To do so I only used individuals that are labeled as J1 (not J1c, J1b, etc.) at FTDNA. In a lot of cases SNPs downstream of J1 were not tested, so I had to help myself: I excluded all individuals that show high similarity with known J1c and J1b individuals. Then, I generated the first tree with 200 individuals.
Polar tree of haplogroup J1 (excluding known J1b and J1c individuals):
J1 is split into two parts: the Arabian Peninsula (highlighted in magenta) and the rest. My assumption is that all these individuals from the Arabian Peninsula have the haplogroup J1c3d2 L222.2+ or at least J1c but they were just not tested for it.
Next, I excluded those individuals, I repeated the analysis with the remaining individuals.
1. Rectangular tree of haplogroup J1:
2. Polar tree of haplogroup J1:
The individuals from Iran (Irn-187962), Iraq (Irq--92829) and Turkey (Tur-191398, Aintab, Turkey) are Assyrians. All other individuals from Iran and most individuals from Turkey (Tur-...) are actually Armenians. Unfortunately, no known Kurd is included in this analysis but based on the names there is one individual from Turkey (Tur-221845, Ahmed) that is Muslim and thus, not an Armenian or Assyrian, so he could be a Kurd.
The oldest branches of haplogroup J1 can be found in Northern Mesopotamia and Eastern Anatolia.