I'm familiar with the Pontic hypothesis, but don't know what evidence suggests an Anatolian origin. Is there significant linguistic and archeological evidence to support an origin in modern Turkey?
The arguments for an Anatolian homeland these days largely rest on fundamental misunderstandings of historical linguistics. See here for a bit of a back-and-forth on Bouckaert et al. 2012, perhaps the most recent paper published in support of the hypothesis. It also came up in the Historical Linguistics AMA.