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Table 1 Posterior median (95% Bayesian credible intervals) of the parameters and the widely applicable information criterion (WAIC) for the top 5 (rank 1–5), full, and null species sensitivity distribution (SSD) models

From: Estimating species sensitivity distributions for microplastics by quantitatively considering particle characteristics using a recently created ecotoxicity database

Parameters

Rank 1

Rank 2

Rank 3

Rank 4

Rank 5

Null model

Full model

Intercept (α)

−1.25 (− 1.88–−0.61)

−1.47 (− 2.30–−0.66)

−1.13 (− 1.91–−0.36)

−1.32 (− 1.98–−0.66)

−1.30 (− 2.16–−0.46)

−1.04 (− 1.65–−0.44)

−0.90 (− 3.61–1.97)

β

       

 Particle length

0.66 (0.10–1.22)

0.61 (0.04–1.18)

0.73 (0.13–1.33)

0.55 (0.00–1.12)

0.63 (− 0.15–1.38)

 

0.53 (− 0.35–1.44)

 Habitat

 

0.53 (− 0.70–1.73)

    

0.46 (− 0.87–1.76)

 Fragment

    

0.16 (− 1.40–1.74)

 

−0.03 (− 2.16–2.08)

 Fiber

−1.76 (− 3.88–0.40)

−1.97 (− 4.17–0.22)

−1.96 (− 4.22–0.29)

 

−1.61 (− 4.10–0.85)

 

−2.35 (− 5.36–0.58)

 Polystyrene

      

−0.56 (− 3.61–2.42)

 Polyethylene

  

−0.36 (− 1.63–0.89)

   

−0.69 (− 2.47–1.04)

SSD SD (σ)

1.75 (1.40–2.28)

1.75 (1.41–2.27)

1.76 (1.40–2.28)

1.79 (1.45–2.32)

1.77 (1.41–2.28)

1.88 (1.51–2.41)

1.80 (1.42–2.35)

WAIC

153.3

154.6

155.0

155.1

155.2

157.0

159.4

delta WAIC

0.0

1.3

1.7

1.8

1.9

3.8

6.1

  1. SD = standard deviation. Delta WAIC is the difference in WAIC values between the model listed and the best model (i.e., Rank 1 model). A model with a smaller WAIC value has higher predictive power, but there is no theoretical criterion for a cut-off value for the delta WAIC. See Eqs. 12 and related text for details of α, β, and σ