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In [1] it is stated that:

the frequency of comutations in FGFR3 and KRAS or PIK3CA and KRAS was lower than predicted by chance, suggesting ... a lack of selective pressure for both mutations to occur

It is not clear to me how lack of selective pressure may produce a frequency of comutations that is lower than predicted by chance. I'd expect the frequency to be the one predicted by chance, if no selective pressure is applied. What am I missing?

[1] S. E. Woodman and G. B. Mills, “Are oncogenes sufficient to cause human cancer?,” Proc. Natl. Acad. Sci. U.S.A., vol. 107, no. 48, pp. 20599–20600, Nov. 2010.

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Often the phenotype caused by a given allele depends on the alleles present in other genes; this is termed epistasis. In the context of tumors, selective pressure is primarily associated with the ability of cells to grow and divide (without dying). It could be possible for two mutations which each confer some tumorigenic properties to conflict with each other, such that when both mutations are present they interact to either kill the cell or otherwise block the effect of the other mutation. The expected result would be that few tumor cells would exist with that combination of mutations because they would proliferate less than those cells with just one.

However, I suspect they are just addressing an non-significant difference from chance that they felt was too big to ignore entirely in discussion. You left out the rest of the sentence including a key word 'either' which I think is entirely misleading here and I wish you would not have done that (emphasis mine):

frequency of comutations in FGFR3 and KRAS or PIK3CA and KRAS was lower than predicted by chance, suggesting either a lack of selective pressure for both mutations to occur or a negative interaction between the consequences of each mutation

Essentially they are hedging the statement that there could be a negative interaction (i.e., selective pressure against) having both mutations with the possibility that there is just no meaningful positive interaction and the observation of a less than chance co-occurrence is not a true result. Note that they have a very small population because these are clinical tumors, and KRAS analysis was only in 59 patients (with only 12 mutants), making the statistical power for interactions very low.

I agree that this wording is imprecise and a bit unclear, so your confusion is understandable, but I think there are two reasons why it is worded this way. First, I believe they are trying to emphasize a possible future research direction and are trying to do so without making a criticism of the paper they are reviewing, because I don't think they view it as a criticism. Had they said "This study doesn't have enough statistical power to determine if there is a negative interaction between these mutations," that would sound overly critical given they are discussing something that wasn't really the intent of the original study. Second, I think the simplest prior expectation (which they do not state but is implied) is that two mutations that contribute to tumor production individually will be even more tumorigenic when present together. By stating the other outcomes: no selective pressure for the two mutations to cooccur or a negative interaction, they are implicitly stating that the simpler outcome, a positive interaction, does not seem to be occurring.

There is also a definite issue of selection bias here (statistically, not evolutionarily). That is, they are investigating a certain type of tumor. If those tumors can be caused by either a mutation in one gene or a mutation in another, then the chance association of those mutations would be the chance in the general population/other types of tumors/noncancerous tissue, which would be low (because most have neither), rather than the chance in patients.

The article you refer to is just a commentary on another article; you should really read Hafner et al instead (and note the original paper doesn't talk much if at all about these co-occurrences).

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    $\begingroup$ Good answer +1. I would add the term epistasis somewhere in here and maybe add that the phrasing is indeed quite misleading. $\endgroup$ – Remi.b Sep 26 '17 at 16:17

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