Estimating constant time shift between two simulated time series. (A) The data shown are expression levels of time series for species 1 (sp1, purple) and species 2 (sp2, light blue), modelled using the sine function with different sets of N and M parameters. We use the DTW-S procedure to align the sp2 time series to sp1, and calculate time shift values for the ages of sp2. The parameters N and M shown above the panels represent the numbers of interpolated time points for sp2 and sp1 time series, respectively. The number of the original time points n = N. (B) Time shift estimates calculated by the DTW-S procedure. Time shift estimates are based on 1,000 simulations of the expression time series shown in (A). The gray lines show the actual time shift values used in for data modelling. The parameter r represents the proportion of the total variance introduced by simulated error (ε).