Predictions - An Introduction to Plant Breeding - page 103

although only two will be covered briefly in this
section:

Method 4 design differs from the Method 2 design as
the inbred parents are not including in the Method 4
design.

Analysis of general and specific combining ability.
These methods are often referred to as Griffing anal-
yses , after B. Griffing who published his, now famous
paper 'Concept of general and specific combining
ability in relation to diallel crossing systems' in 1956.

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Griffing's Analysis allows the option to test for fixed
( Model 1 )or random ( Model 2 ) effects. Fixed effect
models are where inference is made only on the par-
ents that are included in the diallel cross while random
effects models are where inference is made regarding
all possible parents from a crop species. Therefore, in
fixed effect models the parents used in the diallel cross
are specifically chosen (i.e. because a breeder wishes to
have additional information regarding general or spe-
cific combining ability of chosen lines). In random
effects models the parental lines should be chosen com-
pletely at random. If this is done then the analyses can
be interpreted to cover the eventuality that any parents
are used .
Obviously, in most cases where plant breeders are
involved, it is often very difficult to decide whether the
parental lines were chosen or identified at random .In
many cases the parents in diallel crossing designs are
a sample of already commercial cultivars. In this case
some would argue that being commercial cultivars they
cannot be a random sample, as by definition all com-
mercial cultivars are a very narrow subset of all potential
genotypes within a species. On the other hand, others
have argued that plant breeders are only interested in
genotypes of commercial or near-commercial standard
and they can therefore quite rightly term their choice as
a random sample of commercially suitable cultivars.
There are no hard and fast rules regarding fixed or
random models, and usually there is little to be lost or
gained from either argument, provided that the anal-
yses are not treated as one type and interpreted as
another. For example, plant breeders and researchers
often include diverse parental genotypes as parents in
diallel crossing designs (and we believe this to be an
excellent idea). However, do not choose specific parental
lines which show a range of expressions for (say) yield-
ing ability, cross them in a diallel design, and try to infer
from the results what would happen if any different lines
were included.
Griffing's Analysis requires no genetic assumptions
and has been shown by many researchers to provide
reliable information on the combining potential of par-
ents. Once identified the 'best' parental lines (those
with the highest general combining ability) can be
crossed to identify optimum hybrid combinations or

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Analysis of array variances and covariances, often
referred to as Hayman and Jinks analyses , after B.I.
Hayman and J.L. Jinks' paper of 1953, 'The analysis
of diallel crosses'.

Griffing's Analysis

Griffing proposed a diallel analysis technique for deter-
mining general combining ability and specific com-
bining ability of a number of parental lines in cross
combination based on statistical concepts. Griffing
analyses have been used by many plant breeders and
researchers over the past 40 years and in many cases with
good success. Much of the success found in applying
Griffing analyses is the apparent ease of interpretation
of results compared to other analyses available. Parents
used in diallel crosses can be homozygous or heterozy-
gous, for simplicity diallel types are described here in
terms of homozygous (inbred) parents. Four types of
design analyses are available:

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Method 1 . The full diallel where p parents are crossed
in all possible cross combinations (including recipro-
cals). Therefore with p parents the design will consist
of p 2 families ( p 2 p segregating populations or F 1 's

and p inbred parents).

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Method 2 . The half diallel where p parents are
crossed in all possible combinations, parental selfs
are included but that no reciprocals are included.
These types of design will contain p

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[ p + 1 ] / 2 families

([ p segregating populations of F 1 s and p

inbred parents).

[ p − 1 ] / 2 ]

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Method 3 . The full diallel without parent selfs, which
consists of all cross combinations (including recipro-
cals) of p parents. Method 3 differs from Method 1
in that with Method 3 the inbred parents are not
included in the diallel design.

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Method 4 . The half diallel, without parent selfs,
which consists of all p parents crossed in all pos-
sible combinations (but with no reciprocals). The