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They were led during the tournament by Scott Johnson in his capacity as director of rugby and interim head coach.
However, Johnson relinquished his temporary coaching role at the end of the Championship and Dodson admits it will be up to Cotter if his predecessor plays any part on the training field.
"Vern Cotter will have complete control over all aspects of the national squad," Dodson said.
"But obviously there are areas where the two men will have to work very closely together.
"However, Scott will only work with the Scotland national squad as backs or attack coach if Vern wants him to.
"Vern has complete control of the rugby affairs of the Scotland national squad and he will report to me directly, not to Scott Johnson."