Statistical analyses
The statistical analyses were performed using the R version 4.0.4 software program (R Core Team, 2021). Target eDNA concentrations per PCR reaction (2 µL template DNA) were converted into per water sample (1 mL water sample) before the analyses. Linear regressions of the target eDNA concentration (log10-transformed) against the number of zebrafish individuals per tank were performed for each filter pore size and DNA marker length using lm and confint functions, with theirR2 values and slopes with 95% confidence intervals (CIs) estimated. We also conducted a linear model to assess the effects of the eDNA size fraction and target marker length on the accuracy of the relationship between eDNA concentration and species abundance (i.e., the R2 value of linear regression). The R2 values were Fisher’s z-transformed by the package “MAc” in advance (Del Re & Hoyt, 2018) to meet the normality (Yates et al., 2019) and included as the dependent variable. Filter pore size (µm; categorical), marker length (bp; log10-transformed), and interactions were also explanatory variables. Additionally, a linear mixed model using the lmer function in the package “lmerTest” (Kuznetsova et al., 2017) was performed to assess the effects of the eDNA size fraction and marker length on the sensitivity of the eDNA concentration in response to changes in species abundance (i.e., the slope of linear regression [Eichmiller et al., 2016)). The zebrafish eDNA concentration (log10-transformed) was included as the dependent variable. The number of fish individuals per tank, filter pore size, marker length (log10-transformed), and primary interactions of fish individuals with filter pore size and log10-transformed marker length were included as the fixed effects. The tank replicates were included as the random effect.