But despite the extinction of their genes, the Magyars live on in posterity

 From Hungarians as the ghost of the Magyar confederacy by Razib Khan.

Though right at the heart of Europe, Hungary is an ethnolinguistic oddity, with a distinct history and unique language. The Pannonian grasslands that cover most of its territory are the westernmost tendril of the Eurasian steppe. Though called the Nagy Alföld in Hungarian, or “Great Hungarian Plain,” in relation to the vast Pontic steppe to its east, it is quite small, only 10% the size. It has loomed large in European history because the Nagy Alföld is the furthest west that nomadic pastoralists could maintain vast herds of horses, from the Pontic Steppe’s Yamnaya herders 5,000 years ago, down to the Magyars in the early medieval period. It served as the base for Sarmatians who raided the Roman Empire in the 3rd century AD, the Avar Empire that menaced Byzantium in the 6th and 7th centuries, and it was here that in 453 AD Attila the Hun died in a drunken stupor, surrounded by riches plundered from half the continent.

It was with the arrival of the Magyars from the east in 895 AD that the Nagy Alföld came into its own as the heart of what was to become Hungary. The Sarmatians, Huns, and the Avars are all storied names in ancient annals, though terrors whose bite has faded from contemporary consciousness. The Magyars were all that, but they also left a legacy in the Hungarian national identity. Despite entering Europe as steppe barbarians, by the 12th century, the Magyars were at the heart of Christian civilization, erecting great cathedrals, sending knights on Crusade and intermarrying with the nobility of Germany and France. Just 200 years later, they were again on the frontier, the great bulwark of Christendom against the repeated hammer blows of the Ottoman Turks, until they were defeated and Budapest became the northwesternmost outpost of Islam. But they always remained European outsiders, as speakers of a language whose closest relatives are found in Siberia, a cultural mystery whose origins and affinity were only recently clarified by science.

In the modern mind, the Hungarians are connected to the Huns due to phonetic similarity and the fact that the Huns also settled down in the Pannonian plain. But 450 years separate the defeat of Attila the Hun at the Battle of Catalaunian Plains and the arrival of the Magyar tribes to the Carpathian Basin. “Hungary” probably derives from the name of the Turkic tribes that formed the basis for the ancient Bulgar Empire, the Onogur. In the mind of Western Christians, there was confusion between the Turkic nomads of the steppe and the Magyars who were closely allied to them when they weren’t fighting one another (Hungarians refer to their nation as Magyarország, meaning “Magyar country”).

But the Huns were a more ancient Turkic tribe who likely never interacted with the Magyars in the latter’s lightning-fast migration from one end of Eurasia to another. And yet the Huns and Attila both retain a romantic allure for the Hungarian people. Most people today with the name Attila are ethnically Hungarian, while medieval histories of the Magyars begin with the myth that they and the Huns descend from two brothers, Magor and Hunor. With this connection, the Magyars established a legitimacy that tied their conquests to those of the fearsome Huns. Thus the Magyars who rose to power in the 10th century as the raiders par excellence of Europe could claim they were simply resurrecting an imperium that had always been theirs.

It is an excellent article showing how genomic research is beginning to provide answers to historical questions but in doing so, raising new questions.

Are Hungarians genetic descendants of 10 century Magyar invaders?  No.  But . . . 

The genetic data is clear that a substantial number of Conquerors arrived in Hungary during the 10th century. They are distinct and bear all the hallmarks of a Central Eurasian Uralic population. But today, Hungarians are no different than their neighbors, and the impact of distinctive Magyar ancestry seems faint at best. And yet the Conquerors, unlike the Bulgar Turks (or the Sarmatian Serbs and Croats), were not culturally assimilated by the Slavs they conquered. They enduringly propagated their language and identity to the native people of the land. 

Nevertheless, the evidence above also shows that they remained genetically distinct as a ruling caste, with particular lineages that went back to the tribal coalition that had been formed on the Pontic steppe in the 9th century during the medieval period. To the victors go the spoils. But this strategy has downside risks, as local elites can be decimated by constant war. The Conquerors first suffered losses under the Mongols, but it seems likely that their ultimate downfall was the evisceration of the military elite of Hungary at the hands of the Ottoman Turks, who were, ironically, a successor state to that ancient enemy of the Magyars, the Bulgars.

But despite the extinction of their genes, the Magyars live on in posterity. Árpád and Stephen I are immortal in the memory of a whole nation whose sons still commonly bear the name Attila. Genetically, the Magyars are but a ghost, but culturally they remain with us, vibrant and vigorous, the most numerous and assertive of the Uralic people. We all know that historical memory and ethnic identity can be protean, but the Magyars of today illustrate this starkly. The descendants of Slavic peasants, German knights and Walloon artisans have repopulated the land they call Magyarország, and cherish the memory of Magyar hillfolk who transformed themselves into nomadic warriors and terrorized Europe for a century before it was their turn to defend what had become their civilization against the Mongols and Turks. Sometimes language, myth and legend live on long after flesh and blood have been washed away.

Genetic inheritance is influential from generation to generation but so also is culture.  There is an inclination in some quarters to attribute everything to genes as manifest destiny.  IQ is strongly heritable as are some behavioral traits.  Indeed, almost all behavioral traits are heritable to a degree.  The mixes and matches child by child are a wild card.  The average is never the individual.

Cultural attributes are also replicable and also are handed down.  In the long run, both are important in a fashion not readily comprehended.  We are all dealt somewhat random cards but the game is still shaped by how we play those cards.