Mario DAntuono, A bi-variate ASReml model for an

A bi-variate ASReml model for an incomplete
block structure of a long-term nursery study
T. hirtum (Hykon)
Circa 23 years
Mario D’Antuono†, Richard Snowball and Hans-Peter Piepho (University of Hohenheim)
1. Introduction
The south-west agricultural region of Western Australia (WA) has a
Mediterranean climate (dry-hot summers with cool-wet winters).
The collection of germplasm (Accessions) from the Mediterranean region
(Figure 2) has provided material for pasture scientists (agronomists/
breeders) to use for release in the pasture phase of cropping/animal grazing
systems in WA.
Field work evaluating the large set of ‘Lines’ from the Accessions was
completed over 23 consecutive years (RS and support staff) at the same site
(Medina Research Station, Western Australia, latitude 32.33°S longitude
115.81°E), on a Spearwood sand with sprinkler irrigation if required.
It is like an ‘incomplete block’ structure with years as the blocks and some
years had replicates of the control varieties, and most of the ‘Lines’ are not
Figure 1. Field layout (High density or sward plots)
2. Experimental methods
3. Statistical methods
 The origin of pasture legumes (mostly annual species excluding
subterranean clover) from the Mediterranean held in the Department’s seed
bank are from 2764 collection sites. The 8124 lines derive from
5062 accession/plant populations and represent 90 species (in 6 genera).
 About 500 experimental plots were laid out in strips each year. Lines were
allocated at random to one of two density types (individual spaced plants or
swards of multiple plants) with oats as buffers. The sward plots (high density)
ranged in size from were about 2m x 1m to 2.5m x 1m. Plots of individual
spaced plants (low density) ranged in size from 1m x 1m to 1m x 20m.
 This paper examines the statistical analysis of the data from the most
dominant genus Trifolium and the high density plots only.
 The two most important traits examined were seed yield (grams per square
metre) and flowering time (days since planting, around May 1 of each year).
These have been abbreviated to ‘sym2’ and ‘ft’ respectively in the outputs.
 The main question of interest was to ‘... adjust for the year effects and obtain
a ranking of the performance of the Lines/Cultivars …’ Snowball et al. (in
 A bi-variate linear mixed model using ASReml
( as defined in Chapter 8 of the manual
was fitted. A working paper on this work can be downloaded from
our website.
 Using the notation from ASReml release 4, we found that the
following bi-variate model was sufficient (i.e. lowest AIC/BIC),
where idh( ) represents the variance function for independent
with separate variances and us( ) represents the variance
function for a general unstructured covariance matrix.
Figure 2. Collection sites shown in black circles
4. Results and conclusions
A square root transformation was applied to the seed yield data (sqrtsym2).
Variance components and correlations are shown in Table 1.
Plots of the best linear unbiased predictions (BLUPs) are shown in Figure 3.
We have identified some new Lines that have potential to increase yield
production but have later flowering times than Hykon (control) which might be
suitable for the southern regions of the WA agricultural area.
 Software for fitting linear mixed models can vary in its memory requirements,
possible bugs, possible crashes and time to execute.
 Have more than one statistical tool for fitting such models!
 Germplasm nurseries offer a useful guide to selecting species with the
greatest likelihood of commercial success.
ft sqrtsym2 ~ Trait ,
!r idh(Trait).Year+us(Trait).Line+us(Trait).Year.Line
residual id(units).us(Trait)
predict Line Trait
Table 1. Bi-variate model outputs: estimates of the variance components (with
standard errors) and degrees of freedom (df)
Random term
Year x Line
units term
s ft
sxy s sqrtsym2
15 83.23 (31.29)
0 2.65 (0.98)
4720 303.32 (7.69) -10.83 (0.86) 3.25 (0.21)
1070 31.25 (5.06) -2.78 (0.86) 2.75 (0.28)
26.8 (4.46) -1.17 (0.72) 1.28 (0.22)
† Website:
† Email: [email protected]
Day to flowering from sowing (around May 1)
Important disclaimer
The Chief Executive Officer of the Department of Agriculture and Food and the State
of Western Australia accept no liability whatsoever by reason of negligence or
otherwise arising from the use or release of this information or any part of it.
Copyright © Western Australian Agricultural Authority, 2014
Supporting your success
Figure 3. Bi-variate model predictions with controls (cultivars) indicated (with a
label centred on its value/circle), and the ‘Lines’ of Trifolium shown as circles
with no label