bruvo.dist: Bruvo's distance for microsatellites
In poppr: Genetic Analysis of Populations with Mixed Reproduction
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Calculate the average Bruvo's distance over all loci in a population.
Usage
1
bruvo.dist(pop, replen = 1, add = TRUE, loss = TRUE, by_locus = FALSE)
Arguments
pop
a genind or genclone object
replen
a vector of integers indicating the length of the
nucleotide repeats for each microsatellite locus. E.g. a locus with a (CAT)
repeat would have a replen value of 3. (Also see fix_replen)
add
if TRUE, genotypes with zero values will be treated under
the genome addition model presented in Bruvo et al. 2004. See the
Note section for options.
loss
if TRUE, genotypes with zero values will be treated under
the genome loss model presented in Bruvo et al. 2004. See the
Note section for options.
by_locus
indicator to get the results per locus. The default setting
is by_locus = FALSE, indicating that Bruvo's distance is to be
averaged over all loci. When by_locus = TRUE, a list of distance
matrices will be returned.
Details
Bruvo's distance between two alleles is calculated as
d = 1 - (2^(-abs(x)))
, where x
is the number of repeat units between the two alleles (see the Algorithms
and Equations vignette for more details). These distances are calculated
over all combinations of alleles at a locus and then the minimum average
distance between allele combinations is taken as the distance for that
locus. All loci are then averaged over to obtain the distance between two
samples. Missing data is ignored (in the same fashion as
mean(c(1:9, NA), na.rm = TRUE)) if all alleles are missing. See the
next section for other cases.
Polyploids
Ploidy is irrelevant with respect to calculation of Bruvo's
distance. However, since it makes a comparison between all alleles at a
locus, it only makes sense that the two loci need to have the same ploidy
level. Unfortunately for polyploids, it's often difficult to fully separate
distinct alleles at each locus, so you end up with genotypes that appear to
have a lower ploidy level than the organism.
To help deal with these situations, Bruvo has suggested three methods for
dealing with these differences in ploidy levels:
-
Infinite Model - The simplest way to deal with it is to count all
missing alleles as infinitely large so that the distance between it and
anything else is 1. Aside from this being computationally simple, it will
tend to inflate distances between individuals.
-
Genome Addition Model - If it is suspected that the organism has
gone through a recent genome expansion, the missing alleles will be
replace with all possible combinations of the observed alleles in the
shorter genotype. For example, if there is a genotype of [69, 70, 0, 0]
where 0 is a missing allele, the possible combinations are: [69, 70, 69,
69], [69, 70, 69, 70], [69, 70, 70, 69], and [69, 70, 70, 70]. The
resulting distances are then averaged over the number of comparisons.
-
Genome Loss Model - This is similar to the genome addition model,
except that it assumes that there was a recent genome reduction event and
uses the observed values in the full genotype to fill the missing
values in the short genotype. As with the Genome Addition Model, the
resulting distances are averaged over the number of comparisons.
-
Combination Model - Combine and average the genome addition and
loss models.
As mentioned above, the infinite model is biased, but it is not nearly as
computationally intensive as either of the other models. The reason for
this is that both of the addition and loss models requires replacement of
alleles and recalculation of Bruvo's distance. The number of replacements
required is equal to n^k where where n is the number of potential
replacements and k is the number of alleles to be replaced.
To reduce the number of calculations and assumptions otherwise, Bruvo's
distance will be calculated using the largest observed ploidy in pairwise
comparisons. This means that when comparing [69,70,71,0] and [59,60,0,0],
they will be treated as triploids.
Value
an object of class dist or a list of these objects if
by_locus = TRUE
Note
Do not use missingno with this function.
Missing alleles and Bruvo's distance in poppr versions < 2.5
In earlier versions of poppr, the authors had assumed that, because
the calculation of Bruvo's distance does not rely on orderd sets of
alleles, the imputation methods in the genome addition and genome loss
models would also assume unordered alleles for creating the hypothetical
genotypes. This means that the results from this imputation did not
consider all possible combinations of alleles, resulting in either an over-
or under- estimation of Bruvo's distance between two samples with two or
more missing alleles. This version of poppr considers all possible
combinations when calculating Bruvo's distance for incomplete genotype with
a negligable gain in computation time.
If you want to see the effect of this change on your data, you can use the
global poppr option old.bruvo.model. Currently, this option is
FALSE and you can set it by using
options(old.bruvo.model = TRUE), but make sure to reset it to
FALSE afterwards.
Repeat Lengths (replen)
The replen argument is crucial for proper analysis of Bruvo's
distance since the calculation relies on the knowledge of the number of
steps between alleles. To calculate Bruvo's distance, your raw allele calls
are first divided by the repeat lengths and then rounded. This can create a
problem with repeat lengths of even size due to the IEC 60559 standard that
says rounding at 0.5 is to the nearest even number, meaning that it is
possible for two alleles that are one step apart may appear to be exactly
the same. This can be fixed by subtracting a tiny number from the repeat
length with the function fix_replen. Please consider using
this before running Bruvo's distance.
Model Choice
The add and loss arguments
modify the model choice accordingly:
-
Infinite
Model: add = FALSE, loss = FALSE
-
Genome Addition
Model: add = TRUE, loss = FALSE
-
Genome Loss Model:
add = FALSE, loss = TRUE
-
Combination Model
(DEFAULT): add = TRUE, loss = TRUE
Details of each model
choice are described in the Details section, above. Additionally,
genotypes containing all missing values at a locus will return a value of
NA and not contribute to the average across loci.
Repeat Lengths
If the user does not provide a vector of
appropriate length for replen , it will be estimated by taking the
minimum difference among represented alleles at each locus. IT IS NOT
RECOMMENDED TO RELY ON THIS ESTIMATION.
Author(s)
Zhian N. Kamvar
References
Ruzica Bruvo, Nicolaas K. Michiels, Thomas G. D'Souza, and
Hinrich Schulenburg. A simple method for the calculation of microsatellite
genotype distances irrespective of ploidy level. Molecular Ecology,
13(7):2101-2106, 2004.
See Also
fix_replen, test_replen,
bruvo.boot, bruvo.msn
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
# Please note that the data presented is assuming that the nancycat dataset
# contains all dinucleotide repeats, it most likely is not an accurate
# representation of the data.
# Load the nancycats dataset and construct the repeat vector.
data(nancycats)
names(alleles(nancycats)) <- locNames(nancycats) # small bug in this data set
# Assume the alleles are all dinucleotide repeats.
ssr <- rep(2, nLoc(nancycats))
test_replen(nancycats, ssr) # Are the repeat lengths consistent?
(ssr <- fix_replen(nancycats, ssr)) # Nope. We need to fix them.
# Analyze the first population in nancycats
bruvo.dist(popsub(nancycats, 1), replen = ssr)
## Not run:
# get the per locus estimates:
bruvo.dist(popsub(nancycats, 1), replen = ssr, by_locus = TRUE)
# View each population as a heatmap.
sapply(popNames(nancycats), function(x)
heatmap(as.matrix(bruvo.dist(popsub(nancycats, x), replen = ssr)), symm=TRUE))
## End(Not run)
Example output
Loading required package: adegenet
Loading required package: ade4
/// adegenet 2.0.1 is loaded ////////////
> overview: '?adegenet'
> tutorials/doc/questions: 'adegenetWeb()'
> bug reports/feature requests: adegenetIssues()
This is poppr version 2.5.0. To get started, type package?poppr
OMP parallel support: available
fca8 fca23 fca43 fca45 fca77 fca78 fca90 fca96 fca37
FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE TRUE
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N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.4353027
N224 0.4956597 0.5307888
$fca8
N215 N216 N217 N218 N219 N220 N221 N222
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N224 NA NA 0.468750 0.250000 0.250000 0.468750 0.000000 0.468750
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N216
N217
N218
N219
N220
N221
N222
N223
N224 0.718750
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N215 N216 N217 N218 N219 N220 N221
N216 0.4843750
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N221
N222
N223 0.0000000
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$fca43
N215 N216 N217 N218 N219 N220 N221 N222
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N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.687500
$fca45
N215 N216 N217 N218 N219 N220 N221 N222
N216 0.484375
N217 0.375000 0.859375
N218 0.437500 0.375000 0.484375
N219 0.921875 0.437500 0.968750 0.484375
N220 0.484375 0.000000 0.859375 0.375000 0.437500
N221 0.437500 0.375000 0.484375 0.000000 0.484375 0.375000
N222 0.484375 0.000000 0.859375 0.375000 0.437500 0.000000 0.375000
N223 0.437500 0.375000 0.484375 0.000000 0.484375 0.375000 0.000000 0.375000
N224 0.484375 0.000000 0.859375 0.375000 0.437500 0.000000 0.375000 0.000000
N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.375000
$fca77
N215 N216 N217 N218 N219 N220 N221 N222
N216 0.000000
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N224 0.437500 0.437500 0.250000 0.437500 0.625000 0.000000 0.625000 0.625000
N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.375000
$fca78
N215 N216 N217 N218 N219 N220 N221 N222 N223
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$fca90
N215 N216 N217 N218 N219 N220 N221
N216 0.4960938
N217 0.5000000 0.7421875
N218 0.0000000 0.4960938 0.5000000
N219 0.4375000 0.4687500 0.6250000 0.4375000
N220 0.8125000 0.8437500 0.6250000 0.8125000 0.3750000
N221 0.0000000 0.4960938 0.5000000 0.0000000 0.4375000 0.8125000
N222 0.6875000 0.7187500 0.3750000 0.6875000 0.2500000 0.2500000 0.6875000
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N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.3750000
N224 0.3750000 0.0000000
$fca96
N215 N216 N217 N218 N219 N220 N221
N216 0.0000000
N217 0.0000000 0.0000000
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N224 0.9685059 0.9685059 0.9685059 0.0000000 0.9685059 0.4687500 0.4997559
N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.9958496
N224 0.4960938 0.4997559
$fca37
N215 N216 N217 N218 N219 N220 N221 N222 N223
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Warning message:
system call failed: Cannot allocate memory
poppr documentation built on Sept. 11, 2017, 9:04 a.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Calculate the average Bruvo's distance over all loci in a population.
Usage
1 | bruvo.dist(pop, replen = 1, add = TRUE, loss = TRUE, by_locus = FALSE)
|
Arguments
pop |
a |
replen |
a |
add |
if |
loss |
if |
by_locus |
indicator to get the results per locus. The default setting
is |
Details
Bruvo's distance between two alleles is calculated as
d = 1 - (2^(-abs(x)))
, where x
is the number of repeat units between the two alleles (see the Algorithms
and Equations vignette for more details). These distances are calculated
over all combinations of alleles at a locus and then the minimum average
distance between allele combinations is taken as the distance for that
locus. All loci are then averaged over to obtain the distance between two
samples. Missing data is ignored (in the same fashion as
mean(c(1:9, NA), na.rm = TRUE)) if all alleles are missing. See the
next section for other cases.
Polyploids
Ploidy is irrelevant with respect to calculation of Bruvo's distance. However, since it makes a comparison between all alleles at a locus, it only makes sense that the two loci need to have the same ploidy level. Unfortunately for polyploids, it's often difficult to fully separate distinct alleles at each locus, so you end up with genotypes that appear to have a lower ploidy level than the organism.
To help deal with these situations, Bruvo has suggested three methods for dealing with these differences in ploidy levels:
-
Infinite Model - The simplest way to deal with it is to count all missing alleles as infinitely large so that the distance between it and anything else is 1. Aside from this being computationally simple, it will tend to inflate distances between individuals.
-
Genome Addition Model - If it is suspected that the organism has gone through a recent genome expansion, the missing alleles will be replace with all possible combinations of the observed alleles in the shorter genotype. For example, if there is a genotype of [69, 70, 0, 0] where 0 is a missing allele, the possible combinations are: [69, 70, 69, 69], [69, 70, 69, 70], [69, 70, 70, 69], and [69, 70, 70, 70]. The resulting distances are then averaged over the number of comparisons.
-
Genome Loss Model - This is similar to the genome addition model, except that it assumes that there was a recent genome reduction event and uses the observed values in the full genotype to fill the missing values in the short genotype. As with the Genome Addition Model, the resulting distances are averaged over the number of comparisons.
-
Combination Model - Combine and average the genome addition and loss models.
As mentioned above, the infinite model is biased, but it is not nearly as computationally intensive as either of the other models. The reason for this is that both of the addition and loss models requires replacement of alleles and recalculation of Bruvo's distance. The number of replacements required is equal to n^k where where n is the number of potential replacements and k is the number of alleles to be replaced. To reduce the number of calculations and assumptions otherwise, Bruvo's distance will be calculated using the largest observed ploidy in pairwise comparisons. This means that when comparing [69,70,71,0] and [59,60,0,0], they will be treated as triploids.
Value
an object of class dist or a list of these objects if
by_locus = TRUE
Note
Do not use missingno with this function.
Missing alleles and Bruvo's distance in poppr versions < 2.5
In earlier versions of poppr, the authors had assumed that, because the calculation of Bruvo's distance does not rely on orderd sets of alleles, the imputation methods in the genome addition and genome loss models would also assume unordered alleles for creating the hypothetical genotypes. This means that the results from this imputation did not consider all possible combinations of alleles, resulting in either an over- or under- estimation of Bruvo's distance between two samples with two or more missing alleles. This version of poppr considers all possible combinations when calculating Bruvo's distance for incomplete genotype with a negligable gain in computation time.
If you want to see the effect of this change on your data, you can use the
global poppr option old.bruvo.model. Currently, this option is
FALSE and you can set it by using
options(old.bruvo.model = TRUE), but make sure to reset it to
FALSE afterwards.
Repeat Lengths (replen)
The replen argument is crucial for proper analysis of Bruvo's
distance since the calculation relies on the knowledge of the number of
steps between alleles. To calculate Bruvo's distance, your raw allele calls
are first divided by the repeat lengths and then rounded. This can create a
problem with repeat lengths of even size due to the IEC 60559 standard that
says rounding at 0.5 is to the nearest even number, meaning that it is
possible for two alleles that are one step apart may appear to be exactly
the same. This can be fixed by subtracting a tiny number from the repeat
length with the function fix_replen. Please consider using
this before running Bruvo's distance.
Model Choice
The add and loss arguments
modify the model choice accordingly:
-
Infinite Model:
add = FALSE, loss = FALSE -
Genome Addition Model:
add = TRUE, loss = FALSE -
Genome Loss Model:
add = FALSE, loss = TRUE -
Combination Model (DEFAULT):
add = TRUE, loss = TRUE
Details of each model
choice are described in the Details section, above. Additionally,
genotypes containing all missing values at a locus will return a value of
NA and not contribute to the average across loci.
Repeat Lengths
If the user does not provide a vector of
appropriate length for replen , it will be estimated by taking the
minimum difference among represented alleles at each locus. IT IS NOT
RECOMMENDED TO RELY ON THIS ESTIMATION.
Author(s)
Zhian N. Kamvar
References
Ruzica Bruvo, Nicolaas K. Michiels, Thomas G. D'Souza, and Hinrich Schulenburg. A simple method for the calculation of microsatellite genotype distances irrespective of ploidy level. Molecular Ecology, 13(7):2101-2106, 2004.
See Also
fix_replen, test_replen,
bruvo.boot, bruvo.msn
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | # Please note that the data presented is assuming that the nancycat dataset
# contains all dinucleotide repeats, it most likely is not an accurate
# representation of the data.
# Load the nancycats dataset and construct the repeat vector.
data(nancycats)
names(alleles(nancycats)) <- locNames(nancycats) # small bug in this data set
# Assume the alleles are all dinucleotide repeats.
ssr <- rep(2, nLoc(nancycats))
test_replen(nancycats, ssr) # Are the repeat lengths consistent?
(ssr <- fix_replen(nancycats, ssr)) # Nope. We need to fix them.
# Analyze the first population in nancycats
bruvo.dist(popsub(nancycats, 1), replen = ssr)
## Not run:
# get the per locus estimates:
bruvo.dist(popsub(nancycats, 1), replen = ssr, by_locus = TRUE)
# View each population as a heatmap.
sapply(popNames(nancycats), function(x)
heatmap(as.matrix(bruvo.dist(popsub(nancycats, x), replen = ssr)), symm=TRUE))
## End(Not run)
|
Example output
Loading required package: adegenet
Loading required package: ade4
/// adegenet 2.0.1 is loaded ////////////
> overview: '?adegenet'
> tutorials/doc/questions: 'adegenetWeb()'
> bug reports/feature requests: adegenetIssues()
This is poppr version 2.5.0. To get started, type package?poppr
OMP parallel support: available
fca8 fca23 fca43 fca45 fca77 fca78 fca90 fca96 fca37
FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE TRUE
fca8 fca23 fca43 fca45 fca77 fca78 fca90 fca96 fca37
1.99999 2.00000 1.99999 2.00000 2.00000 2.00000 1.99999 1.99999 2.00000
N215 N216 N217 N218 N219 N220 N221
N216 0.2377930
N217 0.3359375 0.5029297
N218 0.4062195 0.5033875 0.5590007
N219 0.3964844 0.2929688 0.4600694 0.3940701
N220 0.4491882 0.3984070 0.4947645 0.5104167 0.4114312
N221 0.2617188 0.3217773 0.4288194 0.2603895 0.2517361 0.4110243
N222 0.4882202 0.4784546 0.5086263 0.5360243 0.4912652 0.2968479 0.4821777
N223 0.3789062 0.5166016 0.3142361 0.4444173 0.5451389 0.4769965 0.3541667
N224 0.5483093 0.4784851 0.5741916 0.3680556 0.4787055 0.3224826 0.3953722
N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.4353027
N224 0.4956597 0.5307888
$fca8
N215 N216 N217 N218 N219 N220 N221 N222
N216 NA
N217 NA NA
N218 NA NA 0.484375
N219 NA NA 0.484375 0.000000
N220 NA NA 0.000000 0.484375 0.484375
N221 NA NA 0.468750 0.250000 0.250000 0.468750
N222 NA NA 0.000000 0.484375 0.484375 0.000000 0.468750
N223 NA NA 0.250000 0.734375 0.734375 0.250000 0.718750 0.250000
N224 NA NA 0.468750 0.250000 0.250000 0.468750 0.000000 0.468750
N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.718750
$fca23
N215 N216 N217 N218 N219 N220 N221
N216 0.4843750
N217 0.0000000 0.4843750
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N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.0000000
N224 0.8710938 0.8710938
$fca43
N215 N216 N217 N218 N219 N220 N221 N222
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N219 0.687500 0.250000 0.375000 0.437500
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N224 0.687500 0.250000 0.375000 0.437500 0.000000 0.468750 0.250000 0.812500
N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.687500
$fca45
N215 N216 N217 N218 N219 N220 N221 N222
N216 0.484375
N217 0.375000 0.859375
N218 0.437500 0.375000 0.484375
N219 0.921875 0.437500 0.968750 0.484375
N220 0.484375 0.000000 0.859375 0.375000 0.437500
N221 0.437500 0.375000 0.484375 0.000000 0.484375 0.375000
N222 0.484375 0.000000 0.859375 0.375000 0.437500 0.000000 0.375000
N223 0.437500 0.375000 0.484375 0.000000 0.484375 0.375000 0.000000 0.375000
N224 0.484375 0.000000 0.859375 0.375000 0.437500 0.000000 0.375000 0.000000
N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.375000
$fca77
N215 N216 N217 N218 N219 N220 N221 N222
N216 0.000000
N217 0.375000 0.375000
N218 0.875000 0.875000 0.687500
N219 0.750000 0.750000 0.375000 0.500000
N220 0.437500 0.437500 0.250000 0.437500 0.625000
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N222 0.500000 0.500000 0.500000 0.843750 0.687500 0.625000 0.687500
N223 0.812500 0.812500 0.625000 0.484375 0.718750 0.375000 0.718750 0.625000
N224 0.437500 0.437500 0.250000 0.437500 0.625000 0.000000 0.625000 0.625000
N223
N216
N217
N218
N219
N220
N221
N222
N223
N224 0.375000
$fca78
N215 N216 N217 N218 N219 N220 N221 N222 N223
N216 0.0000
N217 0.4375 0.4375
N218 0.0000 0.0000 0.4375
N219 0.0000 0.0000 0.4375 0.0000
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N222 0.0000 0.0000 0.4375 0.0000 0.0000 0.4375 0.0000
N223 0.4375 0.4375 0.0000 0.4375 0.4375 0.8750 0.4375 0.4375
N224 0.4375 0.4375 0.8750 0.4375 0.4375 0.0000 0.4375 0.4375 0.8750
$fca90
N215 N216 N217 N218 N219 N220 N221
N216 0.4960938
N217 0.5000000 0.7421875
N218 0.0000000 0.4960938 0.5000000
N219 0.4375000 0.4687500 0.6250000 0.4375000
N220 0.8125000 0.8437500 0.6250000 0.8125000 0.3750000
N221 0.0000000 0.4960938 0.5000000 0.0000000 0.4375000 0.8125000
N222 0.6875000 0.7187500 0.3750000 0.6875000 0.2500000 0.2500000 0.6875000
N223 0.5000000 0.7421875 0.0000000 0.5000000 0.6250000 0.6250000 0.5000000
N224 0.5000000 0.7421875 0.0000000 0.5000000 0.6250000 0.6250000 0.5000000
N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.3750000
N224 0.3750000 0.0000000
$fca96
N215 N216 N217 N218 N219 N220 N221
N216 0.0000000
N217 0.0000000 0.0000000
N218 0.9685059 0.9685059 0.9685059
N219 0.0000000 0.0000000 0.0000000 0.9685059
N220 0.4997559 0.4997559 0.4997559 0.4687500 0.4997559
N221 0.4687500 0.4687500 0.4687500 0.4997559 0.4687500 0.4960938
N222 0.9995117 0.9995117 0.9995117 0.4960938 0.9995117 0.4997559 0.9958496
N223 0.4687500 0.4687500 0.4687500 0.4997559 0.4687500 0.4960938 0.0000000
N224 0.9685059 0.9685059 0.9685059 0.0000000 0.9685059 0.4687500 0.4997559
N222 N223
N216
N217
N218
N219
N220
N221
N222
N223 0.9958496
N224 0.4960938 0.4997559
$fca37
N215 N216 N217 N218 N219 N220 N221 N222 N223
N216 0.000
N217 0.500 0.500
N218 0.000 0.000 0.500
N219 0.000 0.000 0.500 0.000
N220 0.000 0.000 0.500 0.000 0.000
N221 0.000 0.000 0.500 0.000 0.000 0.000
N222 0.375 0.375 0.500 0.375 0.375 0.375 0.375
N223 0.375 0.375 0.500 0.375 0.375 0.375 0.375 0.000
N224 0.000 0.000 0.500 0.000 0.000 0.000 0.000 0.375 0.375
P01 P02 P03 P04 P05 P06
rowInd Integer,10 Integer,22 Integer,12 Integer,23 Integer,15 Integer,11
colInd Integer,10 Integer,22 Integer,12 Integer,23 Integer,15 Integer,11
Rowv NULL NULL NULL NULL NULL NULL
Colv NULL NULL NULL NULL NULL NULL
P07 P08 P09 P10 P11 P12
rowInd Integer,14 Integer,10 Integer,9 Integer,11 Integer,20 Integer,14
colInd Integer,14 Integer,10 Integer,9 Integer,11 Integer,20 Integer,14
Rowv NULL NULL NULL NULL NULL NULL
Colv NULL NULL NULL NULL NULL NULL
P13 P14 P15 P16 P17
rowInd Integer,13 Integer,17 Integer,11 Integer,12 Integer,13
colInd Integer,13 Integer,17 Integer,11 Integer,12 Integer,13
Rowv NULL NULL NULL NULL NULL
Colv NULL NULL NULL NULL NULL
Warning message:
system call failed: Cannot allocate memory
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