Among Slavmacedonian ultranationalists who believe that Greece “has held Macedonian territory illegally for…95 years” and who dream of the re-unification of historical ethnic Macedonia,(among them and the FYROM PM) there is considerable excitement at the prospect of their view that Slavmacedonians “are the oldest people living in the Balkans” being genetically corroborated. Most of today’s Slavmacedonian are in fact citizens of the Former Yugoslav Republic of Macedonia (FYROM), carved out of the remains of Yugoslavia in 1991, with many others living in northern Greece.
Slavmacedonians speak a Slavic language, very close to the Bulgarian; part of a family of language, brought to the Balkans by Slavic tribes in the sixth and seventh centuries, and first began to develop a unique national identity at the turn of the twentieth century. Nonetheless, some of these citizens believe that they are in fact the .......
...... descendants of Alexander the Great of Macedon, and as such “are not Slavs, but have a direct descent from the ancient Macedonians.” Consequently, they claim territorial rights to Greece’s Northern Historical and admistrative Province, also called Macedonia and part of the site of the ancient Macedon kingdom, a Greek ruler kingship.
Genetic Studies of Greeks
Modern studies have constructed Greek genetic trees revealing a strong degree of homogeneity between Greeks from different geographical locations. Median networks revealed that most of the Greek haplotypes are clustered to the five known haplogroups and that a number of haplotypes are shared among Greeks and other European and Near Eastern populations. Within the loci studied, the genetic composition of the Greeks indicates a significantly low level of heterogeneity compared with other European populations. The levels of the R1a1 haplotype, associated by some with Slavic migrations,  have been found to be less than 12% (by way of comparison the relevant percentage for Syria is 10% and Poland 60%). This confirms other studies that disprove the thesis that the Greeks have mingled substantially with Slavic people. A 7%–22% contribution of Y chromosomes by Greeks to Southern Italy was estimated by admixture analysis in the same study. Yet other studies point out the significant frequency drop of the R1a marker over the short geographic distance between Greece and its Slavic northern neighbours. 
Modern scholars and scientists have supported the notion that there is a racial connection to the ancient Greeks. Luigi Luca Cavalli-Sforza, Paolo Menozzi, and Alberto Piazza, have found evidence of a genetic connection between the ancient and modern Greeks.  Recent genetic analyses of Greek populations have provided evidence of statistically significant continuity between ancient and modern Greeks (low admixture attributed to genetic isolation due to physical barriers). 
Modern and ancient Greeks
Some authors in the West and Turkey  have posited that the Greeks of today are not culturally or demographically related to the Greeks of classical antiquity. Notable among them was the 19th century Austrian historian Jakob Philipp Fallmerayer. Fallmerayer, in his work Geschichte der Halbinsel Morea während des Mittelalters, averred that demographic continuity in Greece was interrupted brutally by successive waves of invasion and migration between the 6th and 8th century by Slavs, and later, in the second half of the 14th century by Albanians who occupied and settled mainly in the Peloponnese. According to this narrative, the centre of gravity of the ancient Greek ethnos was shifted outside the boundaries of modern Greece, and so the "demographic evidence is at best tenuous, at worst non-existent".  The traditional view is that the Fallmerayer thesis, rooted in 19th century racialism, provoked an "outraged" Greek response, of which Constantine Paparrigopoulos was the spearhead; however, modern scholarly opinion tends to see both Fallmerayer and Paparrigopoulos as taking positions influenced by and intelligible only within the political and intellectual decline of Western philhellenism. 
Fallmerayer's controversial and racist  views were later incorporated in Nazi theoretician Alfred Rosenberg's Der Mythus des 20es Jahrhunderts and found adherents in the Third Reich who echoed them in their writings.  They were also actively promoted by the Axis occupation authorities in Greece who hoped to extinguish any sympathy their troops might feel for the Greeks.  Other Western authors say that it is Westerners who are the "true heirs" of Greece, since Greeks today, whom they label "modern Greeks", are the product of "genetic dissonance" and "mingling with slaves".  While the point of demographic continuity has been contested by several authors in the West and Greece, ideas of race have never been such a prominent feature in the Greek world, either ancient,  or later. The medieval Greek mythological hero Digenis Acritas was so named because of his dual, Greek and Syrian, parentage. 
The most obvious link between modern and ancient Greeks is their language, which has a documented tradition from at least the 14th century BC to the present day, albeit with a break during the Greek Dark Ages. The Byzantinist Robert Browning, compares its continuity of tradition to Chinese alone. At its inception, Hellenism was a matter of common culture and the national continuity of the Greek world is more certain than its demographic. Even during the Slavic migrations, in Ionia and Constantinople there was a Hellenic revival in language, philosophy and literature and on classical models of thought and scholarship. Such revivals would manifest again in the 10th and 14th century providing a powerful impetus to the sense of cultural affinity with ancient Greece and its classical heritage.  The cultural changes undergone by the Greeks are, despite a surviving common sense of ethnicity, undeniable.At the same time the Greeks have retained their language and alphabet, certain values, a sense of religious and cultural difference and exclusion, (the word barbarian was used by 12th century historian Anna Komnene to describe non-Greek speakers),  a sense of Greek identity and common sense of ethnicity despite the many political and social changes of the past two millennia.
The Arnaiz-Villena controversy
An often-cited study from 2001 by the Spanish lab of the Antonio Arnaiz-Villena et al. (among them were and Slavamcedonian genetists from FYROM-SkopjeUniversity)  which maps 28 world population based on the HLA DRB1 locus, concluded that "the reason why Greeks did not show a close relatedness with all the other Mediterraneans analyzed was their genetic relationship with sub-Saharan ethnic groups now residing in Ethiopia, Sudan, and West Africa (Burkina Faso)." Later that year, the same data was used in another study by the same author published in a different journal.  This second paper dealt specifically with the relatedness of Palestinians and Israelis and was subsequently "deleted from the scientific literature" because, according to the editor-in-chief Nicole Suciu-Foca, it "confounded the elegant analysis of the historic basis of the people of the Mediterranean Basin with a political viewpoint representing only one side of a complex political and historical issue". 
Erica Klarreich's report on the controversy further quotes Suciu-Foca as saying that the reaction against the paper was so severe that "We would have had mass resignations and the journal would have been destroyed if this paper were allowed to remain."  The controversy was further reported on in numerous locations including The Observer. 
Shortly after this, three respected geneticists, Luca Cavalli-Sforza, Alberto Piazza and Neil Risch, argued that the scientific limitations of Arnaiz-Villena's methodology.  They stated that "Using results from the analysis of a single marker, particularly one likely to have undergone selection, for the purpose of reconstructing genealogies is unreliable and unacceptable practice in population genetics.", making specific allusion to the findings on Greeks (among others) as "anomalous results, which contradict history, geography, anthropology and all prior population-genetic studies of these groups."
No multiple-marker analysis has ever duplicated Arnaiz-Villena's results. In The History and Geography of Human Genes (Princeton, 1994), Cavalli-Sforza, Menozzi and Piazza grouped Greeks with other European and Mediterranean populations based on 120 loci (view MDS plot ). Then, Ayub et al. 2003[  did the same thing using 182 loci (view dendrogram ).
Another study was conducted in 2004 at Skopje's University of Ss. Kiril and Metodij, using high-resolution typing of HLA-DRB1 according to Arnaiz-Villena's methodology. Contrary to his earlier conclusion, however, no sub-Saharan admixture was detected in the Greek sample. 
A 2006 study by Tunisian scientists again asserted the relatedness of the Greeks to sub-Saharans by calculating genetic distances at the DRB1 locus,  the same marker used in the controversial Arnaiz-Villena paper. Both papers interpreted those results as suggesting an admixture occurred due to the displacement of Egyptian-Ethiopic people during the Pharaonic period. However, the Tunisian scientists failed to analyze any new Greek genetic material, relying solely on the data contained in the earlier Arnaiz-Villena paper, and no Greek laboratory contributed to their research. 
The credibility of Arnaiz-Villena was seriously damaged after he was suspended without pay from the Hospital Doce de Octubre in Madrid, where he heads the department of immunology and molecular biology, after being charged with embezzlement of funds.  In addition to this charge, Dr Arnaiz-Villena is facing allegations of "moral harassment" at the Universidad Complutense de Madrid, where he chairs a research and teaching immunology unit. All charges against Prof Arnaiz-Villena were proven to be fabricated and false and he was reinstated in his post(see Wikipedia ,link to "Antonio Arnaiz-Villena") 
The disputed data continues to be cited all over the internet, mostly by white supremacists, afrocentrists and Slavmacedonians nationalists (usually VMRO fans and Diaspora Centers like maknews.com) who have political motivations to relate modern and/or ancient Greeks to black Africans. However, it's no longer referenced by population geneticists in contemporary research, mainly due to the criticism of Cavalli-Sforza et al.
The genetics, with its appearance of scientific objectivity, holds obvious—albeit illusory—appeal. As Appelbaums remarked for nations with strong claims to territorial sovereignty, genetic data will be irrelevant; for nations with weak claims, such data will always be inadequate. Advocates who look to genetics for a decisive victory are certain to be disappointed. 
Modern Greeks are the descendants of all the peoples who have adopted and retained that language and that civilization from classical times to the present. I am not claim that genetic purity is an ideal for the Greek people and the others racist thinks.Asa I said even Sforza put two others factors except the clusters and these are the language and the history. Modern Greek nation is not an entirely modern formation, for it is based on much older cultural groups (ethnies). Greek ethnies (like Arvanites, Vlachs, Slavophones etc.) present "permanent cultural attributes" such as memory, value, myths and symbolisms. Greek ethnies present a common cultural origin descending from ancient Greece and Byzantium.Thus, as Smith points out, "the challenge for scholars is to represent more accurately and convincingly the relationship of ethnic, cultural (Greek) past to modern (Greek) nation". 
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