / 3 / 41 / 16 / 25
minb / 0.09 / 0.09 / 1.02 / 1.02 / 1.49 / 2.04 / 2.04 / 2.22
maxc / 5.14 / 4.33 / 5.13 / 5.13 / 1.67 / 5.14 / 4.80 / 5.14
μd / 3.46 / 2.99 / 3.78 / 3.89 / 1.55 / 3.38 / 3.14 / 3.53
σe / 0.97 / 1.05 / 0.94 / 0.82 / 0.10 / 0.77 / 0.83 / 0.70
Cd / Na / 63 / 19 / 26 / 25 / 1 / 18 / 5 / 13
minb / --1.37 / --1.37 / 0.49 / 1.51 / 0.49 / 1.94 / 1.94 / 2.10
maxc / 5.48 / 4.11 / 5.48 / 5.48 / 0.49 / 4.79 / 3.57 / 4.79
μd / 2.89 / 2.19 / 3.27 / 3.38 / 0.49 / 3.09 / 2.37 / 3.37
σe / 1.22 / 1.42 / 1.10 / 0.96 / / / 0.85 / 0.68 / 0.76
Hg / Na / 90 / 9 / 33 / 26 / 7 / 48 / 25 / 23
minb / --0.50 / 1.29 / 0.48 / 0.48 / 1.57 / --0.50 / --0.50 / 0.63
maxc / 4.54 / 3.10 / 4.23 / 3.74 / 4.23 / 4.54 / 4.54 / 3.88
μd / 2.09 / 2.12 / 2.44 / 2.41 / 2.55 / 1.83 / 1.55 / 2.14
σe / 0.94 / 0.54 / 0.70 / 0.66 / 0.86 / 1.07 / 1.18 / 0.85

a number of species included in model; bminimum valueof species toxicity data included in model for the metal; cmaximumvalueof species toxicity data included in model for the metal; d mean of species toxicity data included in model for the metal; e variance of species toxicity data included in model for the metal; f Vertebrates contain fish and amphibians in this research; g Invertebrates contain crustaceans and other Invertebrates in this research.

Table 2Comparison among several good fitting parametric models and non-parametric models for three metals. Parametric models including normal distribution, logistic distribution, log-normal distribution, log-logistic distribution and sigmoid distribution, and parameters including the formula of probability density function (PDF), formula parameters of distribution, and goodness-of-fit evaluation results of the model.

metals / Distribution / PDF / Parameters / pK-S / R2 / RMSE / SSE
Zn / Normal / / μ= 3.46±0.083
σ= 0.97±0.059 / 0.014 / 0.9553 / 0.0610 / 0.518
Logistic / / μ= 3.57±0.078
σ= 0.53±0.038 / 0.361 / 0.9796 / 0.0412 / 0.236
log-normal / / μ= 1.16±0.045
σ= 0.53±0.032 / 7.41E-07 / 0.7889 / 0.1326 / 2.446
log-logistic / / μ= 1.25±0.028
σ= 0.20±0.015 / 0.00898 / 0.9336 / 0.0744 / 0.769
Non- parametric Kernel / / / Bandwidth= 0.296 / 0.907 / / / 0.0175 / 0.0424
Cd / Normal / / μ= 2.89±0.15
σ= 1.22±0.11 / 0.301 / 0.9722 / 0.0481 / 0.146
Logistic / / μ= 2.98±0.15
σ= 0.66±0.069 / 0.354 / 0.9764 / 0.0443 / 0.124
log-normal / / μ= 1.75±0.033
σ= 0.26±0.023 / 0.0715 / 0.9217 / 0.0807 / 0.411
log-logistic / / μ= 1.78±0.026
σ= 0.12±0.013 / 0.00898 / 0.9717 / 0.0486 / 0.149
Non- parametric Kernel / / / Bandwidth= 0.564 / 0.654 / / / 0.0370 / 0.0863
Hg / Normal / / μ= 2.09±0.099
σ= 0.94±0.071 / 0.581 / 0.9816 / 0.0391 / 0.138
Logistic / / μ= 2.12±0.096
σ= 0.52±0.046 / 0.597 / 0.9887 / 0.0307 / 0.0847
log-normal / / μ= 1.61±0.021
σ= 0.20±0.015 / 0.158 / 0.9555 / 0.0609 / 0.334
log-logistic / / μ= 1.63±0.020
σ= 0.11±0.010 / 0.495 / 0.9780 / 0.0428 / 0.165
Sigmoid / / a=1.054
x0=20215
k=1.824 / 0.600 / 0.9913 / 0.0266 / 0.0639
Non- parametric Kernel / / / Bandwidth= 0.368 / 0.897 / / / 0.0233 / 0.0488

Table 3 Comparison among HC5 values derivedby different models for three metals.

models / HC5/(μg·L-1)
Zn / Cd / Hg
Normal / 72.32 / 7.59 / 3.46
Logistic / 101.94 / 10.45 / 3.83
log-normal / 21.68 / 5.4 / 3.98
log-logistic / 88.09 / 13.14 / 5.01
Sigmoid / / / / / 3.72
Non- parametric Kernel / 35.87 / 3.39 / 2.14

Table 4 Comparison of freshwater aquatic criteria.

Group / Deriving methods / WQC(μg·L-1) / Literatures
Zn / Normal-SSD / 36.16 / This research
Logistic-SSD / 50.97
log-normal-SSD / 10.84
log-logistic-SSD / 44.045
Non-parametric Kernel-SSD / 17.935
ExpGro1 / 48.43 / Wu et al.(Wu et al. 2012)
BurrⅢ-SSD / 29.94 / Kong et al.(Kong et al. 2011)
Percentage of toxicity sorting / 120 / US EPA(U.S.EPA 1996)
Evaluation factors / 30 / CCME(CCME 2007)
Cd / Normal-SSD / 3.795 / This research
Logistic-SSD / 5.225
log-normal-SSD / 2.7
log-logistic-SSD / 6.57
Non- parametric Kernel-SSD / 1.695
Slogistic3 / 0.4218 / Wu et al.(Wu et al. 2012)
BurrⅢ-SSD / 2.265 / Kong et al.(Kong et al. 2011)
Percentage of toxicity sorting / 2 / US EPA(U.S.EPA 2001)
Hg / Normal-SSD / 1.73 / This research
Logistic-SSD / 1.91
log-normal-SSD / 1.99
log-logistic-SSD / 2.51
Sigmoid-SSD / 1.86
Non- parametric Kernel-SSD / 1.07
log-Slogistic3-SSD / 1.74 / Zhang et al.(Zhang et al. 2012)
BurrⅢ-SSD / 3.33 / Kong et al.(Kong et al. 2011)
RIVM-SSD / 3.42 / Li et al.(Li et al. 2012)
Percentage of toxicity sorting / 1.4 / US EPA(U.S.EPA 1980)

Table 5 Comparison among HC5 values derived by Non-parametric Kernel models of different taxa for three metals.

Groups / HC5/(μg·L-1)
Zn / Cd / Hg
Plant / 3.01 / 0.11 / /
Vertebrates / 30.93 / 14.36 / 11.4
Fish / 143.49 / 40.03 / 7.67
Amphibians / / / / / 16.12
Invertebrates / 102.37 / 29.28 / 0.79
Crustaceans / 34.07 / 57.08 / 0.38
Other Invertebrates / 160.31 / 92.64 / 3.16