Statistics for the Australian Grains Industry
A one-stage mixed model analysis of Australia’s
National Variety Trial data
Bev Gogel1
2
Alison Smith
1
University of Adelaide, Australia
University of Wollongong, Australia
2
Brian Cullis
2
[email protected]
[email protected], [email protected]
Australasian Applied Statistics Conference, Bermagui, Nov 27 - Dec 2, 2016
A one-stage mixed model analysis of Australia’s National Variety Trial data
Acknowledgments ...
Brian Cullis & Alison Smith
Ky Matthews & Daniel Tolhurst
Robin Thompson
Grains Research and Development Corporation
A one-stage mixed model analysis of Australia’s National Variety Trial data
Outline ...
A one-stage mixed model analysis of Australia’s
National Variety Trial data
•
the NVT system ...
•
a gold standard one-stage analysis of MET data ...
•
the two-stage analysis used for NVT data until very recently ...
•
compare one-stage vs two-stage analyses for an NVT wheat MET data set ...
•
summary ...
A one-stage mixed model analysis of Australia’s National Variety Trial data
NVT system ...
•
crop variety testing programs are conducted around the world
•
in Australia
have the
National Variety Trials (NVT) system
–
jointly funded by Australian Government & Australian grain growers through the GRDC
–
managed by Australian Crop Accreditation System (ACAS) Limited
•
current commercial and near to release varieties are independently evaluated
•
over 600 trials conducted each year spanning the 10 crops
–
•
wheat, barley, canola, chick peas, faba beans, field peas, lentils, lupins, oats, triticale
aim to
... provide growers with information to help them to choose the best
varieties for their particular set of growing conditions ...
A one-stage mixed model analysis of Australia’s National Variety Trial data
NVT system ...
•
each year the data for a given crop
–
combined with the last 4 years of data
–
big across-years multi-environment trial (MET) data set
2011-15 Southern Region Wheat MET data set
–
–
–
–
–
•
188 varieties
192 trials/experiments
4 states: SA, VIC, NSW, Qld
5 years: 2011 - 2015
27741 data records
our job is to
–
get the best (most accurate and precise) predictions of the genetic values (the genetic
effects) for each trial by appropriately modelling genotype by environment interaction
(g × e)
A one-stage mixed model analysis of Australia’s National Variety Trial data
MET analysis ...
•
some pretty powerful modelling technology now being used for the analysis of MET data
sets in most major breeding companies in Australia
•
factor analytic (FA) approach of
Smith, A. B., Cullis, B. R. and Thompson, R. (2001) Analyzing variety by environment
data using multiplicative mixed models and adjustments for spatial field trend. Biometrics
57: 1138-1147
•
has been shown to be particularly effective in explaining the g × e in plant breeding MET
data sets: great tools for interpretation
A one-stage mixed model analysis of Australia’s National Variety Trial data
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MET analysis using the FA approach ...
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site 2
...
•
the data from individual trials is combined for analysis
•
the linear mixed model includes
–
–
–
site p
different mean levels for each each trial
random blocking terms to reflect the randomisation process for each trial ...col reps, row reps,...
extra terms that were not designed for but give a better fit of the data for each trial
...linear covariates,...
–
•
smooth trend effects for spatial variation across each trial
we use a factor analytic (FA) model to model g × e
A one-stage mixed model analysis of Australia’s National Variety Trial data
MET analysis: the g × e interaction effects ...
•
the number of g × e interaction effects in MET analysis typically large
–
especially for NVT data 72380 for wheat MET data set ...
•
u = full set of g × e interaction effects and G = var (u)
•
rather than model this structure outright we instead assume a separable variance
structure, that is, we assume that G is the product of
a genetic variance structure for environments Ge
•
a genetic variance structure for genotypes Gv
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1
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0
0
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0.5
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⊗
0
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1
2
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6
of dimension number of environments
of dimension number of genotypes
site
genetic effect
1
site
resiudal error
•
of dimension number of environments × number of genotypes
1
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genetic effect
residual error
G
•
=
Ge
⊗
we make an assumption about Gv and we model Ge
A one-stage mixed model analysis of Australia’s National Variety Trial data
Gv
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=
–
A one-stage mixed model analysis of Australia’s National Variety Trial data
0
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=
⊗
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0
0
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0
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5
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1
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3
4
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site
site
independent
IID
1
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genetic variance
heterogeneity
0
0
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18
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0.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
=
common
covariance
1
0.5
1.9
2.7
2.4
2.3
1
2
1.9
1.21
1.6
2.8
1.7
1.3
3
2.7
1.6
0.76
1.1
3
2.9
4
2.4
2.8
1.1
0.23
1.2
2.2
5
2.3
1.7
3
1.2
1.72
1.4
6
1
1.3
2.9
2.2
1.4
0.98
1
2
3
4
5
6
⊗
site
1.21
1.6
2.7
1.6
0.76
1.1
4
2.4
2.8
2.7
1.1
0.23
2.4
2.3
1
2.8
1.7
1.3
3
2.9
1.2
2.2
5
2.3
1.7
3
1.2
1.72
1.4
6
1
1.3
2.9
2.2
1.4
0.98
1
2
3
4
5
6
fully
unstructured
1
0.83
0
2
0
0.83
0
3
0
0
0.83
0
4
0
0
0
0.83
0
5
0
0
0
0
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0
6
0
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0
0
0
0.83
5
6
7
8
9
10
11
12
13
14
15
0
0
0
0
0
0
residual error
=
1.9
1.9
3
site
genetic effect
G
0.5
2
site
genetic effect
site
1
site
0
0
site
0.5
2
site
1
site
different genetic variances across trials
different genetic covariance between
pairs of trials
0
0.5
0
residual error
we want to fit a fully unstructured form ...
–
0
0
3
genetic effect
resiudal error
•
of the possible variance structures for
environments Ge ...
0.5
2
site
G
•
1
site
typically assume that the varieties are
independent and identically
distributed: Gv = IID ...
resiudal error
•
1
genetic effect
MET analysis: the g × e interaction effects ...
Ge
⊗
Gv
0
0
0
0
0
0
MET analysis: the g × e interaction effects...
0.5
0
2
0
0.5
0
3
0
0
0.5
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
7
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
1
11
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0.5
0
0
0
0
0
0
0
0
0
0
0
=
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1.9
1.9
1.21
2.7
2.4
1.6
2.8
2.3
1.7
1
1.3
3
2.7
1.6
0.76
1.1
3
2.9
4
2.4
2.8
1.1
0.23
1.2
2.2
site
resiudal error
2
0.5
5
6
2.3
1.7
3
1
1.3
2.9
1
2
3
1.2
1.72
⊗
1.4
2.2
1.4
0.98
4
5
6
site
genetic effect
1
1
0.83
0
2
0
0.83
0
3
0
0
0.83
0
4
0
0
0
0.83
5
0
0
0
0
0
0
6
0
0
0
0
0
7
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0.83
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0.83
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0.83
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0.83
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0.83
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.83
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
0
0
genetic effect
residual error
G
=
Ge
⊗
Gv
•
but this is difficult to achieve for even small MET dat sets let alone big data sets...
•
where the FA approach kicks in ...
A one-stage mixed model analysis of Australia’s National Variety Trial data
the FA model: quick tour ...
•
specifies a multiple regression form for the genetic effects for each variety
ui
–
–
•
=
f1i λ1 + f2i λ2 + . . . + fki λk + δ i
the λ’s are sets of environmental covariates/loadings
the f ’s are corresponding slope coefficients
the full set of effects is then of this form
in order vars in environments
(Λ ⊗ I m )f + δ
Λ is the matrix of loadings λ1 λ2 . . . λk
f is the full vector of slope coefficients
δ is the set of genetic regression residuals
u =
–
–
–
•
the genetic variance structure for environments is then of the form
Ge
–
=
ΛΛ0 + Ψ
Ψ is a matrix of specific variances that account for variation that is not accounted for
by the multiple regression
A one-stage mixed model analysis of Australia’s National Variety Trial data
the FA model ...
=
0.5
1.9
2.7
2.4
2.3
1
2
1.9
1.21
1.6
2.8
1.7
1.3
3
2.7
1.6
0.76
1.1
3
2.9
4
2.4
2.8
1.1
0.23
1.2
5
2.3
1.7
3
1.2
1.72
1.4
6
1
1.3
2.9
2.2
1.4
0.98
1
2
3
4
5
6
site
Ge = ΛΛ0 + Ψ
1
site
•
which is an unstructured variance structure
•
using far less parameters
–
•
avoids technical difficulties in fitting a US structure outright
able to fit the US form we are after for Ge
A one-stage mixed model analysis of Australia’s National Variety Trial data
2.2
FA analysis outputs ...
The key outputs for an FA analysis are
Booleroo Centre
Axe
Magenta
Wallup
Scout
Wyalkatchem
Variety
Mace
0.6
●
●
0.4
the predicted g × e interaction effects
predicted genetic value (t/ha)
•
●
●
0.2
●
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0.0
●
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−0.2
•
the estimated genetic variance matrix for environments G̃e
−→ the estimated genetic correlation matrix for environments C̃ e
2011
1.84
2012
1.61
2013
2.93
2014
3.62
2015
2.68
year and tmy (t/ha)
estimated genetic corr 2011−15: 1−stage
1.0
•
a heatmap representation of C̃ e
0.5
Experiment
•
0.0
−0.5
set of latent regression plots which allow us to
−1.0
Experiment
–
drill down to the factors driving the genetic variation in the
data
Axe
Predicted genetic value adjusted for first and second factors
investigate the responsiveness of the individual genotypes with
reference to these factors
Magenta
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most major plant breeding programs in Australia have embraced
all this ...¡
A one-stage mixed model analysis of Australia’s National Variety Trial data
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estimated loading for third factor
great set of interpretive tools
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•
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−0.2
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0.2
sm
oo
tre th
nd
ex
tra
n
ra eou
nd s
om
sm
oo
tre th
nd
nd
o
ro m
w
ex
tra
n
ra eou
nd s
om
ra
tra
ne
fix ous
ed
ra
nd
blo om
ck
ra
nd
blo om
ck
ra
nd
o
ro m
w
nd
o
ro m
w
ra
1
0.5
0.68
0.68
2
0.68
1.2
0.68
3
0.68
0.68
0.76
4
0.68
0.68
0.68
5
0.68
0.68
0.68
6
0.68
0.68
0.68
1
2
3
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.68
0.2
e
no
ot
yp
ov
er
m al
ea
n
ge
ge
n
se
ov
er
m al
ea
n
on
se
re
sp
on
re
sp
sp
re
a simple variance component model is
assumed for the g × e interaction effects
G =
weight g1
weight g1
weight g1
weight g2
weight g2
weight g2
site
•
ty
p
e
e
no
ty
p
on
se
individual trial means
ov
er
m al
ea
n
ge
– weights a measure of uncertainty of the
ex
combined in a weighted across site mixed
model analysis in Stage 2
ra
nd
blo om
ck
•
tra
ne
fix ous
ed
predicted variety means from the analysis
of single trials in Stage 1
ex
•
sm
oo
tre th
nd
two-stage approach for NVT data ...
why then ... until very recently ... has a two-stage approach
0.68
0.68
0.68
1.7
0.68
0.68
0.68
0.9
4
5
6
site
– when VC analysis known to be inadequate
•
means are reported on a regional level
– when averaging to form regional means known
to average over g × e rather than explain it
weight g3
weight g3
weight g4
weight g4
weight g4
weight g5
weight g5
weight g5
weight g6
weight g6
weight g7
weight g7
weight g8
weight g8
site 1
site 2
weight g8
...
site p
...been used for the NVT?
A one-stage mixed model analysis of Australia’s National Variety Trial data
two-stage approach for NVT data ...
some good reasons ...
•
two-stage approach a legacy of earlier times
–
–
•
storage of individual plot data was difficult
computing power was less
so it was a necessity
but progress has also been hampered by
•
strict protocols and uncertainty from stakeholders expressed as resistance to change/
skepticism
•
any progress has been in small steps with lots of justification/education/convincing
so
A one-stage mixed model analysis of Australia’s National Variety Trial data
sm
oo
tre th
nd
ex
tra
n
ra eou
nd s
om
sm
oo
tre th
nd
–
–
•
still used a two-stage framework
long term regional means still
presented to growers
was a HUGE step forward ...
nd
o
ro m
w
ra
ra
nd
blo om
ck
e
ex
no
ty
p
e
ot
yp
se
on
sp
re
re
re
sp
sp
on
on
s
e
se
ov
er
m al
ea
n
ge
ge
n
an FA model for the g × e effects in the
Stage 2 analysis
ov
er
m al
ea
n
•
ty
p
the FA approach was used for the NVT
for the first time
no
•
ge
in 2014 efforts finally paid off
ov
er
m al
ea
n
•
e
ex
tra
ne
fix ous
ed
tra
ne
fix ous
ed
ra
nd
blo om
ck
ra
nd
blo om
ck
ra
ra
nd
o
ro m
w
nd
o
ro m
w
ex
tra
n
ra eou
nd s
om
sm
oo
tre th
nd
two-stage approach for NVT data ...
weight g1
weight g1
weight g1
weight g2
weight g2
weight g2
weight g3
weight g3
weight g4
weight g4
weight g4
weight g5
weight g5
weight g5
weight g6
weight g6
weight g7
weight g7
weight g8
weight g8
site 1
site 2
weight g8
...
u = (Λ ⊗ I m )f + δ
Ge = ΛΛ0 + Ψ
A one-stage mixed model analysis of Australia’s National Variety Trial data
site p
two-stage approach for NVT data ...
the big achievement in 2015 greater uptake of the
production value (PV)-PLUS plots
–
plot the predicted genetic values
across a selection of environments
clearly reflect
–
the relative performance of varieties across
environments
– varietal stability across environments
is exactly information the growers are after
–
–
Booleroo Centre
Axe
Magenta
Wallup
Mace
Scout
Wyalkatchem
Variety
0.6
●
●
0.4
–
●
predicted genetic value (t/ha)
•
●
0.2
●
●
●
●
●
●
0.0
●
●
●
●
●
●
●
●
●
●
●
●
●
●
−0.2
2011
1.84
2012
1.61
2013
2.93
●
2014
3.62
year and tmy (t/ha)
•
achieved by
–
–
SAGI presenting at field days/written articles/other general promotion of the tools
Smith et al. (2015), upcoming article in the Ground Cover Supplement
A one-stage mixed model analysis of Australia’s National Variety Trial data
●
●
2015
2.68
one-stage FA analysis of NVT data ...
and now in 2016 ...
•
having established the technology
•
with industry acceptance
–
moving to a gold standard one-stage FA analysis for in the NVT for ALL crops
A one-stage mixed model analysis of Australia’s National Variety Trial data
how do one and two-stage FA analyses compare ...
•
have conducted both one and two-stage
analyses of the 2011-15 southern region wheat
MET data set
–
–
–
–
–
•
188 varieties
192 trials/experiments
4 states: SA, VIC, NSW, Qld
5 years: 2011 - 15
27741 data records... 8883 g × e means in
two-stage MET data set
Year
2011
2012
2013
2014
2015
2011
2012
2013
2014
2015
76
40
31
28
28
40
82
43
34
33
31
43
70
43
39
28
34
43
58
44
28
33
39
44
77
•
58 - 82 in a year
•
28 - 44 in common between years
•
reasonably imbalanced
•
typical of MET data sets
•
worse for others
FA model with 5 factors for g × e
A one-stage mixed model analysis of Australia’s National Variety Trial data
predicted genetic values: one vs two stage ...
genetic values 1 vs 2 stage: 2014
WMaA14BIRC3
0.4
•
predicted genetic values 1 stage
vs 2 stage
0.2
0.0
−0.2
WMaA14BOOL5
●
●
●
●● ● ●
● ●● ● ●
●
●●
●
●●● ●●●
●●●
● ●
0.25
0.00
−0.25
−0.75
−0.2
0.0
•
0.0
just 2014 (similar other years)
−0.4
●
●
0.5
0.0
●
−0.5
−1.0
−0.4
0.0
0.4
●
●●
●
●●●
●●●●
●
●
●●
●
●●●
●●●
●
●●
●●
0.25
0.00
−0.25
−0.50
●
●
●●●
●●●●●
●●
●
●●
●
●●●
● ●●●
●●
0.00
●
reasonably good agreement
although some movement some sites
genetic values: 1 stage
•
WMaA14MURR3
0.2
0.1
0.0
−0.1
−0.2
0.00
●
0.0
0.25
0.0
−0.3
●●
●
−0.4 −0.2 0.0 0.2 0.4
0.00
●●
−0.50
−0.75
●
●
●
0.0
−1.0
0.3
−0.4 −0.2 0.0
0.2
0.4
0.0
−0.2
−0.6
0.25
●
●
●
●
●●
●●●●
●●
●
●
●●●
●●
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●
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−0.4 −0.2 0.0 0.2
●●
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0.5
genetic values: 2 stage
A one-stage mixed model analysis of Australia’s National Variety Trial data
0.2
●
●
●
●●●
●
●●●●●●
●●
●●●●
●● ●
●
0.10
0.05
0.00
−0.05
●
●
0.0
0.0
●
−0.2−0.10.0 0.1 0.2 0.3
−0.2
0.0
0.0
●
−0.2
0.0
0.0
−0.4
●
●
−0.4 −0.2 0.0 0.2
WMaA14WARR5
0.00
−0.25
●
−0.50
●
WMaA14WOKU5
●
0.8
0.4
0.0
−0.4
●
●
−0.4
0.0
0.4
●●
●
●
●● ●●●
● ● ●●
●●●● ●
●
●●●
●
●
●●●
−0.2
●
●●●●
●●●●
●●●●
●●●●
●●
● ●●
●●
●●
●
0.2
WMaA14ULTI3
0.2
−0.5 0.0 0.5 1.0
0.25
0.2
●
● ● ●●
●
●● ●
● ●
●●
●
●● ●
●●●●
●●
●●
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0.2
0.1
●●
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●
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●●
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●
●●●●
●●
●●
●
●
●
●●●
●●
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●
●
0.50
●
●
● ●
−0.2
●
−0.5
0.4
●
●●
●
●● ● ● ●
● ●●●
●
0.5
0.2
●●
● ●
●● ●
●● ●
●
● ●●
WMaA14TURR5
0.3
● ●●
●
●● ●
●●
●●
●
●●
●● ● ●
●
●●
● ●●
●
● ●
●●
●
●● ●
−0.2 0.0
0.3
0.2
0.1
0.0
−0.1
−0.2
−0.3
WMaA14PIED5
●
●● ●
●● ●
●● ● ●●
●
●
0.4
● ●
● ●●
●●
● ●●
●●●
●●●
● ●●
●
● ●●
●
●●●●
●●
●
●
●
●
WMaA14MITC5
●
●
●●
−0.3 0.0
0.3
0.2
0.1
0.0
−0.1
−0.2
●●
●●
●
●●●
●●●
● ●
●
● ●●
● ●
●
● ●●
●
●
●
● ●
●
WMaA14WANI5
●
0.2
●
0.4
●
●
−1.0 −0.5 0.0
0.0
−0.3
−0.4
●
−0.25 0.00
0.3
●
●
WMaA14MINT5
0.0
●●
●
●●
●
●●●●●
● ●● ●
●
●●●● ●●
●●
●●
●●
●
● ●
●
●
●
●●
● ●●●●
0.0
−0.2
●
WMaA14SPAL5
0.6
WMaA14WANB5
●
●
●●
●●
●●
● ●
● ● ●●
●
●● ● ● ●
●
●● ●
● ●
● ●
−0.2
●
●●
0.2
●
−0.2
●
●●
●●
●●●●
●●●●
●●●
●
●● ●●
●
●●● ●
●●●
●●
●●●
●●
−0.4 0.0
●●
●●●
● ●
●
●●
●●●●●● ●
●
●●
●●
●●
● ●
●● ●
●●
●●
WMaA14WALP3
0.0
−0.8
●
●●●
●●
●●
●
●●●
●
●●●
●
●
●●●
●
0.5
−0.5
●
−0.6 −0.3 0.0
●
0.2
−0.4
●
●
●
●●
●●
●●
0.4
−0.3−0.2−0.1 0.0 0.1 0.2
WMaA14PENO5
WMaA14SHER5
●
−0.2
−0.2 0.0 0.2 0.4
−0.50−0.250.000.250.50
0.1
0.0
−0.1
−0.2
−0.3
−0.1
0.4
WMaA14PASK5
0.0
●●
●●
●●
●●
0.00
●
−0.1 0.0 0.1 0.2 0.3
0.4
●
●●●
●
●
● ●●●
0.25
−1.0 −0.5 0.0 0.5 1.0
●
●
●
●●
●●
●
●
●
● ●●
●●●●
●
●●●
●
●
●
WMaA14WUNK5
●
● ●●
●●●
●●●
●●
●●
●
●●
●
●
●●
●●
●●
●●●
●●
−0.25
●
●
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●
●
●●
●●
●
●
●●
●●
●●
●●●
●●●
●●●
●●
●●●●
●●
−0.6 ●
−0.6 −0.3 0.0 0.3 0.6
WMaA14WOLS5
0.25
0.0
−1.0
WMaA14URAN5
0.3
●
● ●
●●●●
0.50
−0.25
●
●●●●
●●●
●
●●●
●●
●●●
● ●●
●●
●
●
●
●
●●●
●●
−0.5
−0.1 0.0 0.1 0.2
●
●●●
● ●●
●●●●
●
●
●●●
●● ●
●● ●
−0.2−0.10.0 0.1 0.2 0.3
0.5
0.25
WMaA14PALM5
−0.50
1.0
0.2
−0.2
0.00
0.1
0.0
WMaA14KANI3
●
●● ●
●●
●●●
●●
●●
●● ●
●●●●
●● ●
0.2
WMaA14MINN5
●
−0.25
0.2
0.4
0.0
WMaA14RUDA5
● ● ●
●
●●●
●
−0.2 0.0
● ●
0.2
●
●
●
WMaA14UNGA5
●●
●
●●
●●●
●
●●
●
−0.2
●
●●
● ●●●
●● ● ●
● ● ●
●● ●
● ●●●
0.1
−0.2
●
●●
●●
●●
●● ●
●●
●● ●
●
●●●
●●
●
0.0
●
●
●
0.2
−0.1
●
0.25
−0.25
reassuring that the predicted
genetic values for one and two
stage analyses where there is data
0.00
0.2
WMaA14QUAM3
●
0.00
•
0.25
0.0
−0.2
●
−0.50−0.250.00 0.25 0.50
● ●●
●●●●
●
●● ●●
●
●●●
●●
●●
●●●
●●
−0.25 0.00
range 0.77 - 0.99, mean = 0.96
0.2
●
0.25
−0.2 0.0
0.2
●
● ●●●●
●● ●
●●
●●
● ● ●● ●
● ●●
●●
0.2
WMaA14NUNJ5
●
●●
●
● ●●
●●●●
●●
●● ●
●●
●●●●●
WMaA14PINN5
−0.25
•
0.50
−0.50
0.0
●
●●
0.0
−0.4
●
−0.25
●
●
−0.2
−0.25
WMaA14NANG5
●
● ●
●●
● ●●● ●
● ●
●●●
●
●● ●
●
●
● ●●
● ●
●
0.0
−0.2
−0.2
WMaA14HOPE3
●
●●
●● ●
●● ●
●●●●
●●●
● ●●
●● ●
●
●●
●
●
0.2
WMaA14MERR3
●
●
● ●
●●
● ●●
●
● ●
●
●● ●
●●
● ●
● ●●
● ●
0.25
●
0.4
−0.4
0.5
WMaA14MANA3
−1.2 ●
−0.75 ●
−1.2 −0.8 −0.4 0.0 0.4
−0.6 −0.3 0.0 0.3 0.6
just varieties where there was
data
0.0
●
●●
0.50
WMaA14GERA5
●●
● ●
●●
●●
●●●● ●● ●
●●●
●
●●
●● ●●
● ●
● ●
0.2
−0.2
●
−1.0 −0.5 0.0
WMaA14KIMB5
−0.8
•
●
●
WMaA14CUMM5
●
●●
●
●●
●
●●
● ●
●
●●●●●●
●
●
●●
●
●●
●●●● ●
●●●
●●●
●
●
●
0.2
WMaA14KEIT5
0.4
WMaA14CONM5
●
●
●●
●●●●
●
●●●●
●● ●
●●
●●●
●●●
●●
●
●
●
●●●
−0.50
●
●●
0.50
● ●●
●
●●●●●●
●
●
● ● ●●●
●●●●● ●
●
●●
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●● ●●
●
● ●
●
−0.5
0.0
0.5
predicted genetic values: one vs two stage ...
genetic values 1 vs 2 stage: 2014
WMaA14BIRC3
0.5
0.0
•
predicted genetic values 1 stage
vs 2 stage
−0.5
−1.0
0.8
0.4
0.0
−0.4
●●
−1.0 −0.5 0.0 0.5
−1.0 −0.5 0.0
−0.5
−1.0
●
0.4
0.0
−0.4
●
●
−1.2 −0.8 −0.4 0.0 0.4
●●●●
●●●
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●
−1.0 −0.5 0.0
WMaA14MURR3
•
all varieties whether present or
not present at a site
spanner in the works
−0.5
−1.0
●
●
−0.5
−1.0
●
0.2
0.0
−0.2
0.5
●
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−1.0 −0.5
0.0
−1.0
−1.5
● ●
0.5
●
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0.0
−0.5
−1.0
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−0.6 −0.3 0.0 0.3
−0.3
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−1.0 −0.5 0.0 0.5
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−0.25
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0.0
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−0.4 −0.2 0.0
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−0.25
−0.8 −0.4 0.0 0.4 0.8
0.0
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●
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0
0
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0.0
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0.4
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−1.0−0.5 0.0 0.5 1.0
●
−0.4 −0.2 0.0 0.2
●
−0.5
0.0
−0.1
−0.2
0.5
0.3
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WMaA14WANI5
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WMaA14SPAL5
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genetic values: 2 stage
A one-stage mixed model analysis of Australia’s National Variety Trial data
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WMaA14RUDA5
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WMaA14WOLS5
−0.5
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WMaA14GERA5
0.6
WMaA14MANA3
−1.5 −1.0 −0.5 0.0 0.5
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WMaA14UNGA5
0.0
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concerning particularly where
other interpretive tools make use
of the full set of predictions
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range 0.05 - 0.98, mean = 0.85
−1.0
WMaA14QUAM3
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WMaA14PINN5
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WMaA14NANG5
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genetic values: 1 stage
•
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WMaA14CUMM5
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0.0
just 2014 (similar other years)
WMaA14CONM5
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WMaA14KEIT5
0.5
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WMaA14BOOL5
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−1.5 −1.0 −0.5 0.0 0.5
WMaA14WARR5
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−0.5
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0.0
0.5
WMaA14WOKU5
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1
PV-PLUS graphs ...
Booleroo Centre
Spalding
Axe
Magenta
Wallup
Mace
Scout
Wyalkatchem
Axe
Genotype
Magenta
Wallup
Scout
Wyalkatchem
Genotype
Mace
0.6
•
predicted genetic values
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predicted genetic value (t/ha)
6 varieties, 5 years
predicted genetic value (t/ha)
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2 SA sites: Booleroo Centre &
Spalding
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2011
1.84
2012
1.61
2013
2.93
2014
3.62
2015
2.68
2011
5.01
2012
2.53
2013
4.10
year and tmy (t/ha)
omitted predictions where variety
was not present
2014
3.85
2015
2.83
year and tmy (t/ha)
Booleroo Centre
Spalding
Axe
Magenta
Wallup
Mace
Scout
Wyalkatchem
Axe
Variety
Magenta
Wallup
Scout
Wyalkatchem
Variety
Mace
0.50
0.6
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•
reassuring
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good agreement
predicted genetic value (t/ha)
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2011
1.84
2012
1.61
2013
2.93
year and tmy (t/ha)
A one-stage mixed model analysis of Australia’s National Variety Trial data
●
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2014
3.62
−0.50
2015
2.68
2011
5.01
2012
2.53
2013
4.10
year and tmy (t/ha)
2014
3.85
2015
2.83
estimated genetic variance/correlation ...
estimated genetic corr 2011−15: 2−stage
estimated genetic corr 2011−15: 1−stage
1.0
1.0
0.5
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genetic var: 2 stage
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−1.0
genetic variance: 1 stage
Experiment
estimated genetic
variance
two vs one stage
estimated genetic
correlation matrix:
two-stage analysis
A one-stage mixed model analysis of Australia’s National Variety Trial data
−1.0
Experiment
estimated genetic
correlation matrix:
analysis
estimated genetic correlations 2014 sites: one vs two stage ...
WMaA14BIRC3
WMaA14BOOL5
WMaA14CONM5
WMaA14CUMM5
WMaA14GERA5
WMaA14HOPE3
WMaA14KANI3
WMaA14KEIT5
WMaA14KIMB5
WMaA14MANA3
WMaA14MERR3
WMaA14MINN5
WMaA14MINT5
WMaA14MITC5
WMaA14MURR3
WMaA14NANG5
WMaA14NUNJ5
WMaA14PALM5
WMaA14PASK5
WMaA14PENO5
WMaA14PIED5
1.0
0.5
0.0
−0.5
1.0
0.5
0.0
−0.5
1.0
0.5
confac
cmat.1st
0.0
(15,19]
−0.5
(19,22]
WMaA14PINN5
WMaA14QUAM3
WMaA14RUDA5
WMaA14SHER5
WMaA14SPAL5
WMaA14TURR5
WMaA14ULTI3
1.0
(22,24]
(24,29]
0.5
(29,60]
0.0
−0.5
WMaA14UNGA5
WMaA14URAN5
WMaA14WOLS5
WMaA14WUNK5
WMaA14WALP3
WMaA14WANB5
1.0
0.5
0.0
−0.5
1.0
0.5
0.0
−0.5
−0.5
0.0
0.5
1.0−0.5
0.0
0.5
1.0
cmat.2st
A one-stage mixed model analysis of Australia’s National Variety Trial data
WMaA14WANI5
WMaA14WARR5
WMaA14WOKU5
one vs two stage differences ...
so what might be driving these differences?
•
•
•
Welham et al. (2010) demonstrated good agreement between the one-stage FA approach
and a weighted two-stage FA approach
–
data set highly balanced in terms of varietal connectivity between trials
–
trials with high heritability
we expect
–
data imbalance
–
low heritability to be drivers
will be investigating these and other factors further
A one-stage mixed model analysis of Australia’s National Variety Trial data
Summary ...
... provide growers with information to help them to choose the best
varieties for their particular set of growing conditions ...
•
we can now achieve a fully efficient one-stage analysis of the MET data for all crops in the
NVT system which has both
•
immediate impacts in terms of
–
•
delivering the most accurate and reliable information to growers we can
broader impacts in terms of
–
the longterm productivity of the wider grains industry
A one-stage mixed model analysis of Australia’s National Variety Trial data