INSTRUCTIONS FOR MATRIX ANALYSES PROGRAMS
The functions in this package have been written with the intention of allowing easy modifications to be made for
different types of data.
If you wish to be informed of future additions/corrections please send an email to Derek.Roff@ucr.edu.
Function names are given in bold blue font, variable names in bold red font and parameters in bold black font.
The functions were originally written for a half-sib design but have been modified to accommodate the following
designs: fullsib data, phenotypic data, offspring on parent data, clonal data.
Sample data sets are provided for each type of analysis.
More complex designs, such as a nested fullsib pedigree can be accomplished by modifying the relevant function
(described below) or by a pre-analysis of the data that removes these effects and then uses the residuals.
GENERAL STRUCTURE OF DATA SETS
The function that controls all the other functions and for most cases is the only one that needs to be changed is called
MATRIX.COMPARISONS. The user will have to change the first lines which set the file folder in which the data and the
functions are stored. In the supplied function these refer to a location in my dropbox:
setwd("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/INITIAL.DATA.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/HALF.SIB.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/MATRIX.CALCULATOR.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/RANDOMIZE.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/RANDOM.SKEWERS.FUNCTIONS.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/MANTEL.FUNCTIONS.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/MATRIX.TESTS.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/BARTLETT.FUNCTIONS.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/JACKKNIFE.FUNCTION.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/MANOVA.TESTS.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/JACKKNIFE.EIGEN.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/MANOVA.EIGEN.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/PHENOTYPIC.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/FULL.SIB.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/OFFSPRING.ON.PARENT.r")
source("C:/Users/Derekr/Documents/My Dropbox/MATRIX ANALYSES/CLONAL.r")
Randomization requires a basic unit. For the present designs these are
Half-sib :
Sire families
Full-sib:
Families
Phenotypic:
Individual
Offspring on Parent:
Families
Clonal:
Clone
For convenience this unit is called SIRE in all functions and is created in the function INITIAL.DATA called by the function
MATRIX.COMPARISONS.
The data set of the user should contain a column labeled Unique.Sire that designates the sampling unit. It is necessary
to have unique codes for each sampling unit even if it appears in a different population. The function INITIAL.DATA
takes the data and creates a column called SIRE that is a sequential integer that is made into a factor where necessary.
This variable is the one that is used as the sampling unit and matrix estimation procedure. Thus even for the clonal
analysis the clones must be labeled as Unique.Sire and the formula for the creation of the matrix must use the variable
SIRE .
Thus in the present functions the basic sampling unit is called SIRE
Design
Unit
Label in Data set
Label created by INITIAL.DATA
Half-sib :
Sire families
Unique.Sire
SIRE
Full-sib:
Families
Unique.Sire
SIRE
Phenotypic:
Individual
Unique.Sire
SIRE
Offspring on Parent:
Families
Unique.Sire
SIRE
Clonal:
Clone
Unique.Sire
SIRE
In addition to creating the variable SIRE the function INITIAL.DATA standardizes the trait values within populations by
subtracting the mean, thus removing differences in the randomization due to differences in means among populations.
It may be advisable in the original data set to standardize the traits by subtracting the mean over all populations and
dividing by the standard deviation over all populations: such a transformation may be important if the traits are
measured on very different scales (e.g. body weight and development time).
The function MATRIX.CALCULATOR calls the functions that calculate the relevant matrices/vectors and expects as
output a list called Out that has the relevant matrix/vector .
For the halfsib analysis there are nine possible outputs
# 1 Sire.Gmatrix
= Sire G matrix
# 2 Dam.Gmatrix
= Dam G matrix
# 3 G.Gmatrix
= Genotypic G matrix (= mean of sire and dam)
# 4 Pmatrix
= Phenotypic matrix
# 5 G.Eigen
= Eigenvalues of the Genotypic G matrix
# 6 GPinverse
= GP^-1 for selection skewers test
# 7 P.Eigen
= Eigenvalues of the P matrix
# 8 G.Sire.Eigen
= Eigenvalues of the Sire G matrix
# 9 G.Dam.Eigen
= Eigenvalues of the Dam G matrix
Which of these is passed back to MATRIX.CALCULATOR is determined by the parameter STAT (=1-9) which is set in the
function MATRIX.COMPARISONS. Other methods will not necessarily have the same number of possible outputs but for
consistency in using STAT each of the functions passing back matrices pass back 9 values. For example the fullsib
function FULL.SIB passes back
#
1
2
3
4
5
6
7
8
9
Out <- list(Gmatrix, Gmatrix, Gmatrix, Pmatrix, G.Eigen, GPinverse, P.Eigen, G.Eigen, G.Eigen)
so that the eigenvalues occur in the appropriate position.
As noted above, the guiding function is MATRIX.COMPARISONS. The following components will need to be changed for
a particular analysis
TESTS
Vector that names the available tests
#TESTS
1
2
3
4
5
6
7
TESTS <- c("SELECTION SKEWER","RANDOM SKEWER", "MANTEL TEST", "FLURY","BARTLETT","JACKKNIFE","EIGEN")
The particular test is set by TEST. For example, TEST <- TESTS[3] selects the modified Mantel test
METHODS
Vector that names the available methods
# METHODS
1
2
3
4
5
METHODS <- c("HALF.SIB", "PHENOTYPIC", "FULL.SIB", "OFFSPRING.ON.PARENT", "CLONAL")
The particular method is set by Method. For example, Method <- METHODS[3] determines that the data set consists
of fullsibs.
Nos.of.Rands sets the number of randomizations required. This number includes the observed value. The required
number will depend upon the P value. R functions are not very fast and so a preliminary run of 100-500
randomizations are suggested. If the P value is less than 0.1 more randomizations will be required: for a
discussion of the appropriate number see Roff, D. A. 2006. Introduction to Computer-Intensive Methods of
Data Analysis in Biology. Cambridge University Press, Cambridge.
STAT See above
PRINT Determines if observed and jackknife estimates of the matrices or eigenvalues are printed. “YES” means print
but anything else suppresses printing. This will generally be set as “YES”.
MANOVA.TESTING The function JACKKNIFE calculates the jackknife estimates and pseudovalues of the requested
matrix while the function JACKKNIFE.EIGEN calculates the jackknife estimates and pseudovalues of the
requested eigenvalues. The pseudovalues are passed back to the function MATRIX.COMPARISONS as a matrix
called Data. Differences among matrices or eigenvalues can then be analysed using the pseudovalues. The
program accesses a function MANOVA.TESTS(Data) for matrix analysis or MANOVA.EIGEN(Data) that does the
required analysis. The functions supplied in this package test the data assuming that the only predictor variable
is the population code. If there are more or other predictor variables then the function will have to be modified
accordingly.
Nos.of.Skewers Number of skewers in random and selection skewers test. This is the number used in each
randomization. I have set it to 500, which seems reasonable.
ALL.DATA Data read into this. The data set should have a header giving the variable names – see below for examples.
Note that this data set can contain more populations than are to be analyzed. The function INITIAL.DATA
reduces the data set to those populations specified in Selected.Pop (see below)
Trait.cols A vector giving the column numbers in which the trait values are to be found.
FORMULA Specific to each type of pedigree – see below for further details
Selected.POP a vector giving the identifier codes for the populations. The functions have been written in a manner to
potentially take more than two but I think that this is desirable only for the jackknife analyses.
R SCRIPTS USED FOR THE DIFFERENT METHODS
Functions calculating G matrices are scripts
HALF.SIB.r
FULL.SIB.r
PHENOTYPIC.r
CLONAL.r
Random and Selection Skewers
The only difference is in the value of STAT
Starting with MATRIX.COMPARISONS other functions are in script files
INITIAL.DATA.r
RANDOM.SKEWERS.FUNCTIONS.r
MATRIX.CALCULATOR.r
RANDOMIZE.r
Function for particular pedigree.r
Modified Mantel Test
Starting with MATRIX.COMPARISONS other functions are in script files
INITIAL.DATA.r
MANTEL.FUNCTIONS.r
MATRIX.CALCULATOR.r
RANDOMIZE.r
Function for particular pedigree.r
Hierarchical Tests
Starting with MATRIX.COMPARISONS other functions are in script files
INITIAL.DATA.r
MATRIX.TESTS.r
MATRIX.CALCULATOR.r
RANDOMIZE.r
Function for particular pedigree.r
Bartlett Test
Starting with MATRIX.COMPARISONS other functions are in script files
INITIAL.DATA.r
BARTLETT.FUNCTIONS.r
MATRIX.CALCULATOR.r
RANDOMIZE.r
Function for particular pedigree.r
Jackknife-MANOVA
Starting with MATRIX.COMPARISONS other functions are in script files
INITIAL.DATA.r
JACKKNIFE.FUNCTIONS.r
MATRIX.CALCULATOR.r
Function for particular pedigree.r
MANOVA.TESTS.r
Jackknife-Eigen
Starting with MATRIX.COMPARISONS other functions are in script files
INITIAL.DATA.r
JACKKNIFE.EIGEN.r
MATRIX.CALCULATOR.r
Function for particular pedigree.r
MANOVA.Eigen.r
HALF-SIB ANALYSIS – data set = HALF.SIB.TEST.DATA.txt
Data set: Each sire has a unique code. 3 dams per sire with each dam within a sire labeled A, B, C.
POP code = 10, 11
Traits = X1, X2, X3, X4
Unique.Sire
DAM POP
X1
X2
X3
X4
10001
A
10
1.5121333
-0.806807063 0.149187255 -1.100176232
10001
A
10
0.869343893 -0.589052837 -0.675084689 -0.506138065
10001
A
10
1.250114883 -1.02456129 -1.887249313 -0.808278167
10001
B
10
-0.234388999 2.366183097 -1.062977369 -0.772431036
10001
B
10
-1.278455425 1.619597177 -1.062977369 -1.26404883
10001
B
10
-0.164220793 1.77513591
-1.111463954 -0.362749541
10001
C
10
0.468564325 0.033102097 -0.335678594 0.666575214
10001
C
10
0.976323462 -0.526837343 -2.226655408 0.932868185
10002
A
10
0.535029286 -0.93123805 0.149187255 0.333708999
10002
B
10
0.054823398 0.344179563 -0.141732254 0.559033821
11001
A
11
1.129731777 -0.27797537 -0.529624934 0.902142073
11001
A
11
-1.652593737 0.28196407
-0.820544444 -0.419080747
11001
A
11
-1.244601131 -0.309083117 -0.820544444 -0.598316401
11001
A
11
0.22940101
-0.09132889 -1.450870049 0.559033821
11001
B
11
0.256539718 -0.27797537 -1.353896879 0.02132686
11001
B
11
-0.218415299 -0.526837343 -1.499356634 -0.526622139
11001
B
11
-0.24193367 2.05510563
-1.499356634 0.072537047
11001
B
11
0.833720885 0.00199435
-2.129682238 -1.258927811
11001
C
11
-1.322037647 -0.46462185 -0.044759085 -0.869730391
11001
C
11
-1.686448031 -1.242315517 -0.675084689 0.881657998
Coding in MATRIX.COMPARISONS
if(Method=="HALF.SIB")
{
################# Input for half sib data #################
# Variables are
# 1
2 3 4 5 6 7
# Unique.Sire DAM
POP
X1
X2
X3
X4
Trait.cols
<- c( 4, 5, 6, 7) # Set vector giving the column numbers for the traits
ALL.DATA
<- read.table("HALF.SIB.TEST.DATA.txt", header=TRUE) # Enter data
FORMULA
<- cbind(X1,X2,X3,X4)~ SIRE + DAM%in%SIRE # Formula for estimating matrices for half sib
Selected.POP <- c(10,11)
# Code designating populations
}
Comments:
Traits are in columns 4, 5, 6,7
Population IDs = 10, 11
Data are in text file HALF.SIB.TEST.DATA.txt
FORMULA in this case is the manova function
cbind(X1,X2,X3,X4)~ SIRE + DAM%in%SIRE
FULL-SIB ANALYSIS-data set = FULL.SIB.TEST.DATA.txt
Data set: Each sire has a unique code.
POP code = 10, 11
Traits = X1, X2, X3, X4
Unique.Sire
POP
X1
X2
X3
X4
10001
10
1.5121333
-0.806807063 0.149187255 -1.100176232
10001
10
0.869343893 -0.589052837 -0.675084689 -0.506138065
10001
10
0.99000336
0.126425337 -0.820544444 -0.552227233
10001
10
0.489512533 -0.153544383 -1.014490784 -1.22308068
10001
10
1.315640214 -0.495729597 -1.838762729 -1.463768558
10002
10
0.984918307 0.09531759
-1.305410294 -0.116940645
10002
10
0.054823398 0.344179563 -0.141732254 0.559033821
10002
10
1.117433687 0.064209843 -0.141732254 0.011084822
10002
10
0.781350365 0.157533083 -0.190218839 1.578116539
10002
10
0.318085442 0.09531759
-0.432651764 1.53714839
10002
10
0.0069023
-1.11788453 -0.481138349 1.675415894
10002
10
1.229995759 -0.526837343 -0.675084689 1.982677015
10002
10
1.244062564 -1.67782397 -0.772057859 -0.142545738
10002
10
0.733512175 0.779688017 -0.917517614 -0.25008713
10002
10
-0.202109966 -0.962345797 -1.014490784 0.21592557
11004
11
-0.007192141 1.246304217 -0.917517614 -1.141144381
11004
11
-0.000144921 1.432950697 -1.014490784 -1.023360952
11005
11
-1.906459488 1.246304217 0.537079935 -0.209118981
11005
11
1.057573768 1.49516619
0.39162018
0.185199458
11005
11
0.570624657 0.997442243 0.343133595 0.364435111
11005
11
0.369737422 0.344179563 0.29464701
-0.716099831
11005
11
-0.480433717 0.437502803 0.10070067
-1.279411886
11005
11
1.310803886 0.717472523 0.343133595 -0.654647606
Coding in MATRIX.COMPARISONS
if(Method=="FULL.SIB")
{
################# Input for full sib data #################
# Variables are
# 1
2
3
4
5
6
# Unique.Sire POP
X1
X2
X3
X4
Trait.cols
<- c(3, 4, 5, 6) # Set vector giving the column numbers for the traits
ALL.DATA
<- read.table("FULL.SIB.TEST.DATA.txt", header=TRUE) # Enter data
FORMULA
<- cbind(X1,X2,X3,X4)~SIRE # Formula for full sib model
Selected.POP <- c(10,11)
# Code designating populations
}
Comments:
Traits are in columns 3, 4, 5, 6
Population IDs = 10, 11
Data are in text file FULL.SIB.TEST.DATA.txt
FORMULA in this case is the manova function
cbind(X1,X2,X3,X4)~ SIRE
OFFSPRING ON PARENT ANALYSIS – data set =OFFSPRING.ON.PARENT.DATA.SET
Data set: Each family (=Unique.Sire) has a unique code. The data assume a mean offspring on midparent. The G matrix
must be multiplied by 2 if only one parent is used. However, as this multiplier is the same for both populations
it is not necessary for comparing matrices.
POP code = 1, 2
Traits = Offspring OX1, OX2, OX3, OX4 Parents PX1, PX2, PX3, PX4
Unique.Sire
2
4
5
6
166
168
172
178
179
180
182
183
184
186
OX1
0.61
-0.16
0.24
-1.56
0.57
-0.24
0.01
0.63
-0.75
-0.16
0.78
0.11
-0.54
-1.50
OX2
-0.09
0.30
0.33
-0.27
0.16
-0.08
0.01
0.23
-0.15
-0.19
0.36
0.07
-0.28
-0.43
OX3
0.38
-0.19
0.35
-0.75
0.50
0.07
-0.11
0.27
-0.05
-0.04
0.55
0.32
-0.08
-0.80
OX4
-0.51
-0.34
-0.01
-0.01
0.25
0.96
0.53
-0.47
-0.34
-0.34
0.68
0.03
0.03
0.53
PX1
-0.61
-0.85
-0.21
-1.18
0.95
0.53
-0.64
0.04
-0.29
0.03
-0.13
0.29
-0.80
-1.76
PX2
-0.18
0.34
0.16
-0.18
0.26
-0.10
0.14
0.10
0.00
0.31
0.09
0.08
-0.16
-0.77
PX3
-0.46
-0.23
-0.06
-0.56
0.78
0.18
-0.57
-0.26
-0.38
0.13
-0.23
0.12
-0.33
-0.89
PX4
2.11
0.11
2.11
4.61
-0.35
-0.35
-1.35
-0.85
1.15
-1.35
-0.35
-0.35
-0.85
1.15
POP
1
1
1
1
2
2
2
2
2
2
2
2
2
2
Coding in MATRIX.COMPARISONS
if(Method=="OFFSPRING.ON.PARENT")
{
################# Input for offspring on parent data #################
# Variables are
#
Offspring data
Parent data
# 1
2
3
4
5
6
7
8
9
10
# Unique.Sire OX1
OX2
OX3
OX4
PX1
PX2
PX3
PX4
POP
Trait.cols <- c(6,7,8,9,2,3,4,5)
# Set vector giving the column numbers for the traits
ALL.DATA
<- read.table("OFFSPRING.ON.PARENT.DATA.txt", header=TRUE) # Enter data
FORMULA
<- Trait.cols
# FORMULA for a simple phenotypic analysis
Selected.POP <- c(1,2)
# Code designating populations
}
Comments:
Traits are in columns 6,7,8,9,2,3,4,5 NOTE THAT THE PARENT COLUMNS PRECEDE THE OFFSPRING
Population IDs = 1, 2
Data are in text file OFFSPRING.ON.PARENT.TEST.DATA.txt
FORMULA in this case are the columns for the traits
FORMULA
<- Trait.cols
PHENOTYPIC ANALYSIS-data set – PHENOTYPIC.TEST.DATA
Data set: Each individual (=Unique.Sire) has a unique code.
POP code = 10, 11
Traits = X1, X2, X3, X4
Unique.Sire
1
2
3
4
5
261
262
263
264
265
266
267
268
269
270
POP
10
10
10
10
10
11
11
11
11
11
11
11
11
11
11
X1
1.5121333
0.869343893
0.99000336
0.489512533
1.315640214
-0.253540857
0.356472066
0.256539718
-0.218415299
-0.24193367
0.833720885
-1.322037647
-1.686448031
0.00798011
-0.896109174
X2
-0.806807063
-0.589052837
0.126425337
-0.153544383
-0.495729597
0.28196407
0.56193379
-0.27797537
-0.526837343
2.05510563
0.00199435
-0.46462185
-1.242315517
0.126425337
-1.21120777
X3
0.149187255
-0.675084689
-0.820544444
-1.014490784
-1.838762729
-0.869031029
-1.014490784
-1.353896879
-1.499356634
-1.499356634
-2.129682238
-0.044759085
-0.675084689
-1.159950539
-1.935735898
X4
-1.100176232
-0.506138065
-0.552227233
-1.22308068
-1.463768558
-0.87485141
0.543670765
0.02132686
-0.526622139
0.072537047
-1.258927811
-0.869730391
0.881657998
0.103263159
-0.695615756
Coding in MATRIX.COMPARISONS
if(Method=="PHENOTYPIC")
{
################# Input for Phenotypic data #################
# Variables are
# 1
2 3 4 5 6
# Unique.Sire POP
X1
X2
X3
X4
Trait.cols <- c(3, 4, 5, 6)
# Set vector giving the column numbers for the traits
ALL.DATA <- read.table("PHENOTYPIC.TEST.DATA.txt", header=TRUE) # Enter data
FORMULA
<- Trait.cols
# FORMULA for a phenotypic analysis
Selected.POP <- c(10,11)
# Code designating populations
}
Comments:
Traits are in columns 3, 4,5,6
Population IDs = 10, 11
Data are in text file PHENOTYPIC.TEST.DATA.txt
FORMULA in this case are the columns for the traits
FORMULA
<- Trait.cols
CLONAL DATA- data = CLONAL.TEST.DATA.txt
Data set: Each clone (=Unique.Sire) has a unique code.
POP code = 10, 11
Traits = X1, X2, X3, X4
Unique.Sire
10001
10001
10001
10001
11001
11001
11001
11001
11001
11001
11001
11002
11002
11002
11002
POP
10
10
10
10
11
11
11
11
11
11
11
11
11
11
11
X1
1.5121333
0.869343893
0.99000336
0.489512533
-0.218415299
-0.24193367
0.833720885
-1.322037647
-1.686448031
0.00798011
-0.896109174
0.665389044
0.454110614
0.53024823
1.268575837
X2
-0.806807063
-0.589052837
0.126425337
-0.153544383
-0.526837343
2.05510563
0.00199435
-0.46462185
-1.242315517
0.126425337
-1.21120777
-1.30453101
-1.273423263
-1.522285237
-0.962345797
X3
0.149187255
-0.675084689
-0.820544444
-1.014490784
-1.499356634
-1.499356634
-2.129682238
-0.044759085
-0.675084689
-1.159950539
-1.935735898
-0.772057859
-0.820544444
-0.820544444
-1.644816389
X4
-1.100176232
-0.506138065
-0.552227233
-1.22308068
-0.526622139
0.072537047
-1.258927811
-0.869730391
0.881657998
0.103263159
-0.695615756
-0.429322784
1.429606997
0.60512299
1.752231174
Coding in MATRIX.COMPARISONS
if(Method=="CLONAL")
{
################# Input for clonal data #################
# Variables are
# 1
2 3 4 5 6
# Unique.Sire POP X1 X2
X3
X4
Trait.cols <- c(3, 4, 5, 6) # Set vector giving the column numbers for the traits
ALL.DATA
<- read.table("CLONAL.TEST.DATA.txt", header=TRUE) # Enter data
FORMULA
<- cbind(X1,X2,X3,X4)~SIRE # Formula for simple full sib model
Selected.POP <- c(10,11)
# Code designating populations
}
Comments:
Traits are in columns 3, 4,5,6
Population IDs = 10, 11
Data are in text file CLONAL.TEST.DATA.txt
FORMULA in this case are the columns for the traits
FORMULA
<- Trait.cols
The function calculating the matrices for the clonal model differ from the full-sib function only by a multiplier (2 in fullsib) of the G matrix.
RESULTS FROM TEST DATA SETS
STATS SET AT 3 OR 5
The jackknife values should be the same at any run but the others will change according to the random numbers
generated.
HALF-SIB DATA- using genotypic G matrix (STAT=3) or Genotypic eigenvalues (STAT=5)
Random skewer
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Results of Selection Skewers Test"
"Nos of randomizations (includes observed)"
200
"Nos of skewers per cycle=" "500"
"Obs skewer
Prob"
0.9045917 0.6000000
Modified Mantel Test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Results for modified Mantel Test"
[1] "Nos of randomizations[includes observed] =" "200"
[1] "Obs M, Prob obs M > Null"
[1] 0.8655562 0.3650000
Hierarchical tests
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "*************************************************************************"
[1] "Probabilities are calculated using the jump up approach"
[1] "Thus the probability is calculated relative to unrelated structure"
[1] "Cases in which the determinant could not be calculated are dropped from the
calculations"
[1] "The warnings refer to these cases and can be ignored"
[1] "The total number of randomizations and the number actually used (N.actual) are
reported"
[1] "*************************************************************************"
[1] "Results of randomization"
[1] "Number of randomizations (includes observed)"
[1] 200
[1] "Comparing Equal with unrelated"
[1] "N.actual
Prob "
[1] 195.0000000
0.1487179
[1] "Comparing Proportional with unrelated"
[1] "N.actual
Prob "
[1] 195.0000000
0.2051282
[1] "Comparing CPC with unrelated"
[1] "N.actual
Prob "
[1] 196.0000000
0.1632653
There were 19 warnings (use warnings() to see them)
Bartlett’s Test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "**************************************************"
[1] "Results for Bartlett's Test"
[1] "Chi2" "
df" "
P"
[1] 21.64561 10.00000 0.01702
[1] "Proportion Randomizations >= B =" "0.111675126903553"
[1] "Nos of excluded randomizations=" "4"
Warning messages:
1: In log(Det2) : NaNs produced
2: In log(Det2) : NaNs produced
3: In log(Det3) : NaNs produced
4: In log(Det2) : NaNs produced
JACKKNIFE-MANOVA with MANOVA test of pseudovalues
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "****************************************************************"
[1] "The pseudovalues are returned using the upper portion of the whole matrix"
[1] "For example with 4 traits as in the test data the output is"
[1] "Col 1 = Population code"
[1] "Columns numbers for (co)variances are"
[1] "Trait = X1 X2 X3 X4"
[1] "X1
2
3 4 5"
[1] "X2
6 7 8"
[1] "X3
9 10"
[1] "X4
11"
[1] "****************************************************************"
[1] "Results from Jackknife analysis"
[1] "Population ID = " "10"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.07300021 -0.04706084 -0.03042941 -0.03032750
[2,] -0.04706084 0.32034713 0.06558684 -0.25906717
[3,] -0.03042941 0.06558684 0.70224098 -0.01202863
[4,] -0.03032750 -0.25906717 -0.01202863 0.60692040
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.07315661 -0.04879009 -0.03079185 -0.03063446
[2,] -0.04879009 0.32115341 0.06621227 -0.25973886
[3,] -0.03079185 0.06621227 0.70318007 -0.01403968
[4,] -0.03063446 -0.25973886 -0.01403968 0.60854251
[1] "Population ID = " "11"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.39138982 0.03449551 0.2995181 0.02973964
[2,] 0.03449551 0.68448505 0.2480728 -0.30358834
[3,] 0.29951807 0.24807278 0.7778046 -0.06296790
[4,] 0.02973964 -0.30358834 -0.0629679 0.49459983
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.39031874 0.03057134 0.30074859 0.02930084
[2,] 0.03057134 0.68183804 0.24900829 -0.30595247
[3,] 0.30074859 0.24900829 0.78261171 -0.06391005
[4,] 0.02930084 -0.30595247 -0.06391005 0.49344843
[1] "MANOVA results"
Df
Wilks approx F num Df den Df Pr(>F)
Data$X1
1 0.59362
1.9853
10
29 0.07313 .
Residuals 38
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "*******************************************************"
[1] "ANOVA for covariance #" "2"
Df Sum Sq Mean Sq F value
Pr(>F)
Data$X1
1 1.0059 1.00592 7.4755 0.009446 **
Residuals
38 5.1134 0.13456
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.0630 0.062982 0.3002 0.587
Residuals
38 7.9722 0.209794
[1] "ANOVA for covariance #" "4"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 1.0992 1.09919 4.9244 0.03253 *
Residuals
38 8.4821 0.22321
---
Signif. codes:
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
covariance #" "5"
Sum Sq Mean Sq F value Pr(>F)
0.03592 0.035922 0.5509 0.4625
2.47799 0.065210
covariance #" "6"
Sum Sq Mean Sq F value Pr(>F)
1.3009 1.30093
1.878 0.1786
26.3237 0.69273
covariance #" "7"
Sum Sq Mean Sq F value Pr(>F)
0.3341 0.33414 0.7542 0.3906
16.8346 0.44302
covariance #" "8"
Sum Sq Mean Sq F value Pr(>F)
0.0214 0.021357 0.0787 0.7806
10.3089 0.271288
covariance #" "9"
Sum Sq Mean Sq F value Pr(>F)
0.0631 0.06309 0.0955 0.759
25.0994 0.66051
covariance #" "10"
Sum Sq Mean Sq F value Pr(>F)
0.0249 0.024871 0.0882 0.7681
10.7164 0.282010
covariance #" "11"
Sum Sq Mean Sq F value Pr(>F)
0.1325 0.13247 0.2923 0.5919
17.2208 0.45318
JACKKNIFE-EIGENVALUES with manova test
1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "jackknife of Eigenvalues"
[1] "**********************************************"
[1] "POP ID =" "10"
[1] "Observed eigenvalues"
[1] 0.78452421 0.68417595 0.18684355 0.04696501 1.70250872
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.543484 0.8768023 0.2048298 0.0809165 1.706033
[1] 0.13143216 0.14182497 0.10504744 0.06003318 0.22708639
[1] "T test: Probability that eigenvalue =< 0"
[1] 2.814010e-04 3.055447e-06 3.305196e-02 9.677740e-02 2.103807e-07
[1] "**********************************************"
[1] "POP ID =" "11"
[1] "Observed eigenvalues"
[1] 1.1505258 0.7330359 0.2568046 0.2079131 2.3482793
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.988703 0.8344058 0.182725 0.3423831 2.348217
[1] 0.24937769 0.18316514 0.06825390 0.09878909 0.29549921
[1] "T test: Probability that eigenvalue =< 0"
[1] 4.152852e-04 1.080987e-04 7.452899e-03 1.294280e-03 9.254723e-08
[1] "MANOVA RESULTS"
Df
Wilks approx F num Df den Df Pr(>F)
X6
1 0.77389
2.5565
4
35 0.05586 .
Residuals 38
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "*************************************************"
[1] "ANOVAs Last ANOVA is for eigen sum"
[1] "ANOVA for eigen #" "1"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 1.9822 1.98220 2.4945 0.1225
Residuals
38 30.1962 0.79464
[1] "ANOVA for eigen #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
Residuals
38
[1] "ANOVA for
Df
X6
1
Residuals
38
[1] "ANOVA for
Df
X6
1
Residuals
38
--Signif. codes:
[1] "ANOVA for
Df
X6
1
Residuals
38
--Signif. codes:
0.018 0.01797 0.0335 0.8558
20.392 0.53664
eigen #" "3"
Sum Sq Mean Sq F value Pr(>F)
0.0049 0.004886 0.0311 0.8609
5.9636 0.156936
eigen #" "4"
Sum Sq Mean Sq F value Pr(>F)
0.6836 0.68365 5.1159 0.02951 *
5.0780 0.13363
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
eigen #" "5"
Sum Sq Mean Sq F value Pr(>F)
4.124 4.1240 2.9693 0.09299 .
52.777 1.3889
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
####################################################################
PHENOTYPIC ANALYSIS – Mantel Test, Hierarchical, Bartlett, Jackknife
Modified Mantel Test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Results for modified Mantel Test"
[1] "Nos of randomizations[includes observed] =" "200"
[1] "Obs M, Prob obs M > Null"
[1] 0.9606621 0.0200000
Hierarchical
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "*************************************************************************"
[1] "Probabilities are calculated using the jump up approach"
[1] "Thus the probability is calculated relative to unrelated structure"
[1] "Cases in which the determinant could not be calculated are dropped from the calculations"
[1] "The warnings refer to these cases and can be ignored"
[1] "The total number of randomizations and the number actually used (N.actual) are reported"
[1] "*************************************************************************"
[1] "Results of randomization"
[1] "Number of randomizations (includes observed)"
[1] 200
[1] "Comparing Equal with unrelated"
[1] "N.actual
Prob "
[1] 200.000
0.075
[1] "Comparing Proportional with unrelated"
[1] "N.actual
Prob "
[1] 2e+02 2e-02
[1] "Comparing CPC with unrelated"
[1] "N.actual
Prob "
[1] 200.000
0.015
Bartlett’s Test
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"**************************************************"
"Results for Bartlett's Test"
"Chi2" "
df" "
P"
27.075880 10.000000 0.002533
"Proportion Randomizations >= B =" "0.0149253731343284"
"Nos of excluded randomizations=" "0"
Jackknife-MANOVA
1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"****************************************************************"
"The pseudovalues are returned using the upper portion of the whole matrix"
"For example with 4 traits as in the test data the output is"
"Col 1 = Population code"
"Columns numbers for (co)variances are"
"Trait = X1 X2 X3 X4"
"X1
2
3 4 5"
"X2
6 7 8"
"X3
9 10"
"X4
11"
"****************************************************************"
"Results from Jackknife analysis"
"Population ID = " "10"
"Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.52781358 -0.09797534 -0.01709261 0.05121854
[2,] -0.09797534 0.78482796 0.09018825 -0.21815465
[3,] -0.01709261 0.09018825 0.63536455 0.05302508
[4,] 0.05121854 -0.21815465 0.05302508 0.76623800
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.52781358 -0.09797534 -0.01709261 0.05121854
[2,] -0.09797534 0.78482796 0.09018825 -0.21815465
[3,] -0.01709261 0.09018825 0.63536455 0.05302508
[4,] 0.05121854 -0.21815465 0.05302508 0.76623800
[1] "Population ID = " "11"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.69735516 -0.04798562 0.113608436 0.079147764
[2,] -0.04798562 1.23162242 0.223636353 -0.175342726
[3,] 0.11360844 0.22363635 0.692308357 0.009651753
[4,] 0.07914776 -0.17534273 0.009651753 0.746589861
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.69735516 -0.04798562 0.113608436 0.079147764
[2,] -0.04798562 1.23162242 0.223636353 -0.175342726
[3,] 0.11360844 0.22363635 0.692308357 0.009651753
[4,] 0.07914776 -0.17534273 0.009651753 0.746589861
[1] "*******************************************************"
[1] "MANOVA results"
Df
Wilks approx F num Df den Df Pr(>F)
Data$X1
1 0.95205
2.4073
10
478 0.00849 **
Residuals 487
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "*******************************************************"
[1] "ANOVA for covariance #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
3.51 3.5062 3.2895 0.07034 .
Residuals
487 519.08 1.0659
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
0.30 0.30482 0.4076 0.5235
Residuals
487 364.21 0.74787
[1] "ANOVA for covariance #" "4"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
2.084 2.08375 5.3744 0.02085 *
Residuals
487 188.817 0.38771
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "5"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
0.095 0.09515 0.2146 0.6434
Residuals
487 215.941 0.44341
[1] "ANOVA for covariance #" "6"
Df Sum Sq Mean Sq F value
Pr(>F)
Data$X1
1
24.35 24.3502
9.944 0.001713 **
Residuals
487 1192.53 2.4487
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "7"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
2.172 2.17226 3.7036 0.05488 .
Residuals
487 285.638 0.58653
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "8"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
0.22 0.22357 0.2822 0.5955
Residuals
487 385.82 0.79223
[1] "ANOVA for covariance #" "9"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
0.396 0.39553 0.6609 0.4166
Residuals
487 291.447 0.59845
[1] "ANOVA for covariance #" "10"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
0.229 0.22947
0.477 0.4901
Residuals
487 234.289 0.48109
[1] "ANOVA for covariance #" "11"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1
0.05 0.04709 0.0386 0.8444
Residuals
487 594.37 1.22048
Jackknife-Eigenvalues
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"jackknife of Eigenvalues"
"**********************************************"
"POP ID =" "10"
"Observed eigenvalues"
1.0200048 0.7048607 0.5144478 0.4749307 2.7142441
"Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 1.001819 0.7032324 0.4860581 0.5231345 2.714244
[1] 0.09100778 0.05997284 0.04701251 0.04516678 0.13362502
[1] "T test: Probability that eigenvalue =< 0"
[1] 1.291281e-23 5.518951e-26 1.874911e-21 1.657163e-25 1.619055e-55
[1] "**********************************************"
[1] "POP ID =" "11"
[1] "Observed eigenvalues"
[1] 1.3570659 0.8503447 0.6371630 0.5233022 3.3678758
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 1.338069 0.8437334 0.642348 0.543725 3.367876
[1] 0.12388768 0.06868078 0.07563113 0.04850464 0.16659614
[1] "T test: Probability that eigenvalue =< 0"
[1] 1.350830e-22 2.362929e-27 1.217481e-15 6.850513e-24 2.190753e-53
[1] "MANOVA RESULTS"
Df
Wilks approx F num Df den Df Pr(>F)
X6
1 0.97974
2.5024
4
484 0.04166 *
Residuals 487
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "*************************************************"
[1] "ANOVAs Last ANOVA is for eigen sum"
[1] "ANOVA for eigen #" "1"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
13.79 13.7915 4.9013 0.0273 *
Residuals
487 1370.34 2.8138
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for eigen #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
2.41 2.4079 2.3943 0.1224
Residuals
487 489.78 1.0057
[1] "ANOVA for eigen #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
2.98 2.97954 3.1997 0.07427 .
Residuals
487 453.48 0.93118
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01
[1] "ANOVA for eigen #" "4"
Df Sum Sq Mean Sq F value
X6
1
0.052 0.05172 0.0967
Residuals
487 260.351 0.53460
[1] "ANOVA for eigen #" "5"
Df Sum Sq Mean Sq F value
X6
1
52.11 52.114
9.52
Residuals
487 2665.90
5.474
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01
‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Pr(>F)
0.7559
Pr(>F)
0.002148 **
‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
FULL-SIB ANALYSES STAT=3 or 5
Selection Skewers
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Results of Selection Skewers Test"
"Nos of randomizations (includes observed)"
200
"Nos of skewers per cycle=" "500"
"Obs skewer
Prob"
0.8182714 0.5550000
Mantle Test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Results for modified Mantel Test"
[1] "Nos of randomizations[includes observed] ="
[2] "200"
[1] "Obs M, Prob obs M > Null"
[1] 0.8258491 0.4650000
Hiearchical Test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Determinant=0" "3"
[1] "Determinant=0" "4"
[1] "Determinant=0" "7"
[1] "Determinant=0" "5"
[1] "Determinant=0" "3"
[1] "Determinant=0" "4"
[1] "*************************************************************************"
[1] "Probabilities are calculated using the jump up approach"
[1] "Thus the probability is calculated relative to unrelated structure"
[1] "Cases in which the determinant could not be calculated are dropped from the
calculations"
[1] "The warnings refer to these cases and can be ignored"
[1] "The total number of randomizations and the number actually used (N.actual) are
reported"
[1] "*************************************************************************"
[1] "Results of randomization"
[1] "Number of randomizations (includes observed)"
[1] 200
[1] "Comparing Equal with unrelated"
[1] "N.actual
Prob "
[1] 111
1
[1] "Comparing Proportional with unrelated"
[1] "N.actual
Prob "
[1] 112
1
[1] "Comparing CPC with unrelated"
[1] "N.actual
Prob "
[1] 134
1
There were 50 or more warnings (use warnings() to see the first 50)
Bartlett’s test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Negative eigenvalue in given matrix"
Warning message:
In log(Det2) : NaNs produced
NOTE Bartlett’s test not possible for this data set
Jackknife-MANOVA
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"****************************************************************"
"The pseudovalues are returned using the upper portion of the whole matrix"
"For example with 4 traits as in the test data the output is"
"Col 1 = Population code"
"Columns numbers for (co)variances are"
"Trait = X1 X2 X3 X4"
"X1
2
3 4 5"
"X2
6 7 8"
"X3
9 10"
"X4
11"
"****************************************************************"
"Results from Jackknife analysis"
"Population ID = " "10"
"Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.034060720 -0.02059865 -0.005330794 -0.03862233
[2,] -0.020598650 0.10317894 0.073498186 -0.13507409
[3,] -0.005330794 0.07349819 0.511929484 0.03311990
[4,] -0.038622329 -0.13507409 0.033119902 0.34059116
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.033935473 -0.02160619 -0.004831405 -0.03938084
[2,] -0.021606191 0.10276163 0.074875752 -0.13593860
[3,] -0.004831405 0.07487575 0.513199075 0.03035273
[4,] -0.039380840 -0.13593860 0.030352728 0.34201917
[1] "Population ID = " "11"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.13401795 0.09627359 0.2264788 0.02527265
[2,] 0.09627359 0.37117950 0.2082967 -0.14379427
[3,] 0.22647878 0.20829668 0.6504713 -0.14886080
[4,] 0.02527265 -0.14379427 -0.1488608 0.27688179
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.13289990 0.09270242 0.2286668 0.02504275
[2,] 0.09270242 0.37380194 0.2096080 -0.14751476
[3,] 0.22866680 0.20960803 0.6547071 -0.14994333
[4,] 0.02504275 -0.14751476 -0.1499433 0.27702915
[1] "*******************************************************"
[1] "MANOVA results"
Df
Wilks approx F num Df den Df Pr(>F)
Data$X1
1 0.75969 0.91733
10
29 0.531
Residuals 38
[1] "*******************************************************"
[1] "ANOVA for covariance #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.09794 0.097940 1.2074 0.2788
Residuals
38 3.08246 0.081117
[1] "ANOVA for covariance #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.1307 0.13067 1.1213 0.2963
Residuals
38 4.4283 0.11653
[1] "ANOVA for covariance #" "4"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.5452 0.54521 2.8573 0.09915 .
Residuals
38 7.2509 0.19081
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "5"
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
[1] "ANOVA for
Df
Data$X1
1
Residuals
38
Sum Sq Mean Sq F value Pr(>F)
0.0415 0.041504 0.8061 0.3749
1.9564 0.051484
covariance #" "6"
Sum Sq Mean Sq F value Pr(>F)
0.7346 0.73463 2.5639 0.1176
10.8883 0.28653
covariance #" "7"
Sum Sq Mean Sq F value Pr(>F)
0.1815 0.18153 0.5517 0.4622
12.5036 0.32904
covariance #" "8"
Sum Sq Mean Sq F value Pr(>F)
0.0013 0.00134 0.0067 0.9351
7.5766 0.19938
covariance #" "9"
Sum Sq Mean Sq F value Pr(>F)
0.2002 0.20025
0.348 0.5587
21.8651 0.57540
covariance #" "10"
Sum Sq Mean Sq F value Pr(>F)
0.3251 0.32507 1.2743 0.266
9.6935 0.25509
covariance #" "11"
Sum Sq Mean Sq F value Pr(>F)
0.0422 0.042237
0.171 0.6815
9.3848 0.246967
Jackknife-Eigenvalues
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"jackknife of Eigenvalues"
"**********************************************"
"POP ID =" "10"
"Observed eigenvalues"
0.525623599 0.403648088 0.063526683 -0.003038066 0.989760304
"Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.3707878 0.5347189 0.0670519 0.01935681 0.9919153
[1] 0.08906047 0.16166823 0.06904706 0.03066624 0.17242412
[1] "T test: Probability that eigenvalue =< 0"
[1] 2.638381e-04 1.851098e-03 1.718488e-01 2.677121e-01 7.616854e-06
[1] "**********************************************"
[1] "POP ID =" "11"
[1] "Observed eigenvalues"
[1] 0.89900766 0.31949878 0.19964307 0.01440099 1.43255049
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.8218442 0.2723921 0.2895875 0.05461423 1.438438
[1] 0.26923570 0.13051438 0.10193726 0.04080051 0.32240657
[1] "T test: Probability that eigenvalue =< 0"
[1] 0.0032761671 0.0252961859 0.0052247588 0.0982547945 0.0001337696
[1] "MANOVA RESULTS"
Df
Wilks approx F num Df den Df Pr(>F)
X6
1 0.79779
2.2178
4
35 0.08709 .
Residuals 38
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "*************************************************"
[1] "ANOVAs Last ANOVA is for eigen sum"
[1] "ANOVA for eigen #" "1"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 2.0345 2.0345 2.5299
0.12
Residuals
38 30.5595 0.8042
[1] "ANOVA for eigen #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.6882 0.68815
1.594 0.2144
Residuals
38 16.4048 0.43171
[1] "ANOVA for eigen #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
Residuals
38
--Signif. codes:
[1] "ANOVA for
Df
X6
1
Residuals
38
[1] "ANOVA for
Df
X6
1
Residuals
38
0.4952 0.49522
5.7603 0.15159
3.2669 0.07861 .
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
eigen #" "4"
Sum Sq Mean Sq F value Pr(>F)
0.01243 0.012431 0.4772 0.4939
0.98994 0.026051
eigen #" "5"
Sum Sq Mean Sq F value Pr(>F)
1.994 1.9938 1.4915 0.2295
50.797 1.3368
>
Offspring on Parent analyses
Selection Skewers
1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Results of Selection Skewers Test"
[1] "Nos of randomizations (includes observed)"
[1] 200
[1] "Nos of skewers per cycle=" "500"
[1] "Obs skewer
Prob"
[1] 0.868 0.530
Mantel Test
[1]
[1]
[1]
[1]
[2]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Results for modified Mantel Test"
"Nos of randomizations[includes observed] ="
"200"
"Obs M, Prob obs M > Null"
0.7251841 0.2300000
Hierarchical Test
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Determinant=0" "2"
"Determinant=0" "5"
"Determinant=0" "3"
"Determinant=0" "2"
"Determinant=0" "2"
"Determinant=0" "3"
"Determinant=0" "2"
"Determinant=0" "2"
"Determinant=0" "4"
"Determinant=0" "2"
"Determinant=0" "8"
"Determinant=0" "4"
"Determinant=0" "2"
"Determinant=0" "3"
"Determinant=0" "3"
"Determinant=0" "2"
"Determinant=0" "3"
"Determinant=0" "2"
"Determinant=0" "2"
"Determinant=0" "2"
"Determinant=0" "3"
"Determinant=0" "4"
"Determinant=0" "5"
"Determinant=0" "5"
"Determinant=0" "5"
"Determinant=0" "2"
"Determinant=0" "2"
"Determinant=0" "3"
"*************************************************************************"
[1] "Probabilities are calculated using the jump up approach"
[1] "Thus the probability is calculated relative to unrelated structure"
[1] "Cases in which the determinant could not be calculated are dropped from the
calculations"
[1] "The warnings refer to these cases and can be ignored"
[1] "The total number of randomizations and the number actually used (N.actual) are
reported"
[1] "*************************************************************************"
[1] "Results of randomization"
[1] "Number of randomizations (includes observed)"
[1] 200
[1] "Comparing Equal with unrelated"
[1] "N.actual
Prob "
[1] 62 1
[1] "Comparing Proportional with unrelated"
[1] "N.actual
Prob "
[1] 68 1
[1] "Comparing CPC with unrelated"
[1] "N.actual
Prob "
[1] 112.0000
0.8125
There were 50 or more warnings (use warnings() to see the first 50)
Bartlett’s test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Negative eigenvalue in given matrix"
Warning message:
In log(Det3) : NaNs produced
Note: not possible for this data set
Jackknife-MANOVA
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"****************************************************************"
"The pseudovalues are returned using the upper portion of the whole matrix"
"For example with 4 traits as in the test data the output is"
"Col 1 = Population code"
"Columns numbers for (co)variances are"
"Trait = X1 X2 X3 X4"
"X1
2
3 4 5"
"X2
6 7 8"
"X3
9 10"
"X4
11"
"****************************************************************"
"Results from Jackknife analysis"
"Population ID = " "1"
"Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.14266462 0.05830503 0.08923111 -0.19652021
[2,] 0.05830503 0.02212979 0.03644759 -0.02043572
[3,] 0.08923111 0.03644759 0.04629830 -0.12574850
[4,] -0.19652021 -0.02043572 -0.12574850 0.11365441
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.14266462 0.05830503 0.08923111 -0.19652021
[2,] 0.05830503 0.02212979 0.03644759 -0.02043572
[3,] 0.08923111 0.03644759 0.04629830 -0.12574850
[4,] -0.19652021 -0.02043572 -0.12574850 0.11365441
[1] "Population ID = " "2"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.17217652 0.04733500 0.10180438 -0.01382989
[2,] 0.04733500 0.01534382 0.02574752 -0.01890267
[3,] 0.10180438 0.02574752 0.06173126 -0.01518231
[4,] -0.01382989 -0.01890267 -0.01518231 0.02159135
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.17217652 0.04733500 0.10180438 -0.01382989
[2,] 0.04733500 0.01534382 0.02574752 -0.01890267
[3,] 0.10180438 0.02574752 0.06173126 -0.01518231
[4,] -0.01382989 -0.01890267 -0.01518231 0.02159135
[1] "*******************************************************"
[1] "MANOVA results"
Df
Wilks approx F num Df den Df Pr(>F)
Data$X1
1 0.88923
1.1087
10
89 0.3647
Residuals 98
[1] "*******************************************************"
[1] "ANOVA for covariance #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.0218 0.021774 0.0738 0.7864
Residuals
98 28.9016 0.294914
[1] "ANOVA for covariance #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.0030 0.003009 0.0887 0.7664
Residuals
98 3.3223 0.033901
[1] "ANOVA for covariance #" "4"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.0040 0.003952 0.0451 0.8323
Residuals
98 8.5889 0.087642
[1] "ANOVA for covariance #" "5"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.834 0.83439 2.4729 0.119
Residuals
98 33.067 0.33741
[1] "ANOVA for covariance #" "6"
Df Sum Sq
Mean Sq F value Pr(>F)
Data$X1
1 0.00115 0.0011512 0.2651 0.6078
Residuals
98 0.42560 0.0043429
[1] "ANOVA for covariance #" "7"
Df Sum Sq
Mean Sq F value Pr(>F)
Data$X1
1 0.00286 0.0028623 0.2705 0.6042
Residuals
98 1.03695 0.0105812
[1] "ANOVA for covariance #" "8"
Df Sum Sq
Mean Sq F value Pr(>F)
Data$X1
1 0.00006 0.0000588
0.002 0.9642
Residuals
98 2.84858 0.0290671
[1] "ANOVA for covariance #" "9"
Df Sum Sq
Mean Sq F value Pr(>F)
Data$X1
1 0.00595 0.0059544 0.1906 0.6633
Residuals
98 3.06093 0.0312340
[1] "ANOVA for covariance #" "10"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.3056 0.30562 2.8583 0.09408 .
Residuals
98 10.4785 0.10692
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "11"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.212 0.21189 0.5406 0.464
Residuals
98 38.415 0.39198
Jackknife-Eigenvalues
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"jackknife of Eigenvalues"
"**********************************************"
"POP ID =" "1"
"Observed eigenvalues"
0.403038019 0.018646856 -0.006640981 -0.090296772 0.324747122
"Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.3943244 0.0069568 -0.006870999 -0.06966307 0.3247471
[1] 0.17954492 0.01972606 0.00526349 0.08606252 0.17754540
[1] "T test: Probability that eigenvalue =< 0"
[1] 0.01641852 0.36292402 0.90107472 0.78891434 0.03673720
[1] "**********************************************"
[1] "POP ID =" "2"
[1] "Observed eigenvalues"
[1] 0.247812175 0.027732956 0.003106424 -0.007808613 0.270842943
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.2296914 0.02378479 0.006695276 0.01067145 0.2708429
[1] 0.121134396 0.040870587 0.003553978 0.015750063 0.140337546
[1] "T test: Probability that eigenvalue =< 0"
[1] 0.03192099 0.28163298 0.03276079 0.25062205 0.02970692
[1] "MANOVA RESULTS"
Df
Wilks approx F num Df den Df Pr(>F)
X6
1 0.93348
1.6923
4
95 0.1582
Residuals 98
[1] "*************************************************"
[1] "ANOVAs Last ANOVA is for eigen sum"
[1] "ANOVA for eigen #" "1"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
0.678 0.6776 0.5778 0.449
Residuals
98 114.929 1.1727
[1] "ANOVA for eigen #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.0071 0.007080 0.1375 0.7116
Residuals
98 5.0458 0.051488
[1] "ANOVA for eigen #" "3"
Df
Sum Sq
Mean Sq F value Pr(>F)
X6
1 0.004601 0.0046011 4.5629 0.03516 *
Residuals
98 0.098821 0.0010084
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for eigen #" "4"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.1613 0.16134 0.8431 0.3608
Residuals
98 18.7543 0.19137
[1] "ANOVA for eigen #" "5"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1
0.073 0.07264 0.0567 0.8122
Residuals
98 125.482 1.28042
>
Clonal Analyses STAT= 3or 5
Selection Skewers
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Results of Selection Skewers Test"
"Nos of randomizations (includes observed)"
200
"Nos of skewers per cycle=" "500"
"Obs skewer
Prob"
0.8289512 0.5950000
Mantel test
[1]
[1]
[1]
[1]
[2]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Results for modified Mantel Test"
"Nos of randomizations[includes observed] ="
"200"
"Obs M, Prob obs M > Null"
0.8258491 0.5000000
Hierarchical tests
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
"*****************************************************"
"TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
"Determinant=0" "5"
"Determinant=0" "8"
"Determinant=0" "10"
"Determinant=0" "5"
"Determinant=0" "8"
"Determinant=0" "7"
"*************************************************************************"
"Probabilities are calculated using the jump up approach"
[1] "Thus the probability is calculated relative to unrelated structure"
[1] "Cases in which the determinant could not be calculated are dropped from the
calculations"
[1] "The warnings refer to these cases and can be ignored"
[1] "The total number of randomizations and the number actually used (N.actual) are reported"
[1] "*************************************************************************"
[1] "Results of randomization"
[1] "Number of randomizations (includes observed)"
[1] 200
[1] "Comparing Equal with unrelated"
[1] "N.actual
Prob "
[1] 98 1
[1] "Comparing Proportional with unrelated"
[1] "N.actual
Prob "
[1] 99 1
[1] "Comparing CPC with unrelated"
[1] "N.actual
Prob "
[1] 120
1
There were 50 or more warnings (use warnings() to see the first 50)
Bartlett’s Test
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "Negative eigenvalue in given matrix"
Warning message:
In log(Det2) : NaNs produced
Note: Not possible for this data set
Jackknife-MANOVA
[1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "****************************************************************"
[1] "The pseudovalues are returned using the upper portion of the whole matrix"
[1] "For example with 4 traits as in the test data the output is"
[1] "Col 1 = Population code"
[1] "Columns numbers for (co)variances are"
[1] "Trait = X1 X2 X3 X4"
[1] "X1
2
3 4 5"
[1] "X2
6 7 8"
[1] "X3
9 10"
[1] "X4
11"
[1] "****************************************************************"
[1] "Results from Jackknife analysis"
[1] "Population ID = " "10"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.017030360 -0.01029933 -0.002665397 -0.01931116
[2,] -0.010299325 0.05158947 0.036749093 -0.06753705
[3,] -0.002665397 0.03674909 0.255964742 0.01655995
[4,] -0.019311164 -0.06753705 0.016559951 0.17029558
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.016967736 -0.01080310 -0.002415702 -0.01969042
[2,] -0.010803095 0.05138082 0.037437876 -0.06796930
[3,] -0.002415702 0.03743788 0.256599537 0.01517636
[4,] -0.019690420 -0.06796930 0.015176364 0.17100958
[1] "Population ID = " "11"
[1] "Observed matrix"
[,1]
[,2]
[,3]
[,4]
[1,] 0.06700898 0.04813679 0.1132394 0.01263633
[2,] 0.04813679 0.18558975 0.1041483 -0.07189714
[3,] 0.11323939 0.10414834 0.3252356 -0.07443040
[4,] 0.01263633 -0.07189714 -0.0744304 0.13844089
[1] "Jackknife estimate"
[,1]
[,2]
[,3]
[,4]
[1,] 0.06644995 0.04635121 0.11433340 0.01252137
[2,] 0.04635121 0.18690097 0.10480402 -0.07375738
[3,] 0.11433340 0.10480402 0.32735354 -0.07497167
[4,] 0.01252137 -0.07375738 -0.07497167 0.13851457
[1] "*******************************************************"
[1] "MANOVA results"
Df
Wilks approx F num Df den Df Pr(>F)
Data$X1
1 0.75969 0.91733
10
29 0.531
Residuals 38
[1] "*******************************************************"
[1] "ANOVA for covariance #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.02448 0.024485 1.2074 0.2788
Residuals
38 0.77061 0.020279
[1] "ANOVA for covariance #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.03267 0.032666 1.1213 0.2963
Residuals
38 1.10708 0.029134
[1] "ANOVA for covariance #" "4"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.1363 0.136304 2.8573 0.09915 .
Residuals
38 1.8127 0.047703
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for covariance #" "5"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.01038 0.010376 0.8061 0.3749
Residuals
38 0.48910 0.012871
[1] "ANOVA for covariance #" "6"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.18366 0.183657 2.5639 0.1176
Residuals
38 2.72207 0.071633
[1] "ANOVA for covariance #" "7"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.04538 0.045382 0.5517 0.4622
Residuals
38 3.12590 0.082261
[1] "ANOVA for covariance #" "8"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.00034 0.000335 0.0067 0.9351
Residuals
38 1.89414 0.049846
[1] "ANOVA for covariance #" "9"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.0501 0.050061
0.348 0.5587
Residuals
38 5.4663 0.143850
[1] "ANOVA for covariance #" "10"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.08127 0.081267 1.2743 0.266
Residuals
38 2.42337 0.063773
[1] "ANOVA for covariance #" "11"
Df Sum Sq Mean Sq F value Pr(>F)
Data$X1
1 0.01056 0.010559
0.171 0.6815
Residuals
38 2.34619 0.061742
Jackknife-Eigenvalues
1] "*****************************************************"
[1] "TRAIT MEANS ARE STANDARDIZED BY SUBTRACTING POP MEANS"
[1] "jackknife of Eigenvalues"
[1] "**********************************************"
[1] "POP ID =" "10"
[1] "Observed eigenvalues"
[1] 0.262811800 0.201824044 0.031763341 -0.001519033 0.494880152
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.1853939 0.2673594 0.03352595 0.009678407 0.4959577
[1] 0.04453024 0.08083411 0.03452353 0.01533312 0.08621206
[1] "T test: Probability that eigenvalue =< 0"
[1] 2.638381e-04 1.851098e-03 1.718488e-01 2.677121e-01 7.616854e-06
[1] "**********************************************"
[1] "POP ID =" "11"
[1] "Observed eigenvalues"
[1] 0.449503828 0.159749388 0.099821535 0.007200494 0.716275245
[1] "Jackknife Eigenvalues SEs below"
[,1]
[,2]
[,3]
[,4]
[,5]
[1,] 0.4109221 0.1361961 0.1447938 0.02730712 0.719219
[1] 0.13461785 0.06525719 0.05096863 0.02040025 0.16120328
[1] "T test: Probability that eigenvalue =< 0"
[1] 0.0032761671 0.0252961859 0.0052247588 0.0982547945 0.0001337696
[1] "MANOVA RESULTS"
Df
Wilks approx F num Df den Df Pr(>F)
X6
1 0.79779
2.2178
4
35 0.08709 .
Residuals 38
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "*************************************************"
[1] "ANOVAs Last ANOVA is for eigen sum"
[1] "ANOVA for eigen #" "1"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.5086 0.50863 2.5299
0.12
Residuals
38 7.6399 0.20105
[1] "ANOVA for eigen #" "2"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.1720 0.17204
1.594 0.2144
Residuals
38 4.1012 0.10793
[1] "ANOVA for eigen #" "3"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.12381 0.123805 3.2669 0.07861 .
Residuals
38 1.44008 0.037897
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "ANOVA for eigen #" "4"
Df
Sum Sq
Mean Sq F value Pr(>F)
X6
1 0.003108 0.0031077 0.4772 0.4939
Residuals
38 0.247484 0.0065127
[1] "ANOVA for eigen #" "5"
Df Sum Sq Mean Sq F value Pr(>F)
X6
1 0.4985 0.49846 1.4915 0.2295
Residuals
38 12.6992 0.33419