Context : Strontium has proven itself to be one of the most important neutron-capture elements in the study of metal-poor stars .
Thanks to the strong absorption lines of Sr , they can be detected even in the most metal-poor stars and also in low-resolution spectra .
However , we still can not explain the large star-to-star abundance scatter we derive for metal-poor stars .

Aims : Here we compare Galactic chemical evolution ( GCE ) predictions with improved abundances for Sr i and Sr ii , including updated atomic data , to evaluate possible explanations for the large star-to-star scatter at low metallicities .

Methods : We have derived abundances under both local thermodynamic equilibrium ( LTE ) and non-LTE ( NLTE ) for stars spanning a large interval of metallicities , as well as a broad range of other stellar parameters .
Gravities and metallicities are also determined in NLTE .
We employed MARCS stellar atmospheres and MOOG for the LTE spectrum synthesis , while MAFAGS and DETAIL were used to derive the NLTE abundances .
We verified the consistency of the two methods in LTE .

Results : We confirm that the ionisation equilibrium between Sr I and Sr II is satisfied under NLTE but not LTE , where the difference between neutral and ionised Sr is on average \sim 0.3 dex .
We show that the NLTE corrections are of increasing importance as the metallicity decreases .
For the stars with [ Fe/H ] > -3 , the Sr i NLTE correction is \sim 0.35 / 0.55 dex in dwarfs/giants , while the Sr ii NLTE correction is < \pm 0.05 dex .

Conclusions : On the basis of the large NLTE corrections to Sr i , Sr i should not be applied as a chemical tracer under LTE , while it is a good tracer under NLTE .
Sr ii , on the other hand , is a good tracer under both LTE and NLTE ( down to [ Fe/H ] \sim - 3 ) , and LTE is a safe assumption for this majority species ( if the NLTE corrections are not available ) .
However , the Sr abundance from Sr ii lines depends on determining an accurate surface gravity , which can be obtained from the NLTE spectroscopy of Fe lines or from parallax measurements .
We could not explain the star-to-star scatter ( which remains under both LTE and NLTE ) by the use of the Galactic chemical evolution model , since Sr yields to date have been too uncertain to draw firm conclusions .
At least two nucleosynthetic production sites seem necessary to account for this large scatter .