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A child of a half-sibling has been determined to be a 1st or 2nd cousin; and the explanation is that variability to four degrees. Is it possible that the half-sibling status with his mother creates some sort of anomaly?

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This is completely normal.

The relationship predictions on the various DNA test sites are based on how much DNA you and your match share, and each potential relationship actually has a range for how much DNA will be shared. A really good overview of this is thednageek's blog post The Limits of Predicting Relationships Using DNA.

For your specific case, check out the green chart in that blog post. Group C on that chart is what you want to look at; you'll notice that Group C includes both first cousin and half-nephew.

Another resource to check out is Blaine Bettinger's Shared cM Project. At the linked site, you can input the amount of shared DNA (either cM or percentage), and you'll be shown all the possible relationships. It will also give you a table of likelihoods for various potential relationships.

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