The Use of Association Genetics Approaches in Plant Breeding - Plant Breeding Reviews - page 33

Armitage trend test is suggested because it is independent from the
assumptions of HWE.

2. Structured Association and Model-Based Methods. Similar to GC,
structured association also uses unlinked genetic markers to correct the
effects of population structure. This approach is founded on the proba-
bility that each individual has to be assigned to a subpopulation.
Pritchard et al. (2000) developed a method in which they attempt to
assign individuals to populations on the basis of their genotypes, while
simultaneously estimating population allele frequencies. In order to use
the structure association approach, the number of populations that are in
the study should be identi

ed.
If the number of subpopulations is unknown, the number is esti-
mated using clustering methods. There are two types of clustering
methods: those that are distance based and those that are model based.
Distance-based methods proceed by calculating a pairwise distance
matrix, graphing the matrix, and identifying the clusters. Model-based
methods use a model to determine each cluster based on random
vectors.
Both methods are suitable, but there is a certain range of error when
clusters are determined by eye in the distance-based methods. The use of
model-based methods has several challenges; inference for the parame-
ters corresponding to each cluster is dif cult but could be done with

statistical methods like maximum likelihood or Bayesian methods, so its
accuracy is higher than distance-based methods. The association test is
made after the population structure estimation. The structured popula-
tion association test (STRAT) has as a null hypothesis

that there is no
association between the phenotype and subpopulation allele frequen-
cies at the candidate locus. The alternative hypothesis is where the
phenotype depends on the subpopulation allele frequencies at the
candidate locus (Pritchard et al. 2000).
In the model-based method, the

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first challenge is to specify a suitable
model for observations from each cluster, assuming that each cluster is
modeled by a characteristic allele frequency. The main model assump-
tions are HWE within populations and complete linkage equilibrium
within populations. The model can also be developed assuming no
admixture (individuals are assumed to originate in just one of the
populations) or as an alternative assuming admixture parameters with
Q values as a covariable. In the model, X is the genotype of the sampled
individuals, Z is the population of origin of the individuals (unknown),
and P is the allele frequency in all populations (unknown). With the