2.6 Statistical analyses
We used generalized linear models (glm function within R v.3.5.1,
R Core Team, 2018, running under R Studio v.1.2.5019, RStudio Team,
2019) to evaluate the effect of population (4 levels) on the variables
measured in the field-collected samples of S. cataractae , and the
effects of population (3 levels for C. purpureus ; 4 levels forS. cataractae ), treatment (2 levels: control vs Cd; control vs
Cu) and their interaction on the variables measured in both species
during the common garden experiments using the gamma distribution with
the log link function in most cases (but see Table 1 for more details).
The field samples and the four common garden experiments comprised the
following datasets: i) Field samples: total concentrations of Cd and Cu
in soil; total and relative concentrations of Cd and Cu, and plant
length, leaf length, and leaf width in S. cataractae ; ii) Common
garden: total and relative concentrations of Cd and Cu, and
concentration of MDA in S. cataractae and C. purpureus ;
protonemal growth in C. purpureus , and plant length, leaf length,
and leaf width in S. cataractae . In the common garden, we
compared the responses to each of the specific treatments (Cd enriched
and Cu enriched) to the control conditions for each species.
We graphically inspected residuals of the models for any trends, and
tested for normality and homoscedasticity using the functionsshapiro.test and leveneTest respectively. When these
assumptions were not met, we tried other family distributions to model
the response (inverse gaussian with log link, and gaussian with inverse
link), used standardized variables (mean = 0, standard deviation = 1),
or applied BoxCox transformations (Box & Cox, 1964) in order to improve
the fit of the models (summarized in Table 1). Then we used the functionanova to test for the significance of the main effects of the
models followed by multiple pairwise comparisons using the functionglht (multcomp package, Hothorn, Bretz, & Westfall, 2008) when
the main effects were significant. Finally, all p-values were adjusted
using the Benjamini & Hochberg (1995) method to obtain false discovery
rates (FDR).
We used a Kruskal Wallis test to assess the effect of the treatment on
the total concentrations of Cd and Cu in C. purpureus in the
laboratory without accounting for the population effect due to the low
number of replicates.