We analyse the flux power spectrum and its covariance using simulatedLyα forests. We find that pseudo-hydro techniques are goodapproximations of hydrodynamical simulations at high redshift. However,the pseudo-hydro techniques fail at low redshift because they areinsufficient for characterizing some components of the low-redshiftintergalactic medium, notably the warm-hot intergalactic medium. Hence,to use the low-redshift Lyα flux power spectrum to constraincosmology, one would need realistic hydrodynamical simulations. Bycomparing (one-dimensional) mass statistics with flux statistics, weshow that the non-linear transform between density and flux quenches thefluctuations so that the flux power spectrum is much less sensitive tocosmological 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 belarge, even though the flux power spectrum can be precisely determinedfrom a small number of lines of sight.