Here is what 23andMe has to say about E-V13, for what it is worth.
Origin and Migrations of Haplogroup E-M78
Your paternal line stems from the common ancestor of haplogroup E-M78, a branch of E that dates back approximately 24,000 years. The earliest carriers of the E-M78 lineage likely lived in a population that moved from eastern Africa into northeastern Africa about 14,000 years ago, during the final days of the Ice Age. From northeastern Africa, their descendants expanded to the west between the Sahara and the Mediterranean coastline, and to the east out of Africa into the Middle East, where E-M78 men remain common.
Today, men bearing this haplogroup are also common in southern Europe, including in the Balkans, Iberia, and Italy. In Greece, Bulgaria, and Albania, between 15% and 30% of men bear haplogroup E-M78. Their ancestors were likely relatively late arrivals to the region. While some branches of haplogroup E were carried into Europe nearly 8,000 years ago, recent research suggests that the major spread of E-M78 occurred in the last 5,000 years or so during the Bronze Age. Bronze Age cultures learned to smelt tin and copper to create beautiful and complex bronze items like hardier tools and weapons. They journeyed along river waterways in the Balkans and spread into east-central Europe. Today, men from Ukraine, Hungary, Romania, and Slovakia all carry E-M78 at levels of nearly 10%.
While the majority of E-M78 European males trace their recent ancestry to Turkey and the Middle East, some men carrying E-M78 from Spain, Italy and Greece trace their ancestry directly from North African populations, probably within the last 4,000 years. The ancestors of these men must have sailed across the Mediterranean Sea and settled in communities along the European coast.
Your paternal haplogroup, E-V13, traces back to a man who lived approximately 11,000 years ago.
That's nearly 440.0 generations ago! What happened between then and now? As researchers and citizen scientists discover more about your haplogroup, new details may be added to the story of your paternal line.
Your haplogroup migrated in large numbers from the Balkans into Europe about 4,500 years ago, triggered by the beginning of the Balkan Bronze Age. During this migration, members of your haplogroup mainly followed rivers connecting the southern Balkans to northern-central Europe. Technological leaps often cause lineages to grow dramatically in numbers and in geographic range.
The development of Bronze technology may have given men in your lineage a competitive advantage over other men, causing your lineage to proliferate and become widespread.
References
https://www.ncbi.nlm.nih.gov/pubmed/17351267
https://www.ncbi.nlm.nih.gov/pubmed/27111036
https://www.ncbi.nlm.nih.gov/pubmed/26108492
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