modules, most traits of interest in forest trees are quantitatively

inherited. That is, they are controlled by many genes,

each of which controls a modest amount of the variance

in that trait. A gene that controls some portion of the genetic

variance of a phenotypic trait is called a quantitative trait locus,

or QTL. It is possible to

identify QTL and their relative location in the genome by

placing them on genetic maps. This is done by demonstrating

a statistically significant association between the

quantitative trait phenotype and one or more genetic

markers already located on a map. QTL mapping

is a powerful tool for elucidating the genetic architecture of

complex traits and provides a clearly defined approach for marker-assisted

selection in applied breeding or natural environment settings.

We will identify the key elements of

QTL mapping and give some examples of how it has been done

in forest trees. Additionally, we will reflect on

some of the limitations of the QTL approach using pedigree crosses.

Most of the elements required

to identify and map QTL are those previously noted for

construction of genetic maps themselves. The factors that distinguish

QTL mapping from genetic mapping are 1)

the need for high quality phenotypes for all the progeny being genotyped

and 2) a different set of analytical tools.

Let’s quickly review the points noted here.

Experimental Populations: For the most part,

pedigreed crosses such as those needed for genetic mapping are needed.

For outcrossing trees, ideally, this

means a three generation intercross, though virtually any

cross can be used, including open-pollinated crosses and

two-generation pseudo-testcrosses.

You may improve your chances of detecting QTL by making the crosses

to ensure segregation of the traits of interest in the F2 progeny.

The size of the full sib family used is

important. Studies have shown that 500 or more progeny

are required to avoid bias in the number of QTL identified

and the proportion of variation those QTL explain.

Informative markers: The best

markers are multi-allelic, co-dominant markers that

could potentially tag as many as four alleles

in the QTL. Generally, these will be

the same set of markers used in making your genetic map.

The Map: A good framework map

with enough markers (say, 75-100)

to completely cover the genome is desirable.

Phenotypes: High quality measurement of the

traits of interest are essential. One way to dramatically

improve phenotypic trait estimates is to clonally replicate the progeny

in the study trials. In effect, this results

in an increase in trait heritability. We will leave

comments on the last two points, analytical tools and verification,

for later. Suffice it to say that what we seek are

associations between differences in phenotypic means

of genotypic classes, evaluated one locus at a time.

The subsequent effort to accurately locate significant

markers is the focus of most of the more

sophisticated software.

The figure at right illustrates

the concept of what constitutes a QTL, as might be

found in a three-generation intercross. Note

that the “deck is stacked”, so to speak, in the grandparent

generation. That is, crosses are made between parents that are

contrasting phenotypically. For this example we see that

grandparents that are homozygous for upper case alleles at

markers across a given linkage group appear to be associated with small

stature and trees homozygous for lower case alleles

seem to be of large stature. The F1 offspring of this

cross are intermediate in size, suggesting that the locus that

appears to be affecting tree size must be exhibiting additive gene

action (i.e. heterozygotes are intermediate

to either homozygote). In the segregating F2

generation, one can test mean tree size of all three marker genotypic

classes to determine if they vary from one another.

In this case, only locus B appears to show a relationship

between tree size and genotypic class. The logical

interpretation is that the locus affecting tree size must

reside near the B marker. How close are they to one another?

They may be only a few thousand base pairs apart,

or they may be a few million base

pairs from one another. We can’t tell the difference at this point.

Remember from the genetic mapping module that mapping precision

is largely a function of how many meiotic events you have to look at.

As you will see, the confidence interval around

the location of a QTL is generally quite large.

Now image testing the genotypic classes of 75

markers spread across the genome for this same trait.

You may find no significant associations

or many. Whatever your result, if you have done the

experiment correctly, you can have some confidence that the result is a

reflection of the real situation for that one specific pedigreed cross.

This cartoon is a little more

illustrative of realistic data that come from QTL studies.

Again, the basic concepts of QTL mapping are shown here.

For simplicity, this is illustrated using F2 offspring

derived from the intermating of two inbred lines.

In terms of markers, only three genotypes are possible,

shown here as AA, AB,

and BB. Markers can be widely interspersed,

since recombination will be rare in a single generation.

Frequently, QTL studies are done with framework maps with

markers spaced 10-30 cM apart. Offspring

are grouped by genotype and their phenotypes are examined for

a significant difference among group means, such as using

ANOVA. In this case,

the AB (heterozygous) genotype is intermediate between the

two parental homozygotes, implying the QTL exhibits

additive gene action. The distribution of phenotypes

for the array of individuals with a given genotype clearly

suggests that the effect of that particular QTL on that phenotype

is relatively small, and that many other factors may be

influencing the trait.

Let’s do a quick overview of

QTL mapping. The idea is to find a statistically

meaningful association between genetic markers and phenotypic traits,

and to place the resultant QTL on a genetic map.

This is done using one full-sib family at a time.

To find an association, both the QTL locus

and the marker must be heterozygous in the cross chosen.

Imagine a trait that has a heritability of 0.5,

and it is controlled by ten genes, each of equal influence.

That is, each gene or QTL, accounts

for 5% of the total phenotypic variance for that trait since

half the variance is caused by non-genetic or rather,

environmental factors. It may be that the

cross you are using is homozygous for seven of the ten QTL.

In that case, you would only detect three of them,

assuming the power of your experiment was sufficient.

Identifying and locating those QTL

that are heterozygous in your cross depends on several things.

Certainly, marker density is important, but not nearly

so much as the number of progeny sampled for several reasons we have

articulated previously. Early studies conducted with

relatively few progeny (say, under 100) were shown to

overestimate the size of the QTL effect and to underestimate

the number of QTL. As you might imagine, this

problem increases as the size of the QTL effect decreases.

While breeders had visions of identifying major genes with

large effects, the reality is that we have found most trait

effects to be very small (<5%).

QTL detection and estimation of effect size is also a

function of a number of interactions between the QTL and other loci

(i.e. epistatic effects) and environmental

conditions. Finally, we note there are a

few different analytical approaches to QTL mapping. We will spend the next

several slides discussing each of these approaches.

The simplest analytical approach to QTL

detection is the single-marker method, which, as the name implies,

is a statistical test of the association between phenotype

and genotype class one marker at a time.

If you have 75 markers distributed over 12 linkage groups,

you perform 75 different calculations. This

can be done using simple t-tests, or with very

sophisticated analysis of variance models that seek to

partition experimental variances as much as possible

(i.e. remove non-genetic sources of variance).

A statistically significant result

is evidence that a QTL has a map location somewhere near the marker,

though neither the distance to the marker nor the size of the QTL

effect can be estimated well. It is not necessary

to have a genetic map to use this approach, but having one greatly

increases the amount of information available to you. There

are other drawbacks to this approach. It does not differentiate

between one and multiple QTL when they exist on the same

linkage group. This may result in overestimating the size of the

QTL effect. Conversely, the magnitude of

QTL effect may be underestimated due to increasing,

but unknown, recombination between marker and QTL.

That is, the further the QTL is removed from the marker,

the lower the estimated effect of the QTL.

As noted, single marker testing is relatively simple

and can be done with t-tests, ANOVA, or simple regression.

However, it should be obvious that testing for a significant

association between discreet genotypic classes of

many marker loci and quantitative distributions of

one to many phenotypic traits can result in literally

hundreds of statistical tests. By chance alone,

some tests will prove significant, yielding false positive

QTL detection. Consequently, it is best to

impose a correction for multiple testing, such as the Bonferroni,

Scheffe, or other corrections of significance level available

in most statistical packages. This may be done at the

individual linkage group level or across the entire genome.

The latter is the more conservative measure.

In the figure shown above, which we will see again later in this module,

one can see that 19 individual markers on a single

linkage group have been tested for statistical significance.

As is common practice, significance tests are defined

by the LOD score. The LOD score, which stands

for the logarithm of odds (base 10), compares the likelihood

of obtaining the test data if the two loci are indeed

linked, to the likelihood of observing the same data

purely by chance. Large, positive LOD

scores favor the presence of linkage, whereas small or

negative LOD scored indicate that linkage is less likely.

A LOD of 2 suggests a probability

that an association this strong would occur by chance alone

1 in 100 times; a score of 3,

1 in 1000 times. With multiple testing,

LOD scores higher than 3 are typically embraced.

Here, only one of the 19 loci tested at the

genome wide level is considered significant,

though it would appear that many of them are suggestive of being

suggestive of being significant. More on this later.

As Rebecca Doerge points out, in the paper cited

in the previous slide, single marker analyses investigate

individual markers independently and without reference

to their position or order. When markers are placed in

genetic map order so that the relationship between markers are understood,

the additional genetic information gained from knowing these relationships

provides the necessary setting to address confounding

between QTL effect and location.

The interval mapping approach to detection and

location of QTL was developed by Lander and Botstein

to take advantage of this additional information. Interval

mapping addresses the key weaknesses of single marker analyses using

ANOVA: 1) inability to accurately

detect and locate a QTL, 2)

inability to accurately estimate the QTL effect, due to

recombination, and 3) inability to evaluate

individuals for which genotype data may be missing.

With interval mapping, each location in the genome is

posited, one at a time, as the location of a single

putative QTL. Generally this is done by

evaluating a relatively small region of the genome

at a time, 2 or 5 cM, the distance

chosen being somewhat dependent on the number of markers in your framework

map. The process accounts for missing genotypes by using

predicted genotypes, based on knowledge of the parents

of the cross being used and the other nearby markers.

The statistical estimators in interval

mapping are complex and have computationally demanding solutions.

They often use maximum likelihood procedures.

This figure, borrowed from Georges, illustrates the principles of