Adam, this piece is probably more appropriately called a "Kayseri" rug which is also Turkish. It appears to be old, but probably not from the "early 20th century" as this seller advertises. My best guess is this rug is probably no older than 1950's and could even be of recent production going by the look of the edging and fringe.

The design is "Tree of Life" design. Beware about the seller's claim it is a "silk rug." This is questionable for such rugs. Many of these Kayseri rugs pass for "silk" in the eyes of the inexperienced. Newer rugs are almost always made of mercerized cotton, which is very shiny and deceiving. This is also true even for many older pieces dating back many years.