briefly , gps ( elhaik et al . 2014 ) works in the following way ( fig .
1 ) : 1 ) unsupervised admixture analysis represents a worldwide panel , composed of modern individuals only , as a mixture of an optimal number ( k ) of hypothetical ancestral populations ; 2 ) based on allele frequencies inferred by admixture , k ancestral populations of size n are simulated and used in a supervised admixture run ( alexander and lange 2011 ) ; 3 ) populations from the original panel that supposedly have not migrated in the last few centuries form the reference panel , and test individuals are added ; 4 ) genetic distances among the test individuals and reference populations are calculated based on the comparison of their admixture profiles obtained in the supervised admixture run ( genetic admixture distance is defined as  the minimal euclidean distance between the admixture proportions of an individual to those of all individuals of a certain population , 
das et al . 2016 ) ; 5 ) the test individuals are assigned to best - matching reference populations , based on genetic distances ; and/or 6 ) geographic coordinates of the test individuals are predicted by averaging across reference populations coordinates weighted according to their genetic distance from the test individuals ( only ten best - matching references are used at this step ) .
unsupervised admixture mode often overestimates small admixture coefficients , whereas the supervised mode mitigates this problem , provided that reference populations k are genetically homogeneous and truly ancestral for the other individuals in the dataset ( alexander and lange 2011 ) .
this mode also allows easy analysis of new individuals without recomputing admixture coefficients for the whole dataset , and therefore is extensively used in commercial - oriented applications . 

steps prior to the supervised admixture run are used for the method optimization only , and a typical workflow starts with a supervised admixture run . * * coordinates of test individuals inferred by the gps algorithm were interpreted by das et al .
( 2016 ) as coordinates of ancestral populations (  primeval villages  ) or as the last place where admixture has occurred . a diagram illustrating the gps workflow .
* steps prior to the supervised admixture run are used for the method optimization only , and a typical workflow starts with a supervised admixture run . * * coordinates of test individuals inferred by the gps algorithm were interpreted by das et al .
( 2016 ) as coordinates of ancestral populations (  primeval villages  ) or as the last place where admixture has occurred . in practice
, an unadmixed individual would be positioned by the gps software on the map near its best - matching reference population , whereas an individual representing a two - way mixture of reference populations would be positioned on a line connecting coordinates of the mixture partners :  for an individual of mixed origins , the inferred coordinates represent the mean geographical locations of their immediate ancestors 
thus , gps essentially represents a clustering tool useful for inferring provenance of modern unadmixed genomes , provided a large reference panel is available .
gps predictions should therefore be interpreted as the last place that admixture has occurred , termed here geographical origin .  at another point das et al .
have provided a somewhat different interpretation :  gps infers the geographical origins of an individual by averaging over the origins of all its ancestors .
 we would argue that these interpretations , which lie at the core of the paper discussed here , are simply wrong .
the first conceptual problem is that each individual has thousands of ancestors at the time depth of 1,000 years ( although the theoretical upper limit of distinct ancestors is much higher and equals 2 , where n is the number of generations ) .
localizing all the ancestors to a single primeval village or to  the last place where admixture has occurred  is extremely difficult to imagine : even if we assume that admixture profiles of most individual 's ancestors 1,000 years ago are indistinguishable given the resolution of the gps method , and that those ancestors were located in a limited geographical region , we can not avoid the fact that mixture of genetically distinct populations was a widespread phenomenon in human history , both ancient and recent ( hellenthal et al . 2014 ) .
coordinates of mixture partners can not be interpreted as the last place where admixture has occurred or as averaged coordinates of all individual s ancestors , which is illustrated by simple diagrams showing movement of test and reference populations in time and space ( fig .
second , as a clustering method operating on modern references , gps has no way to trace population movements back in time ( fig .
only studies of ancient genomes and their coordinates in space and time can approach locating ancestral homelands with enough precision ( allentoft et al .
2015 ) . in summary , even if a dense sampling of modern reference populations is available , and if they have not moved for considerable time ( an assumption made by das et al .
2016 ) , inferring correct ancestral locations of test populations that have admixed and/or moved over time is hardly possible with the gps method . 

2.space-time diagrams illustrating behavior of a very simple system of two reference populations ( ref1 and ref2 ) and one test population ( test1 ) .
genetically similar populations are depicted with similar colors ; ancestral locations that would be predicted by the gps algorithm are shown with dark - red vertical lines , and their distances from the true ancestral locations are shown with blue arrows .
spatial coordinates for the ancestral population of test1 would be accurately predicted by gps only in the simplest scenario , when neither test nor references move much in space during a time window appropriate for the method ( a ) . if test1 has moved considerably during its history ( b ) ,
its ancestral location can not be predicted without knowing coordinates of any ancient genomes along its  worldline  . in the scenario b ,
closely related populations ref1 and test1 occupied a large territory in the past , and then their range underwent considerable contraction .
the kets , a yeniseian - speaking siberian ethnic group , represent a good example of this scenario : yeniseian tribes over the last 1000 years have moved a long distance from the south to the north , and their range underwent an extreme contraction under various pressures ( flegontov et al . 2016 ) .
thus , location of the kets today is very far from their original homeland 1000 years ago .
similarly , if a reference moves over time , gps would also make an error in estimating the ancestral location of test1 ( c ) .
if test1 is a one - to - one mixture of ref1 and ref2 , single ancestral location is meaningless for this population ( d ) , and gps would place the ancestral location of test1 on the midpoint between ref1 and ref2 .
the statement  gps predictions should therefore be interpreted as the last place that admixture has occurred , termed here geographical origin 
obviously , location of the mixture partners and of the mixed population can change over time , and gps has no information to trace these past movements , producing an erroneous location of the last admixture event ( the green arrow shows that the inferred last place of admixture is misplaced ) .
space - time diagrams illustrating behavior of a very simple system of two reference populations ( ref1 and ref2 ) and one test population ( test1 ) .
genetically similar populations are depicted with similar colors ; ancestral locations that would be predicted by the gps algorithm are shown with dark - red vertical lines , and their distances from the true ancestral locations are shown with blue arrows .
spatial coordinates for the ancestral population of test1 would be accurately predicted by gps only in the simplest scenario , when neither test nor references move much in space during a time window appropriate for the method ( a ) . if test1 has moved considerably during its history ( b ) , its ancestral location can not be predicted without knowing coordinates of any ancient genomes along its  worldline  . in the scenario b ,
closely related populations ref1 and test1 occupied a large territory in the past , and then their range underwent considerable contraction .
the kets , a yeniseian - speaking siberian ethnic group , represent a good example of this scenario : yeniseian tribes over the last 1000 years have moved a long distance from the south to the north , and their range underwent an extreme contraction under various pressures ( flegontov et al .
thus , location of the kets today is very far from their original homeland 1000 years ago .
similarly , if a reference moves over time , gps would also make an error in estimating the ancestral location of test1 ( c ) .
if test1 is a one - to - one mixture of ref1 and ref2 , single ancestral location is meaningless for this population ( d ) , and gps would place the ancestral location of test1 on the midpoint between ref1 and ref2 .
the statement  gps predictions should therefore be interpreted as the last place that admixture has occurred , termed here geographical origin 
obviously , location of the mixture partners and of the mixed population can change over time , and gps has no information to trace these past movements , producing an erroneous location of the last admixture event ( the green arrow shows that the inferred last place of admixture is misplaced ) .
another fundamental problem lies in data reduction inherent in the gps approach : genotypes at about 100,000 sites ( das et al .
2016 ) are not analyzed directly , but collapsed to just few variables , that is , admixture coefficients for nine hypothetical ancestral populations ( elhaik et al . 2014
( 2016 ) were essentially based on this extremely reduced set of variables ; variables that are themselves biased by the particular sample coverage used to infer them ( see fig .
1 ) . on the contrary , disentangling recent migration and admixture events , for example , those within the 1000-year window , often requires the most sophisticated methods available and the largest amounts of genotype data .
variations in frequencies of common snp alleles , used in high - throughput genotyping arrays , tend to be small in recently diverged populations ( schiffels et al .
2016 ) , and therefore all methods of clustering and admixture inference based on common genetic variants lack resolution in this time window .
extremely rare snp alleles ( with global frequency < 1% ) or autosomal haplotypes provide a much better resolution ( leslie et al .
2016 ) requires whole - genome data , and autosomal haplotypes can be inferred from dense snp array or whole - genome data , and analyzed with the chromopainter , finestructure ( lawson et al . 2012 ) , and globetrotter tools ( hellenthal et al . 2014 ) .
gps has placed 25% of 249 sardinians into their home villages , and 50% within 15 km from their villages
2 , supplementary material online in elhaik et al . 2014 ) lack structure : average proportions of components differ among villages by 2% at most ( in absolute terms ) , and the pair of villages most distant geographically ( villagrande and santantioco ) differs by 2% of the mediterranean , 2% of the middle eastern , and 1% of the north european component , with the other components identical ( supplementary fig .
five components that reach > 1% in sardinia are mediterranean ( 58% ) , north european ( 19% ) , middle eastern ( 16% ) , south  east asian ( 3% ) , and sub - saharan african ( 1% ) ; their distributions are summarized by box plots in supplementary figure s2 , supplementary material online . among 45 possible pairs of villages ,
the anova test shows that only 2 pairs have significantly different fractions of the mediterranean component ( adjusted p - value < 0.05 ) , 10 pairs  of the north european ; 13 pairs  of the middle eastern , 3 pairs  of the sub - saharan african , and no pairs  of the southeast asian component ( supplementary fig . s2 , supplementary material online ) .
apparently , placement of a quarter of sardinians into their home villages was possible due to these differences in admixture profiles .
however , variability of 12% in absolute values is generally considered as noise in admixture analyses , and depends much on dataset composition and on the number of algorithm iterations , among which the best one is selected .
thus , gps results on the sardinian population are , in our view , unreliable due to extreme data reduction . above
we have considered conceptual problems that arise even with idealized densely spaced and stationary references .
ancestral  are influenced by positions of reference populations , which are rather sparse in reality . in the original gps implementation ( elhaik et al .
2014 ) , reference populations were almost lacking in some regions : usa , canada , most of south america , siberia , most of north africa , australia , and southeast asia were not covered . in published gps results ,
quite a few individuals were mapped along straight lines connecting best proxies of their mixture partners ( elhaik et al .
2014 ) : 1 ) many italians and some spanish were placed in greece , on a line connecting the italian and lebanese reference populations ; 2 ) all tunisians and some kuwaiti were placed in the mediterranean sea ; 3 ) most bermudians were placed on a line in the atlantic ocean , connecting the bermudian and yoruba reference populations ; 4 ) most puerto ricans were placed on another line in the atlantic ocean , connecting the puerto rican and spanish reference populations ; 5 ) all peruvians and mexicans were placed on a line connecting the two countries , and crossing the pacific ocean .
these cases are sufficient to illustrate that mapping of test individuals has little or nothing to do with ancestral locations ( see fig .
2 ) , but is determined by their collapsed mixture proportions and by coordinates of sparsely positioned references . in parts of the map more densely populated with references , positioning along straight lines is less common due to differential pull of ten genetically closest references ( das et al .
( 2016 ) , the gps approach introduced in the original publication was used without modification in the work on ashkenazi jews . although the original reference dataset ( elhaik et al . 2014 ) was updated by das et al .
( 2016 ) , the sampling remained sparse , with just 26 reference populations . not surprisingly , similar positioning artefacts are seen in the paper discussed here : 1 ) most italians and apparently all greeks were positioned in bulgaria and in the black sea ; 2 ) all lebanese were scattered along a line connecting egypt and the caucasus ; 3 ) all nogais from the caucasus and pamiri tajiks were placed in turkmenistan or in the caspian sea , to give just few examples . therefore ,
one is left to wonder why so much weight is put on the inferred locations of ashkenazi jews in bulgaria , amid the black sea , and in turkey :  the geographic population structure ( gps ) analysis localized most ashkenazi jews along major primeval trade routes in northeastern turkey adjacent to primeval villages with names that may be derived from ashkenaz 
( das et al . 2016 ) . because ashkenazi jews represent a population with a clear admixture signature ( atzmon et al .
( 2016 ) form a gradient between mixture partners located in europe and in the middle east , or rather between their proxies among the modern reference populations .
moreover , genotypes of ashkenazi jews were obtained from a genetic testing company , ancestry of their grandparents was not controlled , and 86% individuals originated from the usa ( das et al .
based on overwhelming empirical evidence , modern linguistics generally defines primary evidence for genetic relationship of languages as 1 ) a significant number of etymological matches between their basic vocabularies , and 2 ) a significant number of etymological matches between their main grammatical exponents ( such as number , case , person , etc . ) , see , for example , campbell & poser ( 2008 ) .
the germanic ( or , more precisely , high german ) affiliation of yiddish is thus firmly based on two observations : 1 ) the yiddish basic vocabulary is predominantly germanic , and 2 ) the majority of grammatical exponents , including the main ones , are germanic .
this may be easily demonstrated by consulting such standardized basic wordlists as the 200-item wordlist of morris swadesh ( where only a small handful of items are of hebrew or slavic origin ) , or the 700-item t. kaufman s basic concept list , only approximately 10% of which is of slavic , and approximately 5% of hebrew origin .
likewise , the majority of yiddish grammatical exponents are also transparently germanic ( jacobs et al . 1994 ) , regardless of whether they are applied to indigenous germanic or borrowed slavic words ( specific lexical and grammatical examples are listed in the linguistic supplement , supplementary text s1 , supplementary material online ) .
consequently , there is a natural consensus in modern linguistics on the german affiliation of yiddish ( rothstein 2006 ; harbert 2007 ; roberge 2010 , inter alia ) , and it would take much more evidence than has been presented by wexler to support the contrary assertion that yiddish is a  fifteenth slavic language  ( wexler s original proposal , wexler 1991 ) or even a  relexified slavic language . 
, 510% overall ) , it predominantly represents cultural vocabulary . likewise , despite wexler s claim that  yiddish grammar and phonology are slavic ( with some irano  turkic input )  ( das et al . 2016 , similarly in wexler 1991 , 2010 ) , he has managed to offer only a few grammatical / phonological matches between yiddish and slavic , generally confined to secondary grammatical features ( such as semantic shifting of some german aspectual / spatial verbal prefixes and some nominal derivational suffixes towards the functions of their slavic counterparts ) .
typological studies on language contact ( thomason & kaufman 1988 ; van coetsem 2000 ; thomason 2001 ; winford 2003 ) clearly suggest that all these phenomena may be optimally explained as later slavic influence on yiddish . in other words ,
slavic languages functioned as adstrate and superstrate for yiddish , rather than an underlying substrate ( see supplementary text s1 , supplementary material online for details ) . a key point for das et al .
( 2016 ) is that there are allegedly iranian and turkic loanwords in yiddish which should indicate ancient contact between yiddish and anatolian communities ( as das et al .
2016 state :  a slavic origin [ of yiddish ] with strong iranian and weak turkic substrata  ) .
but in reality , however , wexler offers only a few yiddish cultural words which eventually go back to persian or turkic forms , and all reliable cases represent areally diffused words which also happen to be spread across slavic languages ( see supplementary text s1 , supplementary material online for some individual cases ) .
thus , such yiddish terms are explainable as slavic cultural loans , and there is no firm linguistic evidence for positing early yiddish  persian or yiddish  turkic contacts .
in our view , das et al . have attempted to fit together a marginal and unsupported interpretation of the linguistic data with a genetic provenancing approach , gps , that is at best only suited to inferring the most likely geographic location of modern and relatively unadmixed genomes , and tells little or nothing of population history and origin . using explication of the gps workflow and examples from the original gps publication ( elhaik et al .
2014 ) , as well as from the paper discussed here ( das et al .
2016 ) we find that this inference methodology provides no more information on an individual s population origin than a few generations of family history . as opposed to gps and similar tools ( kozlov et al .
2015 ) operating on highly reduced data , we advocate the use of more data - intensive and sophisticated approaches for the study of population history within the last 5,000 years : rarecoal ( schiffels et al .
2016 ) , chromopainter , finestructure ( lawson et al . 2012 ) , and globetrotter ( hellenthal et al . 2014 ) , among others .
support the khazar hypothesis of ashkenazi ancestry , placing their alleged  irano - turko - slavo jewish merchants  within the khazar empire .
designate this empire as the  slavo - iranian confederationa historically meaningless term invented by the authors under review .
having been popular in the mid-20th century , the idea that the khazars directly contributed to ashkenazi ancestry is currently abandoned by practically all historians and linguists .
to say more , according to a recent analysis of historical sources ( stampfer 2013 ) , the conversion of khazars to judaism might have never happened , being a medieval legend .
the khazar hypothesis has previously been advocated in a genetic study ( elhaik 2013 ) reanalyzing autosomal snp data from behar et al .
as no ancient dna of khazars was available , modern armenians and georgians were chosen by the author as genetic proxies for the ancient khazar population ( elhaik 2013 ) .
this questionable choice of modern proxies may have biased the conclusions of the study , and a further analysis of a significantly extended dataset , spanning europe , the middle east , and the region historically associated with the khazar khaganate , has found no particular similarity of ashkenazi jews with populations from the caucasus , including populations in the khazar region ( behar et al .
a large - scale study based on mitochondrial dna ( mtdna ) has also found no evidence for the khazar hypothesis , estimating that > 80% of ashkenazi mtdnas were probably assimilated within europe , and virtually no mtdnas were traced to the north caucasus ( costa et al .
a study focused on the y chromosome has found strong support for the near eastern origin of a significant portion of ashkenazi y chromosomes ( rootsi et al .
genetic studies support the traditional view on the history of the european jewish diaspora : its levantine origin , migration to the north mediterranean followed by substantial local admixture , especially on the maternal side , and subsequent limited east european admixture in the ashkenazi community ( atzmon et al .
supplementary figures s1 and s2 , text s1 , and table s1 are available at genome biology and evolution online ( http://www.gbe.oxfordjournals.org/ ) .
 in a recent interdisciplinary study , das et al . have attempted to trace the homeland of ashkenazi jews and of their historical language , yiddish ( das et al . 
 2016 . 
 localizing ashkenazic jews to primeval villages in the ancient iranian lands of ashkenaz . 
 genome biol evol . 
 8:11321149 ) . 
 das et al . 
 applied the geographic population structure ( gps ) method to autosomal genotyping data and inferred geographic coordinates of populations supposedly ancestral to ashkenazi jews , placing them in eastern turkey . 
 they argued that this unexpected genetic result goes against the widely accepted notion of ashkenazi origin in the levant , and speculated that yiddish was originally a slavic language strongly influenced by iranian and turkic languages , and later remodeled completely under germanic influence . 
 in our view , there are major conceptual problems with both the genetic and linguistic parts of the work . 
 we argue that gps is a provenancing tool suited to inferring the geographic region where a modern and recently unadmixed genome is most likely to arise , but is hardly suitable for admixed populations and for tracing ancestry up to 1,000 years before present , as its authors have previously claimed . 
 moreover , all methods of historical linguistics concur that yiddish is a germanic language , with no reliable evidence for slavic , iranian , or turkic substrata . 
GPS is not Suitable for Inferring Ancestry
Major Problems of the Yiddish Relexification Theory
Conclusions
Supplementary Material