Principles of Plant Genetics and Breeding

Discriminant function analysis
Discriminant function analysis assumes a population
is made up of subpopulations, and that it is possible to
find a linear function of certain measures and attributes
of the population that will allow the researcher to discriminate
between the subpopulations. Consequently,
discriminant procedures are not designed for seeking
population groupings (that is what cluster analysis does)
because the population has already been grouped.
Discriminant analysis may be used in conjunction with
the D2 statistic (Mahalanobis D2 ) to indicate the biological
distance between separated groups.
Cluster analysis
Genetic assessment of germplasm is commonly undertaken
by plant breeders to understand genetic variation
in the germplasm and to discover patterns of genetic
diversity. Cluster analysis, unlike discriminant function
analysis, groups genetically similar genotypes. Clustering
can be done on a morphological or molecular basis (e.g.,
using DNA markers). Analysis of genetic diversity levels
in germplasm helps plant breeders to make proper
choices of parents to use in breeding programs.
Canonical correlation analysis
The canonical correlation analysis is a generalization of
the multiple correlation procedure. The technique is
used to analyze the relationship between two sets of
variables drawn from the same subjects. An assumption
is made that there are unobserved variables dependent
on a known set of variables X, and determining another
known set, Y. The intermediating unobserved variables
are used to canalize the influence of set X on set Y.
Path analysis
Path analysis is a technique for decomposing correla-
Akroda, M.O. 1983. Principal components analysis and
metroglyph of variation among Nigerian yellow yams.
Euphytica 32:565–573.
Cooley, W.W., and P.R. Lohnes. 1971. Multivariate data analysis.
John Wiley & Sons, Inc., New York.
Denis, J.C., and M.W. Adams. 1978. A factor analysis of plant
COMMON STATISTICAL METHODS IN PLANT BREEDING 161
References and suggested reading
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Figure 9.3 The basic concept of path analysis.
tions into different pieces for the interpretation of
effects. The procedure is closely related to multiple
regression analysis. Path analysis allows the researcher
to test theoretical propositions about cause and effect
without manipulating variables. Variables may be
assumed to be causally related and propositions about
them tested. However, it should be cautioned that,
should such propositions be supported by the test,
one cannot conclude that the causal assumptions are
necessarily correct. A breeder may want to understand
the relative contributions of yield components and
morphophenological traits to grain yield.
The general display of a path analysis is shown in
Figure 9.3. Arrows are used to indicate assumed causal
relations. A single-headed arrow points from the
assumed cause to its effect. If an arrow is doubleheaded,
only correlation is present (no causal relations
are assumed). Variables to which arrows are pointed are
called endogenous variables or dependent variables (Y ).
Exogenous variables have no arrows pointing to them;
they are independent variables (X). The direct effect of
a variable assumed to be a cause on another variable
assumed to be an effect, is called a path coefficient.
Path coefficients are standardized partial regression
coefficients.
variables related to yield in dry beans. I. Morphological
traits. Crops Sci. 18:74–78.
Kendall, M.G. 1965. A course in multivariate analysis. Charles
Griffin & Co., London.
Snedecor, G.W., and W.G. Cochran. 1967. Statistical methods,
6th edn. Iowa State University, Ames, IA.