I have another theory which is quite the opposite from the mainstream.
Firstly, there is little or no admixture going on. So, things like Yamnya being a mix of CHG/Iran_N and EHG is an incorrect way of looking at things. What is really happening is that there is divergence from a common dispersal point that gives rise to different groups like ANE (MA1, Botai etc), Anatolian, CHG, Iran_N etc. This dispersal point is either in Central Asia (Steppe DNA) or Northern South Asia.
If we look at Genetic Distance (F3) to South Asians for Steppe groups, we get
Code:
1 ONG.SG Kazakhstan_Eneolithic_Botai Chimp.REF 217. 1.45 149. 62958
2 ONG.SG Russia_Late_Sarmatian.SG Chimp.REF 216. 1.34 162. 73724
3 ONG.SG Russia_HG_Karelia.SG Chimp.REF 215. 1.44 150. 63238
4 ONG.SG Tajikistan_C_Sarazm Chimp.REF 215. 1.46 147. 57720
5 ONG.SG Russia_Andronovo.SG Chimp.REF 214. 1.28 168. 77585
6 ONG.SG Luxembourg_Loschbour Chimp.REF 214. 1.58 135. 52164
7 ONG.SG Russia_Sidelkino_HG.SG Chimp.REF 214. 1.44 148. 60555
8 ONG.SG Russia_Afanasievo Chimp.REF 214. 1.19 179. 86733
9 ONG.SG Russia_MLBA_Sintashta Chimp.REF 214. 1.18 181. 87459
10 ONG.SG Turkmenistan_IA.SG Chimp.REF 213. 1.51 141. 60093
11 ONG.SG Georgia_Kotias.SG Chimp.REF 212. 1.42 149. 72021
12 ONG.SG Turkmenistan_Gonur_BA_1 Chimp.REF 212. 1.29 164. 68232
13 ONG.SG Iran_GanjDareh_N Chimp.REF 212. 1.22 174. 74888
14 ONG.SG Anatolia_N Chimp.REF 212. 1.17 180. 88294
15 ONG.SG Iran_C_TepeHissar Chimp.REF 211. 1.23 171. 73247
16 Ror Russia_Late_Sarmatian.SG Chimp.REF 226. 1.26 179. 74373
17 Ror Kazakhstan_Eneolithic_Botai Chimp.REF 226. 1.35 167. 64085
18 Ror Tajikistan_C_Sarazm Chimp.REF 226. 1.44 157. 58663
19 Ror Russia_HG_Karelia.SG Chimp.REF 226. 1.41 160. 64542
20 Ror Russia_MLBA_Sintashta Chimp.REF 225. 1.14 198. 86678
21 Ror Russia_Afanasievo Chimp.REF 225. 1.15 195. 86057
22 Ror Russia_Andronovo.SG Chimp.REF 225. 1.24 182. 77848
23 Ror Georgia_Kotias.SG Chimp.REF 224. 1.41 159. 73410
24 Ror Russia_Sidelkino_HG.SG Chimp.REF 224. 1.47 152. 61866
25 Ror Turkmenistan_IA.SG Chimp.REF 223. 1.47 152. 61317
26 Ror Iran_GanjDareh_N Chimp.REF 223. 1.19 188. 74948
27 Ror Iran_C_TepeHissar Chimp.REF 222. 1.23 181. 73033
28 Ror Turkmenistan_Gonur_BA_1 Chimp.REF 222. 1.27 176. 68498
29 Ror Anatolia_N Chimp.REF 222. 1.12 198. 87601
30 Ror Luxembourg_Loschbour Chimp.REF 222. 1.50 148. 53596
Below are the top 5 for ONG and Ror
1 ONG.SG Kazakhstan_Eneolithic_Botai Chimp.REF 217. 1.45 149. 62958
2 ONG.SG Russia_Late_Sarmatian.SG Chimp.REF 216. 1.34 162. 73724
3 ONG.SG Russia_HG_Karelia.SG Chimp.REF 215. 1.44 150. 63238
4 ONG.SG Tajikistan_C_Sarazm Chimp.REF 215. 1.46 147. 57720
5 ONG.SG Russia_Andronovo.SG Chimp.REF 214. 1.28 168. 77585
16 Ror Russia_Late_Sarmatian.SG Chimp.REF 226. 1.26 179. 74373
17 Ror Kazakhstan_Eneolithic_Botai Chimp.REF 226. 1.35 167. 64085
18 Ror Tajikistan_C_Sarazm Chimp.REF 226. 1.44 157. 58663
19 Ror Russia_HG_Karelia.SG Chimp.REF 226. 1.41 160. 64542
20 Ror Russia_MLBA_Sintashta Chimp.REF 225. 1.14 198. 86678
Checking for closeness to Ong is important because that rules out the possibility of Steppe Migrations mediating this genetic relationship. Its pretty obvious that the relationship between Steppe and South Asians is not mediated by supposed LBA Steppe Migration into South Asia, rather different groups are most close to South Asians (and ONG). This most likely reflects on-going South Asian genetic influence into Central Asia and the Steppe.
Also note that Steppe is much closer to South Asians than Iran_N or other farmers (Gonur, Hissar). This is interesting and is most likely due to the higher level of mixing between South Asians and Steppe (nomadic peoples moving around and mixing more) while the Iranian farmers had been isolated from this since much earlier times.
IE cannot easily be separated easily by any kind of genetic argument. Most likely alot of these peoples who are non-Indo European such as Semitic and Caucasian probably spoke an IE langauage at one time, but due to their earlier separation those languages have drifted sufficiently to be no longer grouped with the others, and losing all traces to their common IE origin. This makes sense because non-IE peoples like the Caucasians and Semites all originated via the same process (separating from the others via South-Central Asia) but they are just genetically more distant due to having separated earlier.
The known IE speakers, and the R1A lineages found outside India, all tend to me peoples who are closer to South Asians, but more importantly closer to Ong. Checking for closeness to Ong is important because that rules the possibility of Steppe Migrations mediating this genetic relationship. So, R1 and the most 'conservative' IE languages in Europe are those that have expanded last from Central Asia into Europe, hence their genetic and linguistic similarity to South Asians.
Lastly, MOST populations are being modelled as mixes ie Steppe and South Asians, are not actually mixes. Rather, those populations that these are supposedly mixed from actually originated from South Asians and Steppe. So, Steppe DNA has existed in some form for a long time, ANE is the Eastern drfit of Steppe, Anatolian is the Western drift, EHG North-Western, and Iran_N likely has something similar to Steppe DNA going into it from Central Asia.