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The paper aims to study relation between the distributions of the youngstellar objects (YSOs) of different ages and the gas-dust constituents of theS254-S258 star-formation complex. This is necessary to study the time evolutionof the YSO distribution with respect to the gas and dust compounds which areresponsible for the birth of the young stars. For this purpose we usecorrelation analysis between different gas, dust and YSOs tracers. We comparedthe large-scale CO, HCO$^+$, near-IR extinction, and far-IR {\it Herschel} mapswith the density of YSOs of the different evolutionary Classes. The directcorrelation analysis between these maps was used together with thewavelet-based spatial correlation analysis. This analysis reveals a muchtighter correlation of the gas-dust tracers with the distribution of Class IYSOs than with that of Class II YSOs. We argue that Class I YSOs which wereinitially born in the central bright cluster S255-IR (both N and S parts)during their evolution to Class II stage ($\sim$2 Myr) had enough time totravel through the whole S254-S258 star-formation region. Given that the regioncontains several isolated YSO clusters, the evolutionary link between theseclusters and the bright central S255-IR (N and S) cluster can be considered.Despite the complexity of the YSO cluster formation in the non-uniform medium,the clusters of Class II YSOs in the S254-258 star-formation region can containobjects born in the different locations of the complex.

The link between gas and stars in the S254-S258 star-forming region