library(myTAI) options(width = 750) knitr::opts_chunk$set( comment = "#>", error = FALSE, tidy = FALSE)
In the Introduction vignette users learned how to perform the most fundamental computations
and visualizations for phylotranscriptomics analyses using the myTAI
package.
This Intermediate vignette introduces more detailed analyses and more specialized techniques
to investigate the observed phylotranscriptomics patterns (TAI
, TDI
, RE
, etc.) and introduces the statistical framework to quantify the significance of observed phenomena.
Three methods have been proposed to quantify the statistical significance of the observed phylotranscriptomics patterns (Quint et al., 2012; Drost et al., 2015).
Here, we will build the test statistic of each test step by step so that future modifications
or new test statistics can be built upon the existing methods implemented in the myTAI
package.
The Flat Line Test is a permutation test quantifying the statistical significance of an observed phylotranscriptomic pattern. The goal is to detect any evolutionary signal within a developmental time course that significantly deviates from a flat line.
To build the test statistic we start with a standard PhyloExpressionSet.
The myTAI
package provides an example PhyloExpressionSet named PhyloExpressionSetExample
:
library(myTAI) # load an example PhyloExpressionSet stored in the myTAI package data(PhyloExpressionSetExample) # look at the standardized data set format head(PhyloExpressionSetExample, 3)
Phylostratum GeneID Zygote Quadrant Globular Heart Torpedo Bent Mature 1 1 at1g01040.2 2173.635 1911.200 1152.555 1291.4224 1000.253 962.9772 1696.4274 2 1 at1g01050.1 1501.014 1817.309 1665.309 1564.7612 1496.321 1114.6435 1071.6555 3 1 at1g01070.1 1212.793 1233.002 939.200 929.6195 864.218 877.2060 894.8189
Users will observe that the first column of the PhyloExpressionSetExample
stores the Phylostratum assignments of the corresponding genes.
The permutation test is based on random sampling of the Phylostratum assignment of genes. The underlying assumption is that
the TAI
profile of correctly assigned Phylostrata is significantly deviating from TAI
profiles based on randomly assigned Phylostrata.
# TAI profile of correctly assigned Phylostrata
TAI(PhyloExpressionSetExample)
Zygote Quadrant Globular Heart Torpedo Bent Mature 3.229942 3.225614 3.107135 3.116693 3.073993 3.176511 3.390334
Visualization:
data(PhyloExpressionSetExample) # Visualize the TAI profile of correctly assigned Phylostrata PlotSignature( ExpressionSet = PhyloExpressionSetExample, p.value = FALSE )
# randomly permute the Phylostratum assignment of all genes randomPhyloExpressionSetExample <- data.frame( sample(PhyloExpressionSetExample[ , "Phylostratum"]), PhyloExpressionSetExample[, 2:9] ) # TAI profile based on randomly assigned Phylostrata TAI(randomPhyloExpressionSetExample)
Zygote Quadrant Globular Heart Torpedo Bent Mature 3.543700 3.573999 3.554707 3.543376 3.582905 3.562813 3.523409
Visualization:
# Visualize the TAI profile based on randomly assigned Phylostrata PlotSignature( ExpressionSet = randomPhyloExpressionSetExample, p.value = FALSE )
Users will observe that the visual pattern of the correctly assigned TAI
profile and the randomly assigned TAI
profile differ qualitatively.
Now we investigate the variance of the two observed patterns.
# Variance of the TAI profile based on correctly assigned Phylostrata
var(TAI(PhyloExpressionSetExample))
[1] 0.01147725
# Variance of the TAI profile based on randomly assigned Phylostrata
var(TAI(randomPhyloExpressionSetExample))
[1] 0.0004102549
We observe that the variance of the randomly assigned TAI profile is much smaller than the variance of the correctly assigned TAI profile. Here we use the variance to quantify the flatness of a given TAI profile. In theory the variance of a perfect flat line would be zero. So any TAI profile that is close to zero would resemble a flat line. But how exactly are the variances of randomly assigned TAI profiles distributed? For this purpose the bootMatrix()
function was implemented.
The bootMatrix()
takes an PhyloExpressionSet or DivergenceExpressionSet as input and computes N TAI
or TDI
profiles based on randomly assigned Phylostrata or Divergence-Strata.
# Compute 1000 TAI profiles based on randomly assigned Phylostrata randomTAIs <- bootMatrix( ExpressionSet = PhyloExpressionSetExample, permutations = 1000 ) head(randomTAIs)
Zygote Quadrant Globular Heart Torpedo Bent Mature 1 3.578000 3.577732 3.552230 3.556756 3.555627 3.553580 3.510978 2 3.590339 3.564544 3.589012 3.598754 3.583721 3.597553 3.633530 3 3.615284 3.616286 3.569486 3.566816 3.575761 3.554789 3.601522 4 3.501172 3.506554 3.486261 3.491282 3.531536 3.541634 3.494997 5 3.450857 3.458339 3.447274 3.463692 3.444261 3.468433 3.497926 6 3.539454 3.543827 3.595298 3.588149 3.582898 3.588062 3.565487
Based on this booMatrix
we can compute the variance of each random TAI profile.
# compute the variance of the random TAI profile for each row variance_vector <- apply(randomTAIs, 1 , var) # and visualize the distribution of variances hist(variance_vector, breaks = 100)
Now it is interesting to see where we can find the variance of the correctly assigned TAI.
# variance of the TAI profile based on correctly assigned Phylostrata var_real <- var(TAI(PhyloExpressionSetExample)) # visualize the distribution of variances hist( x = c(variance_vector,var_real), breaks = 100, xlab = "variance", main = "Histogram of variance_vector" ) # and plot a red line at the position where we can find the # real variance abline(v = var_real, lwd = 5, col = "red")
This plot illustrates that variances based on random TAI
profiles seem to have a smaller variance than the variance based on the correct TAI
profile. To obtain a p-value that now quantifies this difference, we need to fit the histogram of variance_vector
with a specific probability distribution.
Visually it would be possible to choose a gamma distribution to fit the histogram of variance_vector
. To validate this choice a Cullen and Frey graph provided by the fitdistrplus package can be used.
# install.packages("fitdistrplus") # plot a Cullen and Frey graph fitdistrplus::descdist(variance_vector)
Based on the observation that a gamma distribution is a suitable fit for variance_vector
, we can now
estimate the parameters of the gamma distribution that fits the data.
# estimate the parameters: shape and rate using 'moment matching estimation' gamma_MME <- fitdistrplus::fitdist(variance_vector,distr = "gamma", method = "mme") # estimate shape: shape <- gamma_MME$estimate[1] # estimate the rate: rate <- gamma_MME$estimate[2] # define an expression written as function as input for the curve() function gamma_distr <- function(x){ return(dgamma(x = x, shape = shape, rate = rate)) } # plot the density function and the histogram of variance_vector curve( expr = gamma_distr, xlim = c(min(variance_vector),max(c(variance_vector,var_real))), col = "steelblue", lwd = 5, xlab = "Variances", ylab = "Frequency" ) # plot the histogram of variance_vector histogram <- hist(variance_vector,prob = TRUE,add = TRUE, breaks = 100) rug(variance_vector) # plot a red line at the position where we can find the real variance abline(v = var_real, lwd = 5, col = "red")
Using the gamma distribution with estimated parameters the corresponding p-value of var_real
can
be computed.
# p-value of var_real pgamma(var_real, shape = shape,rate = rate, lower.tail = FALSE)
Hence, the variance of the correct TAI profile significantly deviates from random TAI profiles and this allows us to assume that the underlying TAI profile captures a real evolutionary signal.
FlatLineTest()
FunctionThis entire procedure of computing the p-value having the variance of TAI profiles as test statistic is done by the FlatLineTest()
function.
# Perform the FlatLineTest FlatLineTest( ExpressionSet = PhyloExpressionSetExample, permutations = 1000 )
This function returns the p-value of the test statistic.
Additionally the FlatLineTest()
function allows to investigate the goodness
of the test statistic.
# perform the FlatLineTest and investigate the goodness of the test statistic FlatLineTest( ExpressionSet = PhyloExpressionSetExample, permutations = 1000, plotHistogram = TRUE )
The plotHistogram
argument specifies whether analytics plots shall be drawn
to quantify the goodness of the test statistic returned by the FlatLineTest
.
The three resulting plots show:
a histogram of the test statistic and the corresponding gamma distribution that was fitted to the test statistic
a plot showing the p-values (p_flt
) for 10 individual runs.
Since the underlying test statistic is generated by a permutation test,
the third plot returned by FlatLineTest()
shows the influence of different permutations to the corresponding p-value
In other words, to test whether or not the underlying permutation of the permutation test
is causing the significance of the p-value, you can specify the runs
argument
within the FlatLineTest()
function to perform several independent runs.
In case there exists a permutation that causes a previous significant p-value to
become non-significant, the corresponding phylotranscriptomic pattern shouldn't be considered as
statistically significant.
The Reductive Hourglass Test has been developed to statistically evaluate the existence of a phylotranscriptomic hourglass pattern based on TAI or TDI computations. The corresponding p-value quantifies the probability that a given TAI or TDI pattern (or any phylotranscriptomics pattern) does not follow an hourglass like shape. A p-value < 0.05 indicates that the corresponding phylotranscriptomics pattern does indeed follow an hourglass (high-low-high) shape.
To build the test statistic again we start with a standard PhyloExpressionSet.
library(myTAI) # load an example PhyloExpressionSet stored in the myTAI package data(PhyloExpressionSetExample) # look at the standardized data set format head(PhyloExpressionSetExample, 3)
Phylostratum GeneID Zygote Quadrant Globular Heart Torpedo Bent Mature 1 1 at1g01040.2 2173.635 1911.200 1152.555 1291.4224 1000.253 962.9772 1696.4274 2 1 at1g01050.1 1501.014 1817.309 1665.309 1564.7612 1496.321 1114.6435 1071.6555 3 1 at1g01070.1 1212.793 1233.002 939.200 929.6195 864.218 877.2060 894.8189
And again compute the TAI()
profile of the PhyloExpressionSetExample
.
# TAI profile of correctly assigned Phylostrata
TAI(PhyloExpressionSetExample)
Zygote Quadrant Globular Heart Torpedo Bent Mature 3.229942 3.225614 3.107135 3.116693 3.073993 3.176511 3.390334
Visualization:
# visualize the TAI profile of correctly assigned Phylostrata PlotSignature( ExpressionSet = PhyloExpressionSetExample, p.value = FALSE )
The Reductive Hourglass Test is a permutation test based on the following test statistic.
1) A set of developmental stages is partitioned into three modules - early
, mid
, and late
- based on prior biological knowledge (see Drost et al., 2015 for details).
2) The mean TAI or TDI value for each of the three modules $T_{early}$, $T_{mid}$, and $T_{late}$ are computed.
3) The two differences D1 = $T_{early}$ - $T_{mid}$ and D2 = $T_{late}$ - $T_{mid}$ are calculated.
4) The minimum $D_{min}$ of D1 and D2 is computed as final test statistic of the Reductive Hourglass Test.
In order to determine the statistical significance of an observed minimum difference $D_{min}$ the following permutation test was performed. Based on the bootMatrix()
$D_{min}$ is calculated from each of the permuted TAI or TDI profiles, approximated by a Gaussian distribution with method of moments estimated parameters returned by fitdistrplus::fitdist()
, and the corresponding p-value is computed by pnorm
given the estimated parameters of the Gaussian distribution. The goodness of fit for the random vector $D_{min}$ is statistically quantified by a Lilliefors (Kolmogorov-Smirnov) test for normality.
To perform the Reductive Hourglass Test you can use the ReductiveHourglassTest()
function.
Using this function you need to divide the given phylotranscriptomic pattern into
three developmental modules:
This can be done using the modules
argument: module = list(early = 1:2, mid = 3:5, late = 6:7)
.
In this example (PhyloExpressionSetExample
) we divide the corresponding developmental process
into the three modules:
# Perform the Reductive Hourglass Test ReductiveHourglassTest( ExpressionSet = PhyloExpressionSetExample, modules = list(early = 1:2, mid = 3:5, late = 6:7), lillie.test = TRUE )
The corresponding output shows the p-value returned by the Reductive Hourglass Test,
the standard deviation of randomly permuted TAI profiles returned by bootMatrix()
(apply(bootMatrix(PhyloExpressionSetExample) , 2 , sd)
) and in case the argument lillie.test = TRUE
,
a logical value representing the goodness of fit statistic returned by the Lilliefors (Kolmogorov-Smirnov) test for normality. In case lillie.test
is TRUE
the corresponding
Lilliefors (Kolmogorov-Smirnov)
test passed the goodness of fit criterion. In case lillie.test
is FALSE
the corresponding goodness of fit by a normal distribution is not statistically significant.
Analogous to the plotHistogram
argument that is present in the FlatLineTest()
function,
the ReductiveHourglassTest()
function also takes an argument plotHistogram
. When plotHistogram = TRUE
,
the ReductiveHourglassTest()
function returns a multi-plot showing:
A Cullen and Frey skewness-kurtosis plot. This plot illustrates which distributions seem plausible to fit the resulting permutation vector $D_{min}$. Here a normal distribution seems most plausible.
A histogram of $D_{min}$ combined with the density plot is visualized. $D_{min}$ is then fitted by a normal distribution. The corresponding parameters are estimated by moment matching estimation.
A plot showing the p-values for N independent runs to verify that a specific p-value is biased by a specific permutation order.
A bar plot showing the number of cases in which the underlying goodness of fit (returned by Lilliefors (Kolmogorov-Smirnov) test for normality) has shown to be significant (TRUE
) or not significant (FALSE
).
This allows to quantify the permutation bias and their implications on the goodness of fit.
# perform the Reductive Hourglass Test and plot the test statistic ReductiveHourglassTest( ExpressionSet = PhyloExpressionSetExample, modules = list(early = 1:2, mid = 3:5, late = 6:7), plotHistogram = TRUE, lillie.test = TRUE )
The corresponding output shows the summary statistics
of the fitted normal distribution
as well as the p-value, standard deviation, and Lilliefors (Kolmogorov-Smirnov) test result.
This example output nicely illustrates that although the Lilliefors (Kolmogorov-Smirnov) test for normality is violated for some permutations, the Cullen and Frey graph shows that there is no better approximation than a normal distribution (which is also supported visually by investigating the fitted frequency distribution). The corresponding p-value returned by ReductiveHourglassTest()
is significant and illustrates that the observed phylotranscriptomic pattern of PhyloExpressionSetExample does follow the Hourglass Model assumption.
The Early Conservation Test has been developed to statistically evaluate the existence of a monotonically increasing phylotranscriptomic pattern based on TAI or TDI computations. The corresponding p-value quantifies the probability that a given TAI or TDI pattern (or any phylotranscriptomic pattern) does not follow an early conservation like pattern. A p-value < 0.05 indicates that the corresponding phylotranscriptomics pattern does indeed follow an early conservation (low-high-high) shape.
To build the test statistic again we start with a standard PhyloExpressionSet.
library(myTAI) # load an example PhyloExpressionSet stored in the myTAI package data(PhyloExpressionSetExample) # look at the standardized data set format head(PhyloExpressionSetExample, 3)
And again compute the TAI()
profile of the PhyloExpressionSetExample
.
# TAI profile of correctly assigned Phylostrata
TAI(PhyloExpressionSetExample)
Zygote Quadrant Globular Heart Torpedo Bent Mature 3.229942 3.225614 3.107135 3.116693 3.073993 3.176511 3.390334
Visualization:
# Visualize the TAI profile of correctly assigned Phylostrata PlotSignature( ExpressionSet = PhyloExpressionSetExample, p.value = FALSE )
The reductive early conservation test is a permutation test based on the following test statistic.
1) A set of developmental stages is partitioned into three modules - early
, mid
, and late
- based on prior biological knowledge.
2) The mean TAI or TDI value for each of the three modules $T_{early}$, $T_{mid}$, and $T_{late}$ are computed.
3) The two differences D1 = $T_{mid}$ - $T_{early}$ and D2 = $T_{late}$ - $T_{early}$ are calculated.
4) The minimum $D_{min}$ of D1 and D2 is computed as final test statistic of the Reductive Early Conservation Test.
In order to determine the statistical significance of an observed minimum difference $D_{min}$ the following permutation test was performed. Based on the bootMatrix()
$D_{min}$ is calculated from each of the permuted TAI or TDI profiles, approximated by a Gaussian distribution with method of moments estimated parameters returned by fitdistrplus::fitdist()
, and the corresponding p-value is computed by pnorm
given the estimated parameters of the Gaussian distribution. The goodness of fit for the random vector $D_{min}$ is statistically quantified by an Lilliefors (Kolmogorov-Smirnov) test for normality.
To perform the Reductive Early Conservation Test you can use the EarlyConservationTest()
function.
Using this function you need to divide the given phylotranscriptomics pattern into
three developmental modules:
This can be done using the modules
argument: module = list(early = 1:2, mid = 3:5, late = 6:7)
.
In this example (PhyloExpressionSetExample
) we divide the corresponding developmental process
into the three modules:
# Perform the Reductive Early Conservation Test EarlyConservationTest( ExpressionSet = PhyloExpressionSetExample, modules = list(early = 1:2, mid = 3:5, late = 6:7), lillie.test = TRUE )
Analogous to the plotHistogram
argument that is present in the FlatLineTest()
and ReductiveHourglassTest()
function,
the EarlyConservationTest()
function also takes an argument plotHistogram
. When plotHistogram = TRUE
,
the EarlyConservationTest()
function returns a multi-plot showing:
A Cullen and Frey skewness-kurtosis plot. This plot illustrates which distributions seem plausible to fit the resulting permutation vector $D_{min}$. Again a normal distribution seems most appropriate.
A histogram of $D_{min}$ combined with the density plot is visualized. $D_{min}$ is then fitted by a normal distribution. The corresponding parameters are estimated by moment matching estimation.
A plot showing the p-values for N independent runs to verify that a specific p-value is biased by a specific permutation order.
A bar plot showing the number of cases in which the underlying goodness of fit (returned by Lilliefors (Kolmogorov-Smirnov) test for normality) has shown to be significant (TRUE
) or not significant (FALSE
).
This allows to quantify the permutation bias and their implications on the goodness of fit.
# perform the Reductive Early Conservation Test and plot the test statistic EarlyConservationTest( ExpressionSet = PhyloExpressionSetExample, modules = list(early = 1:2, mid = 3:5, late = 6:7), plotHistogram = TRUE, lillie.test = TRUE )
This example output nicely illustrates that although the Lilliefors (Kolmogorov-Smirnov) test for normality is violated, the Cullen and Frey graph shows that there is no better approximation
than a normal distribution (which is also supported visually by investigating the fitted frequency distribution). The corresponding p-value
returned by the EarlyConservationTest()
is highly non-significant and illustrates that the observed phylotranscriptomic pattern of PhyloExpressionSetExample
does not follow the Early Conservation Model assumption.
This example shall illustrate that finding the right test statistic is a multi-step process of investigating different properties of the underlying permutation test. Although single aspects might fit or fit not corresponding criteria, the overall impression (sum of all individual analyses) must be considered to obtain a valid p-value.
Motivated by the discussion raised by Piasecka et al., 2013, the influence of gene expression transformation on the global phylotranscriptomic patterns does not seem negligible. Hence, different transformations can result in qualitatively different TAI or TDI patterns.
Initially, the TAI and TDI formulas were defined for absolute expression levels. So using the initial TAI and TDI formulas with transformed expression levels can result in qualitatively different patterns when compared with non-transformed expression levels, but might also belong to a different class of models, since different valid expression level transformation functions result in different patterns.
The purpose of the tf()
function is to allow the user to study the qualitative impact of different transformation functions on the global TAI and TDI pattern,
or on any subsequent phylotranscriptomic analysis.
The examples using the PhyloExpressionSetExample
data set show that using common gene expression transformation functions: log2 (Quackenbush, 2001 and 2002), sqrt (Yeung et al., 2001), boxcox, or inverse hyperbolic sine transformation, each transformation results in qualitatively different patterns. Nevertheless, for each resulting pattern the statistical significance can be tested using either the FlatLineTest()
, ReductiveHourglassTest()
, or EarlyConservationTest()
(Drost et al., 2015) to quantify the significance of observed patterns.
The tf()
function takes a standard PhyloExpressionSet
or DivergenceExpressionSet
and transformation function and returns the corresponding ExpressionSet
with
transformed gene expression levels.
library(myTAI) data(PhyloExpressionSetExample) # a simple example is to transform the gene expression levels of a given PhyloExpressionSet # using a sqrt or log2 transformation PES.sqrt <- tf(PhyloExpressionSetExample, sqrt) head(PES.sqrt)
PES.log2 <- tf(PhyloExpressionSetExample, log2) head(PES.log2)
Phylostratum GeneID Zygote Quadrant Globular Heart Torpedo Bent Mature 1 1 at1g01040.2 11.085894 10.900263 10.170620 10.334745 9.966149 9.911358 10.728284 2 1 at1g01050.1 10.551722 10.827588 10.701574 10.611727 10.547204 10.122367 10.065625 3 1 at1g01070.1 10.244117 10.267960 9.875289 9.860497 9.755251 9.776772 9.805452 4 1 at1g01080.2 9.989991 9.870956 10.206206 10.376639 10.443610 10.330888 9.750306 5 1 at1g01090.1 13.479852 14.034298 15.068722 15.279598 15.779093 16.031451 12.924174 6 1 at1g01120.1 9.721170 9.621306 9.747567 9.863595 9.880877 9.765307 9.630730
# in case a given PhyloExpressionSet already stores gene expression levels # that are log2 transformed and need to be re-transformed to absolute # expression levels, to perform subsequent phylotranscriptomics analyses # (that are defined for absolute expression levels), # one can re-transform a PhyloExpressionSet like this: PES.absolute <- tf(PES.log2 , function(x) 2^x) # which should be the same as PhyloExpressionSetExample : head(PhyloExpressionSetExample) head(PES.absolute)
> head(PhyloExpressionSetExample) Phylostratum GeneID Zygote Quadrant Globular Heart Torpedo Bent Mature 1 1 at1g01040.2 2173.6352 1911.2001 1152.5553 1291.4224 1000.2529 962.9772 1696.4274 2 1 at1g01050.1 1501.0141 1817.3086 1665.3089 1564.7612 1496.3207 1114.6435 1071.6555 3 1 at1g01070.1 1212.7927 1233.0023 939.2000 929.6195 864.2180 877.2060 894.8189 4 1 at1g01080.2 1016.9203 936.3837 1181.3381 1329.4734 1392.6429 1287.9746 861.2605 5 1 at1g01090.1 11424.5667 16778.1685 34366.6493 39775.6405 56231.5689 66980.3673 7772.5617 6 1 at1g01120.1 844.0414 787.5929 859.6267 931.6180 942.8453 870.2625 792.7542 > head(PES.absolute) Phylostratum GeneID Zygote Quadrant Globular Heart Torpedo Bent Mature 1 1 at1g01040.2 2173.6352 1911.2001 1152.5553 1291.4224 1000.2529 962.9772 1696.4274 2 1 at1g01050.1 1501.0141 1817.3086 1665.3089 1564.7612 1496.3207 1114.6435 1071.6555 3 1 at1g01070.1 1212.7927 1233.0023 939.2000 929.6195 864.2180 877.2060 894.8189 4 1 at1g01080.2 1016.9203 936.3837 1181.3381 1329.4734 1392.6429 1287.9746 861.2605 5 1 at1g01090.1 11424.5667 16778.1685 34366.6493 39775.6405 56231.5689 66980.3673 7772.5617 6 1 at1g01120.1 844.0414 787.5929 859.6267 931.6180 942.8453 870.2625 792.7542
When transforming the ExpressionMatrix
of the PhyloExpressionSetExample
using different transformation functions,
the resulting phylotranscriptomic patterns qualitatively differ:
data(PhyloExpressionSetExample) # plotting the TAI using log2 transformed expression levels # and performing the Flat Line Test to obtain the p-value PlotSignature( ExpressionSet = tf(PhyloExpressionSetExample, log2), TestStatistic = "FlatLineTest", xlab = "Ontogeny", ylab = "TAI" )
data(PhyloExpressionSetExample) # plotting the TAI using sqrt transformed expression levels # and performing the Flat Line Test to obtain the p-value PlotSignature( ExpressionSet = tf(PhyloExpressionSetExample, sqrt), TestStatistic = "FlatLineTest", xlab = "Ontogeny", ylab = "TAI" )
For the PhyloExpressionSetExample
all transformations result in a significant
phylotranscriptomics pattern deviating from a flat line.
Nevertheless, it is not clear which transformation is the most appropriate one since the original TAI and TDI measure were defined for absolute expression levels.
The same accounts for TDI
profiles:
data(DivergenceExpressionSetExample) # plotting the TDI using log2 transformed expression levels # and performing the Flat Line Test to obtain the p-value PlotSignature( ExpressionSet = tf(DivergenceExpressionSetExample, log2), TestStatistic = "FlatLineTest", xlab = "Ontogeny", ylab = "TDI" )
data(DivergenceExpressionSetExample) # plotting the TDI using sqrt transformed expression levels # and performing the Flat Line Test to obtain the p-value PlotSignature( ExpressionSet = tf(DivergenceExpressionSetExample, sqrt), TestStatistic = "FlatLineTest", xlab = "Ontogeny", ylab = "TDI" )
As a result, observed patterns should always be quantified using statistical tests
(for ex. FlatLineTest()
, ReductiveHourglassTest()
, and EarlyConservationTest()
).
In case the observed pattern is significant, qualitative differences of the observed patterns based on different data transformations must be investigated in more detail,
since most data transformations are known to cause different effects on a measure that
isn't robust against data transformations.
Domazet-Loso, T. & Tautz, D. A phylogenetically based transcriptome age index mirrors ontogenetic divergence patterns. Nature 468, 815-8 (2010).
Quint, M. et al. A transcriptomic hourglass in plant embryogenesis. Nature 490, 98-101 (2012).
Drost, H.G. et al. Evidence for Active Maintenance of Phylotranscriptomic Hourglass Patterns in Animal and Plant Embryogenesis. Mol. Biol. Evol. 32 (5), 1221-1231 (2015).
Piasecka, B. et al. The hourglass and the early conservation models - co-existing patterns of developmental constraints in vertebrates. PLoS Genet. 9:e1003476 (2013).
Quackenbush, J. Computational Analysis of Microarray Data. Nature Reviews. 2, 418-427 (2001).
Quackenbush, J. Microarray data normalization and transformation. Nature Genetics. 32, 496-501 (2002).
Yeung, K.Y. et al. Model-based clustering and data transformations for gene expression data. Bioinformatics. 17, 977-987 (2001).
Yeung, K.Y. et al. Supplement to Model-based clustering and data transformations for gene expression data - Data Transformations and the Gaussian mixture assumption. Bioinformatics. 17, 977-987 (2001).
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