RA 00110.pdf - OAR@ICRISAT

Table 3. Two analyses of variance showing that the location * entry interaction is the appropriate test either with or
without replication at each location
Analysis of Variance I
Source
Locations
Entries
L x E
df
l-1
e-1
(l-1)(e-1)
E.M.S.
Source
Locations
Replications in Locations
Entries
L x E
Error
Analysis of Variance II
df
l-1
/(r-1)
e-1
(l-l)(e-1)
/(r-1)(e-1)
E.M.S.
ments may be sampled with a given number of replications
rather than precisely evaluating each entry in
a smaller number of environments.
Blocking
In testing families, the breeder usually is faced with
experiments containing many entries. Blocking is
required in order to remove environmental variation
arising from differences in the field from one part of
a replication to another. Lattices work well but a
simpler approach is to use incomplete blocks. For
example, a test of 100 entries could be divided into
10 incomplete blocks of 10 entries each. Each
incomplete block will contain the same entries in all
replications. In a blocks-in-replication design, the
blocks are randomized in each replication. In a
replication-in-blocks design all the replications of a
block containing the same entries are grown together
in the block to minimize the error term. The blocksin-replication
design is somewhat better from a
selection point of view, and is also adaptable to
testing entries with one replication in each location
since locations can be substituted for replications.
However, the replication-in-blocks is slightly favored
for estimating genetic variances. Analyses of variance
and further discussion of these designs are
found in Ross and Gardner (1985). Whatever the
type of experimental design used, some sort of
blocking is almost always required.
When making selections there are two ways to
handle the blocks. One way is to calculate the mean
of each block and the overall mean, and then adjust
the entries in the block by the deviation of the block
mean from the overall mean. The other way to make
selections is to select equally from each block. Both
systems work well, but care is necessary not to have
the blocks too small. The fraction (where e is
the number of entries per block) of the genetic variance
will go into block-to-block variance and be
lost. If e is large enough (say 10 or more) this fraction
may not be sufficiently large to cause worry. Blocks
that are too large (say 50 or more), however, may not
remove enough of the environmental variance.
Improving Populations or Varieties
and their Crosses
Intrapopulation (Variety) Improvement
Methods most usually seen are mass, half-sib,
including ear-to-row, full-sib, and line per se selection,
or some combination of these.
In the prediction equations for each method
(Table 4a, b, c, d), some common terms are used so
the schemes can be compared with each other.
N e = effective population size
= gain per cycle
k = selection coefficient based on proportion selected
= total genetic variation
= additive genetic variance
= dominance genetic variance
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