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The pair shot seven-under-par opening rounds of 65 around the 2014 Ryder Cup venue to hold a slender lead over a group of players at six-under-par.
Wiesberger produced a flawless round of golf that included seven birdies and no dropped shots as the two-time winner on the European Tour hopes to make an early claim for a Ryder Cup spot next year.
Gonzalez on the other hand produce a far more erratic round of golf, carding two bogeys and an eagle to go alongside seven birdies and eight pars.
Ryder Cup captain Paul McGinley also pulled on his golf clothing this week as the Irishman starts to make preparations towards setting up the venue for next year's matches.
"The jury is still out at the moment, but it's been a huge learning curve to go to the other end of the scale in terms of the set up of the golf course this week," McGinley said.
The European team qualification process begins next week at the ISPS Handa Wales Open at Celtic Manor, which hosted the previous Ryder Cup on European soil in 2010.
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