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Campaigners had appealed to the highest administrative court in Sweden less than a week before the start of the hunt. The Supreme Administrative Court has not yet decided whether or not to grant them leave to appeal, but said it would not call off the hunt at the eleventh hour in the meantime.
Eight wolves were shot on Tuesday, two of whom were found to have scabies, reports hunting magazine Svensk Jakt.
Twenty-two wolves are to be culled in the licensed hunt, which takes place in five counties between January 2nd and February 15th, with a limit on the number which may be killed in each county.
A maximum of two wolves may be killed in Örebro and Gävleborg, while the limit for Dalarna, Västmanland and Värmland is six.
Sweden has a total wolf population of around 355 animals, according to recent estimates, and authorities have previously said it should have a minimum of 300 wolves.
Various organizations, including the Swedish Carnivore Association, had called for the hunt to be stopped. On the other hand, organizations including the National Hunting Association had requested that it be extended.