Anderson, the Glasgow Caledonians prop, is rewarded for a series of consistent displays in this season's European Cup campaign while the New Zealand- born flanker Mather makes the step up after coming close to Test selection on the summer tour of Australia.
Elsewhere, there are three positional changes from the side that crushed Portugal 85-11, with the wingers Cammy Murray and Kenny Logan swapping flanks. Martin Leslie, who started on the blind side flank against Portugal, switches to open side with Budge Pountney demoted to the bench and Rob Wainwright dropping out of the 22 altogether. David Hilton will revert to his role as replacement prop with Paul Burnell also omitted from the squad for this match.
The Scotland coach, Jim Telfer, keen to give everyone in his core squad a run-out in these World Cup qualifying matches, insisted that the time was right to give Anderson and Mather their head.
"Willie has been performing very well for Glasgow Caledonians this season and we want to give him a shot at this level to see how he does. Hopefully, this will be a stern test," he said. "Cammy was with us in Australia and played very well even though he didn't make the Test selection. He has been dogged with injuries since he came back but he has done well in his last two or three matches for the Edinburgh Reivers."
Telfer believes Spain will provide a much harder test than Portugal. "I think they will be stronger in the forwards and more adventurous in the backs," he added.
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