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In many genetic studies, PCA is often utilized to examine genetic cluster in human populations. Rarely is the % variance reported for the components. With human data it's been my experience that the first three components (which are often plotted) tend to contain very little % of the variance. How meaningful are your visual results (i.e. clustering) when the first three components cumulatively account for only (say) 10% of the variance?

To answer this question, I constructed a theory based on the following assumptions.

One theory. For human, the proportion of variation within groups (i.e. same ethnic group) account for ~85% of the genetic variation within individuals. Conversely, the variation within populations (i.e. continental scale) account for only ~15% of the genetic variation within individuals.

Even though the first three components (i.e. PC1, PC2, PC3) contained only a small fraction of the total variance, most often the magnitude of associated eigenvalues can be 50 to 70 times that of higher components. In other words, the first three components can explain substantially more (50x-70x) variance than any other component when comparing by individual basis.

While sometimes these higher components do explain hidden substructure within groups, bear in mind that individuals from the same group has ~85% genetic variation among themselves. Hence, most of the higher components might just be explaining this within groups variation. For analysis of genetic clusters, this is of no interest to geneticists. These higher components can thus be treated as background noises. Geneticists are mainly interested in variation within populations, which often is very ancient and strongly separated. Thus, when population clusters are formed in the first three components, it can be argued that they form mainly due to the variation within populations.

Summary: The low variance (<10%) cumulatively accounted by the first three components can be justified by the fact that variation within populations is only ~15% of the genetic variation within individuals.

My question is: Does the theory to my own question seem reasonable?

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  • $\begingroup$ I'm sure you agree this is a question about statistics, not biology. Geneticists use statistics, but many of us are not experts and often require recurring reminders from statisticians on how best to interpret, analyze and visualize data, preserving both clarity and validity. I agree; the principal components should always account for as large amount of variation in the data as possible, otherwise it would make little sense - at least in my limited understanding of it. I defer to others on this question! $\endgroup$ – S Pr Jul 19 '18 at 13:11

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