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Kruskal Wallis test with post hoc Dunn's test was performed using PMCMR package for R (Pohlert 2014) while correlation analyses used the stats package for R (R 2015).
If this model converged, indicating the presence of a diel pattern for a specific seal on a given day, these initial parameter estimates were used to fit a final model using the nls function (in the standard stats package for R).
For all of the statistical tests, we used the stats package for R [ 19].
The LM function in the STATS package for the R Statistical System (R Development Core Team, 2007) was used to perform these calculations.
Hierarchical clustering was performed using the stats package for R utilizing the Euclidean distance for computing the distance matrix and the complete method for the agglomeration.
Computations were carried out in C++ using a Borland 5 compiler and Optivec 5.0 vector and matrix libraries, and R version 2.6.1 (including R "stats" package for smooth.spline and isoreg functions).
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The lm function in the stats package of R was used for calculations [ 105].
Next, differences in N2 fixation activity under the different O2 conditions, presence of 13C CH4 and sites (oligotrophic or mesotrophic), were tested using a 3-way ANOVA (stats-package; for sample size (n) see Additional file 1: Table S5).
Stats package was used for the others analysis.
We employed the function lm within the stats package in R for calculations.
To obtain fitted values in the original scale, particularly for w o and w s, we used the function predict within the stats package in R. For significance of replicate population effects (intercept of the models) and generation (slope) from zero, we employed z-tests as implemented in the multcomp R package cftest function [ 67].
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