We analyse the flux power spectrum and its covariance using simulated Lyα forests. We find that pseudo-hydro techniques are good approximations of hydrodynamical simulations at high redshift. However, the pseudo-hydro techniques fail at low redshift because they are insufficient for characterizing some components of the low-redshift intergalactic medium, notably the warm–hot intergalactic medium. Hence, to use the low-redshift Lyα flux power spectrum to constrain cosmology, one would need realistic hydrodynamical simulations. By comparing (one-dimensional) mass statistics with flux statistics, we show that the non-linear transform between density and flux quenches the fluctuations so that the flux power spectrum is much less sensitive to cosmological parameters than the one-dimensional mass power spectrum. The covariance of the flux power spectrum is nearly Gaussian. As such, the uncertainties of the underlying mass power spectrum could still be large, even though the flux power spectrum can be precisely determined from a small number of lines of sight.