1. Multivariate Analysis
Pattern Analysis
Finding patterns among objects on which two or more independent variables have been measured
Principal Coordinates Analysis (PCO)
Principal Components Analysis (PCA) (Flury 1988)
Cluster analysis (Everitt 1992)
Allow the projection of multivariate phenotypic or genotypic measurements in lower dimensional spaces so that the underlying patterns or structures can be described and visually displayed
The ‘genetic’ patterns among a set of entities (genetic materials) is difficult to discern from DNA fingerprints (raw multivariate data)
Patterns among the entities can be ‘extracted’ by PCA, PCO or cluster analyses of pairwise genetic distance matrices

3. Principal Components Analysis (PCA)
Neighbor-Joining Cladogram

4. Similarity and Dissimilarity (Genetic Distance) Measures
Applications include:
Assessment genetic relationships
Prediction of heterosis
Heterotic group definition
Identification of duplicates in collections
Assessment of genetic diversity
Plant variety protection

5. Similarity and Dissimilarity (Genetic Distance) Measures
Choice of distance measure is affected by:
Properties of marker system
Genealogy of germplasm
Lines or populations
Objectives of study
Subsequent multivariate analysis

6. Genetic distance (Dissimilarity) measures based on allele frequency data
The first step is to build a matrix of pair-wise measures of dissimilarity
Multiple indexes can be used to estimate dissimilarity

7. Genetic distance measures based on allele frequency data
(Reif et al Crop Science 45 (1), 1-7

8. Genetic distance measures based on allele frequency data
Euclidean (dE) - No underlying genetic concept. Can be used with multivariate methods that require Euclidean distances
Roger (1972) (dR) - Linearly related to coefficient of coancestry
Modified Roger’s (dW) - dW2 is linearly related to panmictic-midparent heterosis
Cavalli-Sforza and Edwards (1967) (dCE) - Based on Kimura’s (1954) model of selective drift

9. Genetic distance measures based on allele frequency data
Reynolds et al. (1983) (dRE) – Based on a model where mutation and selection can be neglected and drift is the major evolutionary force
Nei (1972) (dN72) - Based on the infinite-allele model (Kimura and Crow, 1964)
Nei et al. (1983) (dN83) - For homozygous inbred lines, dN83 = dR and, hence, dN83 is also linearly related to the coancestry coefficient

10. Similarity Measures for Binary Data
Entity i
Entity j
Count
Condition
Present (1)
a (vij)
Positive match
Absent (0)
b (wij)
Mismatch
c (xij)
d (yij)
Negative match
Simple matching
Jaccard (1908)
Dice (1945)

11. Shared allele distance
S = No. of shared alleles
u = No. of loci
(Bowcock et al. 1994)

12. Similarity Measures for Binary Data
Individual
Marker1
Marker 2
Marker 3
Marker 4
Marker 5
Marker 6
Marker 7
Marker 8
Marker 9
Marker 10 1 3
Similarity
Simple matching
Rank
Shared alleles
Jaccard’s
Dice’s
s12
0.70 2
0.40 1
0.57
s13
0.50 3
0.00
s23
0.80
0.33

13. PRINCIPAL COORDINATES ANALYSIS (PCO or PCoA)
Distance between Oregon towns (miles)
Genetic distance between barley varieties (Nei et al., 1983 index)

14. Principal Coordinates Analysis is a method to visualize similarities or dissimilarities of data.
It starts with a distance matrix (dissimilarity) and assigns for each item a location in a 2 or 3 dimensional space

15. PRINCIPAL COMPONENTS ANALYSIS (PCA)
Transforms a number of possibly correlated variables (in this case allelic states) into a smaller number of uncorrelated variables called principal components.
The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible

16. The goal of PCA is to reduce the dimensionality of the data while retaining as much as possible of the variance of the observed variables: Reduces the number of observed variables to a smaller number of principal components which account for most of the variance
The total amount of variance in PCA is equal to the number of observed variables being analyzed.
Observed variables are standardized, e.g., mean=0, standard deviation=1
The first principal component identified accounts for most of the variance in the data. The second component identified accounts for the
second largest amount of variance in the data and is uncorrelated with the first principal component and so on.
Components accounting for maximal variance are retained while other components accounting for a trivial amount of variance are not retained.
Eigenvalues indicate the amount of variance explained by each component.
Eigenvectors are the weights used to calculate components scores.

17. Distance-based methods (starting from a distance matrix)
Cluster Analysis: Individuals with similar descriptions are mathematically gathered into a cluster.
Distance-based methods (starting from a distance matrix)
UPGMA (Unweighted Pair Group Method with Arithmetic Mean)
Neighbor-Joining
Model-Based methods
Neighbor-Joining Cladogram

18. POPULATION STRUCTURE
Marker 1
Marker 2
Marker 3
Marker 4
Marker 5
Marker 6
Marker 7
Marker 8
Marker 9
Marker 10
Individual 1 1
Individual 2
Individual 3
Individual 4
Individual 5
Individual 6
Individual 7
Individual 8
Individual 9
Individual 10
Individual 11
Individual 12
Individual 13
Individual 14
Individual 15
Individual 16
Individual 17
Individual 18
Individual 19
Individual 20
Hypothesis 1: There is one population that has intermediate frequencies at all loci and all individuals are from that population
Hypothesis 2: There are two populations: blue and pink, with high allele frequency at some loci and low allele frequency at other loci

19. POPULATION STRUCTURE It is important to estimate:
How many subpopulations there are
- To which subpopulation each individual belongs (%)