Unfortunately, with any sort of semiprecious or precious stone, it is usually not possible to definitively make such a determination without examining them with the appropriate gemogical tools.
In the case of turquoise, too, even natural turquoise is often dyed, and even more often chemically stabilized, as well as faked, usually with dyed howlite, which in its natural form is kind of a chalky white or greyish white and may or may not have darker markings. So, even the presence of obvious dye doesn't necessarily prove whether it is fake or natural turquoise.
That said, a number of the beads in this piece have light, fairly white patches where it looks like the color has rubbed off, and even flaked off, so I'd lean towards suspecting dyed howlite, although the matrix pattern on some of the beads looks like it could *possibly* be natural. The uncolored patches most likely tell the tale, though.
