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After partialling out the differences in sampling effort among sites, the biological data were detrended through RDA on X and Y geographic coordinates to remove the effect of a linear spatial gradient.
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The data were detrended with least squares procedures to remove spurious trends [18].
Raw yaw torque data were detrended by taking the first difference of the series.
The line-scanning data were detrended and transposed into an intensity carpet analogous to that described for the orbital scanned data (Fig. 4 B ).
The time-series data were detrended by a 24-hr running average and then subjected to FFT-NLLS analysis to calculate periods and phases.
To obtain stationarity in the time series [see [ 47] for details], data were detrended following [ 48] by including year as covariate in all models.
Lumicycle data were detrended to remove baseline changes and then fit with a damped sine wave in order to determine circadian period, amplitude and phase as in [ 22].
Bleaching contributes to the ACF as a slowly relaxing component that can completely mask other fast dynamic processes; therefore, the data were detrended to remove the bleaching component before analysis (see Materials and Methods).
The TEC data are detrended with a 10-min running average.
One thing that is essential and standard practice in any study that looks to uncover evidence for cyclicity is that the data be detrended.
The raw data was detrended and normalized by dividing each data point by the corresponding point of a trend curve (fitted by a 72 h low-pass Butterworth filter), as described [42].
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