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What are the genes associated with female breast size and natural variation thereof in human beings?

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It's frequently helpful to do a little research with e.g. Google before asking questions here. I searched "human breast size genetics" and found a lot of information.

Also note that in genetics it is usually misleading to say "the genes for X" or similar constructions. We can point to specific genetic variants (e.g. DNA variations, which are not genes) that have a statistical association with some phenotype (such as breast size). This is the best we can do here.

To directly answer your question, looking at some of the papers there is not strong evidence for any specific gene being associated with breast size. The total proportion of variation explained by all the variants detected is on the order of 2%-3%. In other words, those genes don't seem to be very important for breast size. You can read more about these variants here or here, and in other similar papers that you can find on google scholar.

Some (such as those papers) have estimated that variation in breast size is up to 50% due to genetics, which is to say that "heritability" is 30%-50%. Some people interpret this to mean that we just need to look harder to find more variants. However heritability is a notoriously unreliable estimator, so it may be truly a much smaller percentage of breast size variation that is heritable. To read more about how to interpret this try this paper.

Hope that helps.

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