St Johnstone midfielder Davidson's call-up was confirmed by the
Barr has one Scotland cap, earned while a Falkirk defender in a goalless draw against Northern Ireland at Hampden in August 2008.
His career stalled after a move to Hearts but he finally won a regular first-team place earlier this year after being converted to a defensive midfielder.
The 27-year-old scored in the Scottish Cup final win over Hibernian and has been an ever-present this season.
Davidson, 24, is uncapped but was previously called up for matches against Faroe Islands in November 2010 and Brazil in March 2011.
The call-ups mean Stark now has 19 players booked to travel to Luxembourg.
Stark handed debut calls to Kilmarnock midfielder Liam Kelly, Hibernian striker Leigh Griffiths and Inverness midfielder Andrew Shinnie on Sunday.
Huddersfield Town left-back Paul Dixon, who played in the opening 2014 FIFA World Cup qualifiers against Serbia and FYR Macedonia, and St Mirren goalkeeper Craig Samson were also brought in.
Cardiff City goalkeeper David Marshall (groin), Sunderland pair Phil
Bardsley (hamstring) and Steven Fletcher (ankle), midfielders Shaun
Maloney (abdominal), Barry Bannan (knee), Charlie Adam and James
Morrison (both groin), Blackpool winger Matt Philips (toe) and Queens Park Rangers
forward Jamie Mackie (ankle) all pulled out.
Davidson told St Johnstone's official website: "I'm delighted. I've been involved before and got on the bench in games against the Faroes and Brazil but have been out of the scene for a wee while so it's great to be given this chance."
Griffiths admitted he was surprised by his call-up.
The 22-year-old scored his 12th goal of the season as Hibs went top of the Scottish Premier League with a 2-1 victory over Dundee United.
Griffiths told his club's official website: "I'm delighted - I didn't think I had a chance. I'm just so happy that I'm making my kids proud of me.
"I've been pleased with how everything has gone for me and the team so far this season. I've already beaten my tally for last season and I just want to see where it takes me.
"I've scored 12 goals, but that is because the rest of the boys have been creating the chances for me - it's been a team effort.
"Everybody is working hard towards achieving the same goal - winning games for Hibs."