What do you mean where it originated? A mutation is stationary in a gene and doesnt move. Should a mutation occur in another location it is a seperate mutation. You cannot really time a mutation, however you can determine the homology between genes and their differences (could be referred to as mutations) and somewhat give an estimate when the genes went from one to become two seperate similar genes. If you are taking somatic mutations like those given rise to cancer, they always appear mostly within a decade at the most before the cancer becomes apparent to the individual.

Thank you for your response, but I believe my question was not specific enough. What i am curious about concerns the “history” of genetic mutations. For example, it is believed that humans didn’t develop the “dairy-digesting” genetic mutation until about 6000 years ago. How did they come to that conclusion?

The appearance of new genes can be tracked by sequencing of populations and the appearance of the gene in the population. It involves looking at the specific genes and homology to other conserved genes in a population. Often it also involves tracing migration and behavior of humans in the past. Then you often see a correlation with human migration and settlement in a environment where such a mutation is beneficial.

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The way they track these mutations in time is by creating a huge family tree and puzzling the way back up. If a group of people is known to have split up e.g. 5000 years ago and none of them have that mutation, it likely occured less than 5000 years ago in the main population. It's not perfect but with enough samples and meta info we can create accurate philogenetic trees.

It also helps a lot that we have found a couple mummified people with intact DNA from different places and points in time.

You can (estimate the) date the nodes of a tree and find in which branch the mutation appeared, thus estimating when it occurred.

Without getting into excessive detail: today we genotype or sequence DNA from many many people. We can cluster people into groups that have a higher than expected number of shared alleles (genetic variations). This happens when people share common ancestry because at some point their ancestors were isolated to an area, or had moved to a new area and founded a new settlement that grew, establishing a large group with common genetic history. This is effectively what the ancestry DNA companies do. You can plot that information on a map and to show where those people groups are most prevalent.

That same information can be used to make something like a pedigree of people groups, tracing the divergence and convergence of populations in time and geography.

Given that information, you can then ask where in that tree is the allele most common? Can you trace a line between people groups that carry the specific mutation? Sometimes you can, and you can estimate when and where the mutation first occurred. In some cases, you simply can’t — perhaps because the mutation is very common and doesn’t seem to have a strong correlation with any people group.

You track populations.

For example, if there is a gene variation that you see in African Americans, but not in people in Africa, and is more common in African Americans than in Americans not of African descent, then it probably originated in the American South; and depending on how distributed around the US is it and how many people have the gene variation, you might be able to guess how old it is.

A notable real-world case is a specific mutation in the Y-chromosome found in about 8% of Asia stretching from northern China to eastern Europe. Because it's on the Y chromosome, it's (almost) entirely male-linked; and the working hypothesis is that the gene originated in Mongolia (it's more common there), and spread with Genghis Khan's conquests. The fact that this gene shows up more or less the same amount over such a wide area suggests that it showed up about the same time in all those places - and Genghis Khan explains that nicely.

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