Dear list,

I am analyzing RNA-Seq data with edgeR for a typical two factors design:

$samples
                 group lib.size norm.factors
R4.Hot     HotAdaptedHot 17409289    0.9881635
R5.Hot     HotAdaptedHot 17642552    1.0818144
R9.Hot    ColdAdaptedHot 20010974    0.8621807
R10.Hot   ColdAdaptedHot 14064143    0.8932791
R4.Cold   HotAdaptedCold 11968317    1.0061084
R5.Cold   HotAdaptedCold 11072832    1.0523857
R9.Cold  ColdAdaptedCold 22386103    1.0520949
R10.Cold ColdAdaptedCold 17408532    1.0903311


I found something quite interesting and is that non-native populations have
systematically higher coefficient of variation than native populations.
This is: CV (R4.Hot-R5Hot) < CV(R9.Hot-R10.Hot) and CV(R4.Cold-R5.Cold) >
CV(R9.Cold-R10.Cold).

Here you have the variables and calculations:

C.V.R4.R5HC = sqrt (data$R4.R5.HC.disp)
C.V.R9.R10HC = sqrt (data$R9.R10.HC.disp)

var_R4.R5_HC=Conc.R4.R5.HC*(1+R4.R5.HC.disp*Conc.R4.R5.HC)
var_R9.R10_HC=Conc.R9.R10.HC*(1+R9.R10.HC.disp*Conc.R9.R10.HC)


The attached plot is the result of comparing variances (V = mu *( 1 +
dispersion * mu ), according to
http://seqanswers.com/forums/showthread.php?t=5591&highlight=edgeR+variance)
and C.V. (C.V. = sqrt(dispersion)) between biological groups at Hot
temperature (i.e., comparin R4.Hot-R5.Hot vs. R9.Hot-R10.Hot).

According to the left plot we can conclude that for most genes the variance
is equal and then the assumption of equal variances is true. Hence we can
perform DE test. Am I right?

However, something I cannot understand is that the sqrt(R9.R10) >
sqrt(R4.R5), i.e., the coefficient of variation of gene expression is
systematically higher for all genes from R9.R10 than those in R4.R5. For
this to be true, since variances are equal and C.V. = sqrt(var)/mean, then
the mean of R9.R10 (i.e., Con.R9.R10) should be lower than that for R4.R5,
which is obviously false. The reciprocal analysis for these samples at cold
temperatures produces the equivalent, but  inverted, result.

What am I missing? How can this happen?


Any help would be appreciated.

Many thanks,
Miguel Gallach

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