PBG/MCB 622 – QTL Mapping
Fall 2012
Homework Problem
Due Date:
Background
Sax (1923) pioneered an approach to identify mendelian factors underlying a quantitative trait.
In his seminal paper, Sax found a statistically significant association between a qualitative factor
that affected seed coat pigmentation (P locus) and a quantitative trait (seed weight). Sax argued
that this association was due to genetic linkage between the P locus and a factor that affected
seed weight. If one had a sufficient number of scattered qualitative factors (DNA-based markers)
in the genome, one could use Sax’s association approach to detect and tag loci that affected a
given quantitative trait in a given population. If linkage relationships between these qualitative
factors were available, the probable location of factors that affected a quantitative trait could also
be deduced. This is the basic strategy still used today to genetically dissect a quantitative trait
using markers and linkage maps.
The assignment
The Excel file “spike_marker_assoc_12” contains the mean spike internode length (cm) for the
Oregon Wolfe Barley (OWB) population (94 DH lines). In addition, the dataset also contains
genotypes for five linked markers on chromosome 2H (Bmag0125- 29.7 cM - ABG072 - 15.6
cM - cnx1- 20.5 cM - GBM1019 - 18.3 cM - MWG949A). Use this dataset to determine markertrait associations.
1. Draw a histogram showing the distribution of spike internode length in this population.
Describe the distribution of values. Is the distribution unimodal or multimodal? What might this
suggest with regard to the number of genetic factors that affect this trait?
2. Calculate mean trait (spike internode length) values for each genotypic class (A vs. B) at each
locus (Bmag0125, ABG072, cnx1, GBM1019, and MWG949A) individually. Present your data
using bar graphs for each locus.
3. Use analysis of variance to determine if the mean spike internode length of each genotypic
class (A vs. B), at each locus, was significantly different. Show your analysis of variance tables
and describe your findings.
a. Which marker(s) showed a statistically significant association to the trait?
b. Which allele (A or B) of a given locus was associated with long spike internodes and
which one was associated with short spike internodes. Does this make sense? Explain
your answer.
4. Perform a simple linear regression of spike internode length (response variable y) and
genotypic class (regressor variable x). Use the model y   0  1 x   where y is the response
variable,  0 is an unknown constant,  1 is the slope of the curve, x is the regressor variable, and
 is the random error. The null hypothesis H 0 : 1  0 implies no relationship between marker
genotype and trait value. Since linear regression requires numbers for the analysis, you need to
use dummy variables in place of the A and B genotype codes. For this analysis, use ‘1’ for A
and ‘-1’ for B.
a. Which marker(s) showed a statistically significant association to the trait?
b. Which allele (A or B) of a given locus was associated with long spike internodes and
which one was associated with short spike internodes?
c. Was this analysis consistent with the analysis in 3.
d. What proportion of the phenotypic variance was explained by each marker?
5. Draw a linkage map with Bmag0125, ABG702, cnx1, GBM1019, and MWG949A and show the
most likely location of a genetic factor that affects spike internode length.
References
SAX, K., 1923 The association of size differences with seed-coat pattern and pigmentation in
Phaseolus vulgaris. Genetics 8: 552-560.