There exists in population genetics the notion of a “ghost population”  – one with which one or more of our sampled populations has experienced gene flow but which itself remains unobserved. A famous example would be the “ancient northern Eurasian population” inferred by Patterson et al. 2012 to have “contributed genetic material to both the ancestral population of the Americas and the ancestral population of northern Europe” but apparently no longer exist in unadmixed form .
There’s a natural counterpart to this in historical linguistics: extinct languages which were never (or only very fragmentarily) committed to writing but which bequeathed an identifiable legacy (most straightforwardly, loanwords) to extant or at least historically better-documented languages. As was the case for the “ancient northern Eurasians” after the sequencing of the Upper Paleolithic Mal’ta child’s genome , it remains at least theoretically conceivable (though exceedingly unlikely for participants in many of the most interesting contact events) that something more definitive could be said about the identity of a comparably mysterious donor language through the linguistic equivalent of ancient DNA: some fortuitous new textual discovery — a thick sheaf of birchbarks or brittled scrolls — or a decipherment breakthrough.
Even in lieu of such windfalls, internal and extra-linguistic lines of evidence may already have strongly implicated a candidate; witness the common identification of the Andronovo culture as the likely source of certain seemingly early Iranian elements in Finno-Ugric languages (one of several strata of Indo-European contact).
Another interesting paper from Eugen Helimski, kindly shared with me by Christopher Culver, problematizes this particular position:
Helimski, E. (1997). The southern neighbours of Finno-Ugrians: Iranians or an extinct branch of Aryans (‘Andronovo Aryans’)? In: Hahmo, S.-L., Hofstra, T., Honti, L., van Linde, P., & Nikkilä, O. (Eds.), pp. 117–125. Finnisch-ugrische Sprachen in Kontakt, Vorträge des Symposiums aus Anlaß des 30-jährigen Bestehens der Finnougristik an der Rijksuniversiteit Groningen, 21.-23. November 1996. Maastricht: Shaker Publishing.
The aim of this paper consists not in presenting any radically new evidence, but in reexamining the traditional view, according to which the numerous and well known Aryan [i.e., Indo-Iranian] loanwords in Finno-Ugric and its daughter branches were borrowed from a Late Indo-European (Pre-Aryan) dialect that underwent during the period of contacts, between the 3rd and the 1st millennium B.C., a gradual transformation first into Proto-Aryan, then Proto-Iranian, and then into Eastern Iranian Scytho-Sarmatian dialects. It was perhaps the convincing affirmation of the Iranian origin of the Scythian and Sarmatian tribes that laid the foundations of this tradition. Since the notion of the Andronovo archaeological culture acquired (mainly during the 1950s) its fame, it is also widely believed that the population of this culture, which lived in the direct vicinity to Finno-Ugrian (Permian and especially Ugrian) tribes and obviously exercised a strong cultural and linguistic influence upon its northern neighbors, constitutes an intermediate link in this chain of transformations. The Andronovo population is therefore qualified as Proto-Iranian or Early Iranian.
The most numerous and representative portion of words, which are usually viewed as Iranian borrowings in Ob-Ugrian (Ugrian) and in Permian, do not show any specifically Iranian or Early Iranian features (category C). They could be equally well called Indo-Aryan or Early Indo-Aryan borrowings, if only such designation had any historical sense. If these words stem from the language(s) of the Andronovo population – which is very likely, – then they bear positive evidence only for qualifying this population as Aryan, not as Proto- or Early Iranian.
[. . .] It must be added that the Aryan loanwords present only in Western Finno-Ugric languages (in Finno-Permian or in its individual branches), and probably representing therefore a relatively late layer of borrowings, also do not exhibit, on the whole, more similarity to Iranian than to Indo-Aryan. Neither do they reflect the Common Iranian development of *s into ʯ.
The proposed resolution:
Taking the chronology and the linguistic evidence and into consideration, the Andronovo population and its language(s) should rather be qualified as the third (or fourth), extinct since the 1st mill. B.C., branch of Indo-Iranian – approximately equally close to both Iranian and Indo-Aryan. This branch cannot also be simply equated with Proto-Indo-Iranian (Proto-Aryan), because at least in the second half of the 2nd mill. B.C. it existed simultaneously with the Indo-Aryan and Iranian branches.
(“Fourth” would be alongside Nuristani.)
Lamberg-Karlovsky 2002: Fig. 2. Principal archaeological sites and cultures mentioned in text. Sites: A, Mikhailovka; B, Petrovka; C, Arkhaim; D, Sintashta; E, Botai; F, Namazga; G, Gonur; H, Togolok; I, Dashly Oasis; J, Sapelli; K, Djarkutan; L, Hissar; M, Shahr-i-Sokhta; N, Sibri; O, Shahdad; P, Yahya; Q, Susa. Cultures: 1, Tripolye; 2, Pit Grave/Catacomb; 3, Sintashta/Arkhaim; 4, Abashevo; 5, Afanasievo; 6, Andronovo; 7, Bactrian Margiana archaeological complex; 8, Indus; 9, Akkadian; 10, Hurrian; 11, Hittite.
Worth keeping in mind through all of this are the archaeological critiques of a simple equation of either Andronovo or BMAC with ancestral Indo-Iranians. As C.C. Lamberg-Karlovsky frames it :
Not a single artifact of Andronovo type has been identified in Iran or in northern India, but there is ample evidence for the presence of Bactrian Margiana materials on the Iranian Plateau and in Baluchistan (e.g., at Susa, Shahdad, Yahya, Khurab, Sibri, Miri Qalat, Deh Morasi Ghundai, Nousharo [for a review see Hiebert and Lamberg-Karlovky 1992]). It is impossible, however, to trace the continuity of these materials into the 1st millennium and relate them to the known cultures of Iranian-speakers—the Medes or the Achaemenids (or their presumed Iron Age ancestors [see Ghirshman 1977, Young 1967]). The only intrusive archaeological culture of the 2d millennium that directly influences Iran and northern India is the Bactrian Margiana archaeological complex, but it cannot be linked to the development of later 2d- and 1st millennium archaeological cultures on the Iranian Plateau.
His model (which explicitly leaves open the possibility that not all divisions or expressions of Andronovo — “if any!”, I think he’d add — were even necessarily Indo-European-speaking):
. . . one might imagine the Andronovo culture as consisting of “polyethnic confederations” which had varying archaeological expressions—Alakul, Petrov, Abashevo, “the country of towns,” etc.—each maintaining its “traditional linguistic, cultural, and even political organization.” The identification of the Andronovo culture as a singularity, in both a cultural and a linguistic sense, transforms the multiple and the complex into the singular and simple.
J. P. Mallory is largely in agreement  that: “We find it extraordinarily difficult to make a case for expansions from this northern region to northern India . . . where we would presume Indo-Aryans had settled by the mid-second millennium BC.”
His somewhat tongue-in-cheek solution: envisioning Indo-Iranian as a Kulturkugel (‘cultural bullet’) with a durable linguistic midsection and a frangible, rapidly swappable tip of archaeologically visible elements: “the material culture of the Indo-Iranian Andronovo culture is shed in impact with BMAC although the language trajectory continues.” That would do it, for sure, but it is awfully convenient.
 Beerli, P. (2004). Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations. Molecular Ecology 13: 827–836.
 Patterson, N., Moorjani, P., Luo, Y., Mallick, S., Rohland, N., Zhan, Y., Genschoreck, T., Webster, T., Reich, D. (2012). Ancient admixture in human history. Genetics 192(3): 1065–1093.
 Raghavan, M., Skoglund, P., Graf, K.E., Metspalu, M., Albrechtsen, A., Moltke, I., Rasmussen, S., Stafford, T.W., Jr., Orlando, L., Metspalu, E., Karmin, M., Tambets, K., Rootsi, S., Mägi, R., Campos, P.F., Balanovska, E., Balanovsky, O., Khusnutdinova, E., Litvinov, S., Osipova, L.P., Fedorova, S.A., Voevoda, M.I., DeGiorgio, M., Sicheritz-Ponten, T., Brunak, S., Demeshchenko, S., Kivisild, T., Villems, R., Nielsen, R., Jakobsson, M., Willerslev, E. (2014). Upper Palaeolithic Siberian genome reveals dual ancestry of Native Americans. Nature 505(7481): 87–91.
 Lamberg-Karlovsky, C.C. (2002). Archaeology and Language: The Indo-Iranians. Current Anthropology 43(1): pp. 63–88.
 Mallory, J.P. (1998). A European Perspective on Indo-Europeans in Asia. In Mair, V.H. (Ed.), The Bronze Age and Early Iron Age Peoples of Eastern and Central Asia (Vol. 1), pp. 175–201. Philadelphia: University of Pennsylvania Press.
Kuzʹmina, for her part, acknowledges the appeal of the Kulturkugel model but rejects to the extent that it requires Andronovan descendants — contrary to Rigvedic descriptions of Aryan livelihood — to have lost their stock-breeding orientation as they passed through the urban farming zone of BMAC (whose Iranian attribution she denies):
Kuzʹmina, E. E., & Mallory, J.P. (Ed.). (2007). The origin of the Indo-Iranians. Leiden, The Netherlands: Brill.
commenter “j.” (July 10, 2014, 8:43 PM):
There is of course also the sizable number of “Finno-Permic” vocabulary of unknown origin, including e.g. key agricultural terms such as *wešnä “wheat” (Finnic, Mordvinic, Mari), *(u)skal “cow” (Mordvinic, Mari, Permic). Frequently full of irregularities just as well. We have much still to learn about the ancient contact languages of Uralic.
More discussion of some terms for domesticates.