Paul Eckermann, Developing Variety Rankings for

Developing Variety Rankings for Frost Tolerance in Wheat and Barley
Paul Eckermann1, Timothy March1, Michael Laws1, Ben Biddulph2 and Jason Eglinton1
1
School of Agriculture, Food and Wine, University of Adelaide
2 Department of Agriculture and Food, Western Australia
Overview
Statistical Models
Damage due to frost is a significant issue for wheat and barley growers in Australia and a large amount of money has been
invested in characterising the level of frost tolerance of particular varieties. This is a challenging problem due to issues such as low
heritability, difficulty in determining an appropriate phenotype to measure, maturity differences between varieties at the time of a
frost, and the unpredictability of when a frost event will occur and its severity.
Previous studies have involved relatively small trials and many results have been inconclusive. The Australian National Frost
Program (ANFP) was funded by the Grains Research and Development Corporation to develop a ranking system for frost tolerance
for a larger number of wheat and barley genotypes in three states across Australia.
Here we describe the analysis of wheat trials from this program in 2012 and 2013 and provide a ranking system for frost tolerance
for the genotypes included. A similar system has been developed for barley and further trials grown in 2014 will be used to update
the results.
Experiments
The trait analysed as the response variable is the percentage of the total grains that were sterile, known as frost induced sterility
(FIS), with the observational unit being the tillers within each plot. This was transformed onto the logit scale using an empirical
logistic transformation:
f /100 + 1/2n
z = ln
(1)
1 − f /100 + 1/2n
where z is the transformed FIS, f is the untransformed FIS and n is the total number of grains for each tiller. This converts the
data from an [0, 100] scale to an unbounded scale with the transformed data more closely approximating a normal distribution.
Quantile residual plots were used to check normality assumptions for each frost event.
The design of each trial is known as a longitudinal TOS block design. A model is then formulated that respects both the
randomisation process required for the design and the longitudinal aspect of the data arising from the multiple frosts measurements
per site. The randomised factor is Genotype, and the unrandomised factors are Site, Event, TOS, Rep, Row, Column,
Plot and Tiller, with genotypes being randomised to plots. Genotype is fitted as a random effect as the genotypes can be seen
as a random selection of genotypes from a larger population of genotypes relevant for breeding in Australia. Events are numbered
1 to n with n being the total number of events recorded across all sites. Therefore Site does not need to be fitted explicitly and
the final model formulae are given by:
fixed = ∼ Event,
random = ∼ Genotype:Event + Site:TOS + Event:TOS + Site:Rep + Event:Rep +
Site:Row + Event:Row + Site:Column + Event:Column +Site:Plot + Event:Plot,
rcov = ∼ Event:units
To allow for genetic correlations between events, the model was extended to a factor analytic model (Smith et al. 2001),
with the event factor being equivalent to the site factor used in standard plant breeding applications of factor analytic models. All
models were fitted using the R (R Core Team, 2014) package ASReml-R (Butler et al. 2009).
Results
A factor analytic model was fitted with five factors which explained 97.5% of the genetic variation in the data. The model gave
estimates of the genetic correlation between each pair of sites which are visualised in the heatmap below. The events are ordered
by state and year, with red squares indicating strong positive correlations, and blue squares indicating negative correlations. The
overall pattern shows relatively high correlations between the SA and WA events in both 2012 and 2013, with little correlation
between these states and NSW. However there are some strong correlations between events within NSW.
A summary of the trial sites used, and the configuration of each trial is given below. Trials at Loxton in 2010 and 2011 were not
part of the ANFP but are included because they had many genotypes in common with the ANFP trials. At each trial, between 6
and 11 times of sowing (TOS) were planted as separate blocks in the field to maximise the chance that any given genotype is at
the right developmental stage when a frost event occurs. Each TOS block included two replicate blocks of each genotype, arranged
in a grid of rows and columns. The full set of 65 genotypes were sown in SA, with a subset of lines used in the other states.
State
NSW
NSW
SA
SA
SA
SA
WA
WA
Location
Narrabri
Narrabri
Loxton
Loxton
Loxton
Loxton
Merredin
Wickepin
Year TOS Rows Columns Genotypes Frost Events Ave Genos Tagged
2012 7
12
5
30
9
19.6
2013 7
8
8
32
5
25.0
2010 6
14
5
35
2
26.0
2011 6
18
4
36
2
29.5
2012 11
10
13
65
5
52.0
2013 10
10
13
65
6
46.2
2012 7
24
4
48
3
34.3
2013 6
9
12
54
10
37.3
Sterility Measurements
Rankings
Ranking the genotypes across multiple events is a challenge due to the incomplete nature of the data as only a subset of genotypes
are tagged at any frost event. Firstly a baseline genotype is used to which all other genotypes are compared. In wheat this
genotype is Wyalkatchem, as it is a well known variety that has consistently high levels of sterility over many years of testing. The
standard error of difference (SED) is calculated for each genotype compared to Wyalkatchem for each event. From this, a z-score
is calculated which is the test statistic for the null hypothesis:
The aim of these trials is to evaluate the reproductive frost tolerance of genotypes by measuring the sterility of grains. Heads
of grain were tagged in the field according to a protocol described below, and later harvested, with the number of sterile grains
counted along with the total number of grains for each head. The three methods in which plots were tagged were:
• After a frost occurs, plots with plants that are flowering are identified, and a selection of heads at this developmental stage
are tagged. This is believed to be the stage where heads are most susceptible to frost damage.
• To investigate the effects of developmental stages, some plots at an earlier stage were tagged at the time of a frost - at booting
in SA and NSW, and at ear peep in WA.
• At some trials, a random sample of heads were tagged from all plots in a subset of time of sowing blocks. This was due to
either a lack of tagging opportunities from actual frost events, or when frost damage is only noticed in hindsight after the
opportunity to tag at flowering has passed.
H0: The true FIS of genotype i at event j is higher or equal to the FIS of Wyalkatchem at event j.
The table below is an excerpt from the full table showing the average z-scores for genotypes overall and by state. A simple colour
coding of ratings is proposed which is presented in the table on a state by state basis with the following three colours used:
• Yellow Rating > 6 : Very strong evidence this genotype has lower FIS than Wyalkatchem in this state
• Orange Rating > 3 : Strong evidence this genotype has lower FIS than Wyalkatchem in this state
• Red Rating < 3 : No strong evidence this genotype has lower FIS than Wyalkatchem in this state
Genotype
Genotype
Genotype
Genotype
Genotype
1
2
3
4
5
..
Wyalkatchem
Some plots in a trial were tagged more than once, although the same head was never tagged more than once.
The figure below plots average sterility against minimum temperature for each tagging event, coded by state and tagging
stage. Overall there appears to be a relationship between temperature and sterility but the relationship is confounded by state
effects. NSW events were colder with higher sterility, WA events were warmer with lower sterility and SA events in between.
Overall Overall
SA
SA
WA
WA NSW NSW
Rating Events Rating Events Rating Events Rating Events
6.43
23
7.13
8
9.73
9
2.18
6
5.50
16
6.44
7
8.17
9
0
5.20
26
6.32
8
8.45
10
0.65
8
4.96
26
5.40
9
7.67
9
1.60
8
4.88
26
3.47
10
7.67
8
3.12
8
..
..
..
..
..
..
..
..
0
27
0.00
9
0.00
9
0.00
9
75
Conclusion
State
NSW
Mean FIS
SA
WA
50
Stage
Boot
This project is an important first step in providing frost tolerance rankings to growers. Consistent results have been obtained
for many genotypes across multiple frost events, particularly in SA and WA. More research is needed to test if these results are
reproducible over a wider range of sites, and to quantify the relationship between sterility and yield loss. Another aspect of further
investigation is the impact of tagging stages.
Ear Peep
Flowering
25
Random
References:
Butler, D., Cullis, B., Gilmour, A., Gogel, B. (2009). ASReml-R Reference Manual, release 3.
R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing.
Smith, A., Cullis, B., Thompson, R. (2001). Analyzing variety by environment data using multiplicative mixed models and
adjustments for spatial field trend. Biometrics 57, 1138-1147.
0
−5.0
−2.5
0.0
Minimum Temperature
2.5
Contact details: [email protected]
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