Context : Aims : Molecular emission lines originating in the nuclei of luminous infra-red galaxies are used to determine the physical properties of the nuclear ISM in these systems . Methods : A large observational database of molecular emission lines is compared with model predictions that include heating by UV and X-ray radiation , mechanical heating , and the effects of cosmic rays . Results : The observed line ratios and model predictions imply a separation of the observed systems into three groups : XDRs , UV-dominated high-density ( n \geq 10 ^ { 5 } cm ^ { -3 } ) PDRs , and lower-density ( n = 10 ^ { 4.5 } cm ^ { -3 } ) PDRs that are dominated by mechanical feedback . Conclusions : The division of the two types of PDRs follows naturally from the evolution of the star formation cycle of these sources , which evolves from deeply embedded young stars , resulting in high-density ( n \geq 10 ^ { 5 } cm ^ { -3 } ) PDRs , to a stage where the gas density has decreased ( n = 10 ^ { 4.5 } cm ^ { -3 } ) and mechanical feedback from supernova shocks dominates the heating budget .