The Reductive Late Conservation Test aims to statistically evaluate the
existence of a monotonically decreasing phylotranscriptomic 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 late conservation like pattern. A p-value < 0.05 indicates that the corresponding phylotranscriptomics pattern does
indeed follow an late conservation (high-high-low) shape.
Usage
LateConservationTest(
ExpressionSet,
modules = NULL,
permutations = 1000,
lillie.test = FALSE,
plotHistogram = FALSE,
runs = 10,
parallel = FALSE,
gof.warning = FALSE,
custom.perm.matrix = NULL
)
Arguments
- ExpressionSet
a standard PhyloExpressionSet or DivergenceExpressionSet object.
- modules
a list storing three elements: early, mid, and late. Each element expects a numeric vector specifying the developmental stages or experiments that correspond to each module. For example,
module
= list(early = 1:2, mid = 3:5, late = 6:7) divides a dataset storing seven developmental stages into 3 modules.- permutations
a numeric value specifying the number of permutations to be performed for the
ReductiveHourglassTest
.- lillie.test
a boolean value specifying whether the Lilliefors Kolmogorov-Smirnov Test shall be performed to quantify the goodness of fit.
- plotHistogram
a boolean value specifying whether a Lillifor's Kolmogorov-Smirnov-Test shall be performed to test the goodness of fit of the approximated distribution, as well as additional plots quantifying the significance of the observed phylotranscriptomic pattern.
- runs
specify the number of runs to be performed for goodness of fit computations, in case
plotHistogram
=TRUE
. In most casesruns
= 100 is a reasonable choice. Default isruns
= 10 (because it takes less computation time for demonstration purposes).- parallel
performing
runs
in parallel (takes all cores of your multicore machine).- gof.warning
a logical value indicating whether non significant goodness of fit results should be printed as warning. Default is
gof.warning = FALSE
.- custom.perm.matrix
a custom
bootMatrix
(permutation matrix) to perform the underlying test statistic. Default iscustom.perm.matrix = NULL
.
Value
a list object containing the list elements:
p.value
: the p-value quantifying the statistical significance (low-high-high pattern) of the given phylotranscriptomics pattern.
std.dev
: the standard deviation of the N sampled phylotranscriptomics patterns for each developmental stage S.
lillie.test
: a boolean value specifying whether the Lillifors KS-Test returned a p-value > 0.05,
which indicates that fitting the permuted scores with a normal distribution seems plausible.
Details
The reductive late 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_early - T_late and D2 = T_mid - T_late 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 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.
In case the parameter plotHistogram = TRUE, a multi-plot is generated showing:
(1) A Cullen and Frey skewness-kurtosis plot generated by descdist
.
This plot illustrates which distributions seem plausible to fit the resulting permutation vector D_min.
In the case of the reductive late conservation test a normal distribution seemed plausible.
(2) A histogram of D_min combined with the density plot is plotted. D_min is then fitted by a normal distribution.
The corresponding parameters are estimated by moment matching estimation using the fitdist
function.
(3) A plot showing the p-values for N independent runs to verify that a specific p-value is biased by a specific permutation order.
(4) A barplot 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.
References
Drost HG et al. (2015) Mol Biol Evol. 32 (5): 1221-1231 doi:10.1093/molbev/msv012
Quint M et al. (2012). A transcriptomic hourglass in plant embryogenesis. Nature (490): 98-101.
Piasecka B, Lichocki P, Moretti S, et al. (2013) The hourglass and the early conservation models co-existing patterns of developmental constraints in vertebrates. PLoS Genet. 9(4): e1003476.
Examples
data(PhyloExpressionSetExample)
# perform the late conservation test for a PhyloExpressionSet
# here the prior biological knowledge is that stages 1-2 correspond to module 1 = early,
# stages 3-5 to module 2 = mid (phylotypic module), and stages 6-7 correspond to
# module 3 = late
LateConservationTest(PhyloExpressionSetExample,
modules = list(early = 1:2, mid = 3:5, late = 6:7),
permutations = 1000)
#> The phylotranscriptomic pattern may not follow a late conservation pattern (high-mid-low or high-high-low).
#>
#> [ Number of Eigen threads that are employed on your machine: 12 ]
#>
#> [ Computing age assignment permutations for test statistic ... ]
#>
[=========================================] 100%
#> [ Computing variances of permuted transcriptome signatures ... ]
#>
#> $p.value
#> [1] 0.9999978
#>
#> $std.dev
#> [1] 0.05554746 0.05429588 0.05269882 0.05206943 0.05079230 0.05281953 0.05594038
#>
#> $lillie.test
#> [1] NA
#>
# use your own permutation matrix based on which p-values (LateConservationTest)
# shall be computed
custom_perm_matrix <- bootMatrix(PhyloExpressionSetExample,100)
#>
#> [ Number of Eigen threads that are employed on your machine: 12 ]
#>
#> [ Computing age assignment permutations for test statistic ... ]
#>
[=========================================] 100%
#> [ Computing variances of permuted transcriptome signatures ... ]
#>
LateConservationTest(PhyloExpressionSetExample,
modules = list(early = 1:2, mid = 3:5, late = 6:7),
custom.perm.matrix = custom_perm_matrix)
#> The phylotranscriptomic pattern may not follow a late conservation pattern (high-mid-low or high-high-low).
#> $p.value
#> [1] 0.9999946
#>
#> $std.dev
#> Zygote Quadrant Globular Heart Torpedo Bent Mature
#> 0.05410165 0.05188825 0.04945213 0.04701504 0.04954394 0.05426393 0.06388890
#>
#> $lillie.test
#> [1] NA
#>