I2b2 is a very rare subclade of Haplogroup I and was only discovered in May 2005. It is purely European. There is still much to discover about it, but its story is being advanced by gifted hobbyists such as Hans de Beule who has published a number of articles on the wanderings of I2b2 people. Haplogroup I was one of the earliest groups to settle on the continent around 40,000 years ago. Today I2b2 is thinly spread over Europe but its frequency is highest in the Upper Rhine region of Germany, making it a likely point of origin around 6-7,000 years ago. Given its subsequent spread across Europe over the millenia, it is entirely possible that I2b2 people moved northwards into Denmark and possibly southern Norway to eventually become Vikings. Certainly, there were complex movements of peoples all over the Continent over this period, complicating the DNA picture considerably.
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Scandinavian communities in northern England and Ireland merged with the local populations, as evidenced by the modern connection between Danish and German I2b2 samples with northern English and Irish ones, suggesting that some I2b2s mingled with north German and Scandinavian populations and migrated to England and Ireland as Vikings. The impact on culture and language of this Anglo-Scandinavian assimilation in northern England is still felt to this day, particularly in the distinctive dialects of English spoken in the north, which can still be unintelligible to people from the south!
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This map, courtesy of Worldnames showing the modern distribution of people with the surname Rimmer in northwest Europe supports this. It shows an unusually high concentration in west Lancashire, as well as a moderate frequency in Denmark (and a very low frequency in Norway and Sweden). A prehistoric origin, or an Anglo-Saxon origin, would explain a more uniform frequency of I2b2s from the continent across the length and breadth of England, but does less to explain the later presence of a high concentration of people with a common surname in such a localised area.