Paul Casey ruled out of Ryder Cup after committing to PGA rather than European Tour

Casey, who is based mainly in Arizona, gave up his membership after deciding to concentrate on the PGA Tour in order to get back into the world's top 50.

The move has paid off with the former world No 3 climbing from 75th at the end of last season to his current position of 24th, but even this week's change in membership criteria has not been enough to persuade the 38-year-old to rejoin.

In a statement, Casey said: "Having given the matter a great deal of thought, I have decided not to take up European Tour membership for the coming season.

"With my wife and young son as my priority, I have decided to continue to concentrate on the PGA Tour, which has worked well for us this past year as I have climbed back up the rankings.

"I am very sad not to have the chance to qualify for the 2016 European Ryder Cup team, but I believe this decision will help me to be the best I can be both on and off the course and is the right decision for my family."

Casey played in the record nine-point wins in 2004 and 2006 and Europe's last defeat at Valhalla in 2008, but was in tears after being overlooked for a wild card by captain Colin Montgomerie in 2010, when he was ranked seventh in the world.

Clarke, who played alongside Casey at Oakland Hills in 2004 and the K Club in 2006, said: "It is obvious that representing Europe in the Ryder Cup is not on Paul's priority list, which is disappointing, but I wish him all the best for the future.

"For me the focus is firmly on the players who are committed to the European cause as we move towards Hazeltine and I look forward to working with these players over the next 10 months."

European Tour chief Pelley said on Tuesday he was optimistic Casey would rejoin after reducing the number of tournaments required to maintain membership from 13 to five, excluding majors and WGC events.

And on Saturday it was announced that next year's Alstom Open de France would count as two of the required events after being pitted against the WGC-Bridgestone Invitational.

"I respect Paul's decision but, as I said on Tuesday of this week, we have made it very easy for players to retain their membership of the European Tour by only having to play five out of 37 tournaments outside the majors and World Golf Championships," Pelley said.

"If that is not feasible for Paul, then there is not much else we can do."