Statistical analyses
To reveal the potential effects of MnSO4 concentration and selection line on fish growth, we extracted the average relative growth rate of the rearing groups with
(SL2/SL1)(1/t )-1
where SL2 is the average SL at age 218 dpf (the last measurement), SL1 is the average SL at age 70 dpf (the first measurement) and t is the time the experiment lasted (148 days). We then used generalized additive model (GAM) with Gaussian error distribution and maximum likelihood estimation with the relative growth rate and condition factor as response variables and concentration, selection line, and their interaction as predictive variables (1). Selection-line replicate was not set as a random variable because in some concentrations we only had one rearing group per selection-line replicate. As fish SL varied among concentrations and selection lines at the time we started the experiment, we additionally added the average body size at the time the growth experiment was initiated (SL at age 70 dpf) as a predictive variable in the model (1). SL at age 70 dpf was not explained by the selection line (F=0.226, P =0.637) or by the MnSO4 concentration (F=0.014, P =0.905). Growth rate was estimated as an average relative growth rate across all individuals within a rearing group, hence the rearing group could not be added as a random variable in the model.
(1) GAM (Growth rate ~ Selection line * Concentration + SL at age 70 dpf, family=Gaussian)
Condition factor, on the other hand, was calculated for each individual fish at the end of the experiment (at age 218 dpf), not as rearing group averages as when estimated growth rates. Therefore, the effect of rearing group could be added as a random factor in the model (edf=2.611,P = 0.108). Selection-line replicate (both selection lines had two replicates) could not be added as a random variable as in some concentrations we only had five fish, i.e., one rearing group, per selection-line replicate. Relative condition factor (Le Cren 1951; Froese 2006) was calculated for each fish as
WM/(a *SLb )
where WM is the wet mass (g) at age 218 dpf, SL the standard length (mm) at age 218 dpf, a is the intercept and b the slope of a linear regression of ln(WM) on ln(SL) (t=5.406, P <0.01). The standard length–weight regression parameters of our zebrafish population were estimated as a =0.0555 and b =2.619 using fish in the control treatment (i.e., 0 Mn mg L-1).
(2) GAM (Condition factor ~ Selection line * Concentration + SL at age 70 dpf + (1|Rearing group), family=Gaussian)
Behavioral traits (activity and feeding probability) were tested twice to demonstrate consistency in fish behavior over time. This was studied with a correlation test between the two measurements per individual fish. We used (generalized) linear mixed-effect model (G/LMER) to study the effects of MnSO4 concentration and selection line on fish behavior. Activity (distance moved in cm) and feeding behavior (feeding probability) were set as response variables and selection line, MnSO4 concentration, their interaction, and fish SL at the time of measuring the behavior as predictive variables (3,4). Individual fish (as each fish was measured twice) and rearing group were set as random variables.
(3) LMER (Activity ~ Selection line * Concentration + SL + (1|Fish ID) + (1|Rearing group))
(4) GLMER (Feeding probability ~ Selection line * Concentration + SL + (1|Fish ID) + (1|Rearing group), family = Binomial)
Generalized additive model was used to study the effects of MnSO4 concentration and selection line (predictive variables) on average metabolic rates (SMR and MMR) and aerobic scope (response variables). As metabolic rates were estimated for groups of fish originating from one rearing group, it could not be added as a random variable in the model (5). Number of fish in one respirometer chamber during the measurement varied slightly (i.e., we did not always have exactly five fish in a chamber at a time) and therefore the effect of number of fish in a chamber during the measurement could be tested as adding it as a random variable (edf=0.5927, P =0.122).
(5) GAM (SMR / MMR / AS ~ Selection line * Concentration + (1|Number of fish in chamber))
Finally, we used linear model (LM) to study the effects of MnSO4 concentration and selection line (predictive variables) on Mn-concentration (mg Mn/g fish WM) accumulated in the fish head and in the body (6).
(6) LM (Mn-concentration ~ Selection line * Concentration)
To estimate differences in growth rate, condition factor, standard metabolic rate, behavior and Mn accumulation in fish head and body in different Mn concentrations and between the selection lines, we first fitted the full model and then used the stepwise model reduction. Results were considered statistically significant at P < 0.05. Data was analyzed using R version 4.1.2 (R Core Team 2020) and packages nlme, lme4, mgcv, and pscl.