1. CH22 Quantitative Genetics
BIOL 2416 Genetics
CH22 Quantitative Genetics

2. Quantitative Genetics
Study of traits that exhibit a wide range of possible phenotypes
Known as continuous traits (grayscale)
As opposed to regular Mendelian discontinuous/discrete traits (black vs. white)
Caused by multiple genes (a.k.a polygenic inheritance)
Individual contributing loci called
QTL = Quantitative Trait Loci
May be additive
Often multifactorial
Due to genotype + environment

3. The simplest case: a trait determined by two loci
RRCC (dark red) x rrcc (white)
F1= all RrCc (intermediate red kernel color)

4. F1 x F1 Might expect a typical 9:3:3:1…
Instead, with both R and C contributing to the same phenotype, will observe phenotypes falling into five different classes: 1:4:6:4:1
Obviously, not a case of simple Mendelian inheritance…

5. Note that 1:4:6:4:1 corresponds to the coefficients in the
Binomial expansion (a+b)4:
RRCC
rrcc
RRCc or RrCC
RRcc or rrCC or RrCc
rrCc or Rrcc

7. In reality…
Much more complicated
Many more genes
2 contributing genes > 5 phenotypic classes
3 contributing genes > 7 phenotypic classes
etc
Plus environmental factors
Requires lots of statistics

8. Will want to ask the question: how much phenotypic variation (VP) is due to genetic variation (VG), and how much is due to environmental variation (VE)?
Where VP = VG + VE

9. How do we measure traits in big populations?
Pick a subset
Must be LARGE enough to avoid sampling errors
Must be RANDOMLY picked!!!
Extrapolate to describe the entire population

10. How do we describe variation?
Normal, (phenotypic) distributions look like symmetrical, bell-shaped curves
All we need to describe these are the
Mean ( )
A.k.a. average
Center of the curve
Add up values and divide by the number of values (n)
Variance (S2)
For each value add up deviation from the mean; square the sum of the deviations, and divide by n-1
Width of the curve

11. Same mean, three different variances (S2):
Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

12. Standard Deviation

13. A theoretical normal distribution:
within 3 std deviations from mean
within 2 std deviations from mean
within 1 std deviation from mean
Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

14. Correlation Organisms are composites of many traits
Some traits may be related, e.g. height and weight are measurements of size
Genes and environmental factors that affect development likely to affect both height and weight
There is a correlation between height and weight

15. Covariance Shows to what extent two variables change together
Covariance values span a wide range of numbers:
Zero means the two variables are uncorrelated
Negative means they change out-of-sync: if one is above the expected value, the other will be below the expected value
Positive means they change in-sync: if one is above the expected value, the other will also be above the expected value

16. Covariance
Very similar to calculating variance, except instead of squaring the deviation from the mean for one of the variables, you multiply the deviation from the mean of one variable (x) by the deviation from the mean of the other variable (y):
“co” means dealing with TWO variables

17. Correlation Coefficient (r)
Covariance can be turned into a unitless, standardized version called the correlation coefficient
Narrows the range of possible values (-1 to +1)
Still measures the strength of the association between 2 variables, usually within a given individual
Positive r = both variables increase
The closer to +1, the stronger the positive correlation
Zero r = no correlation/relationship
Negative r = one increases, the other decreases
The closer to -1, the stronger the negative correlation
strong none strong
negative positive

18. (n = 12)
(mean x)
(mean y)
(square root of variance)
(square root of variance)
(positive number means x and y change in-sync)
(close to +1 means a strong positive correlation: when one goes up, the other goes up as well)

19. (The closer r is to 0, the weaker the correlation)
Fig Scatter diagrams showing the correlation of x and y variables
none
+ weak + + -
+ strong
(The closer r is to 0, the weaker the correlation)
Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

20. Beware…
Correlations say NOTHING about cause and effect!

21. To answer these quantitative questions, we must do regression analysis
Correlation coefficient r is a qualitative, NOT a quantitative measure…
can tell us about the strength of the association between variables, and whether the relationship is positive or negative, that’s IT
Once we know there is a correlation, we may want to ask more specific questions
E.g. if a father is 6 ft tall, what is the most likely height for his son?
To answer these quantitative questions, we must do regression analysis
Involves plotting real father-son height data points
Finding line of best fit through the data
The slope of this regression line is the regression coefficient
shows how much son height is expected to increase for e.g. every 1 inch increase in dad height (0.5 inches if slope = 0.5)

22. Fig. 23.7 Regression of sons’ height on fathers’ height
one father-son pair
data point
slope b
Also equal to
Regression line minimizes
distance of individual data
points to the line:
y = a + bx
y intercept a
Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

23. But to what extent is variation seen in a given trait genetic?

24. ANOVA ANalysis Of VAriance Powerful statistical technique
“partitions” the variance into genetic and environmental variance
Can answer questions like “How much of the variation in milk production among cows results from genotype differences, and how much results from environmental differences?
Depending on the answer, we may want to focus on selective breeding or on optimizing the environment to try and increase milk production

25. Heritability
The proportion of a population’s phenotype that is attributable to genetic factors
Remember VP = VG + VE?

26. Broad-Sense Heritability
Symbolized by H2
The proportion of the total phenotypic variance that is genetic
Ranges from 0 to 1
0 means none of phenotypic trait variation in the population is due to (any kind of) genetic differences between individuals
1 means the phenotypic trait variation in the population is genetically determined

27. Broad-Sense Heritability
Why do we care about this number?
Used to estimate the importance of the environment
Can tell if breeding programs in general might result in e.g. a herd of top milk-producers, or if you should concentrate on controlling the environment instead
E.g. “(broad) heritability of IQ” is shorthand for “heritability of variations in IQ”
Cannot answer meaningless question: “To what extent is an individual person’s IQ genetic?” (questions need to be population-specific)
But can be used to answer meaningful (difficult…) question: “How much of the differences in IQ between people in a particular country at a particular time are caused by their genetic differences of any kind, and how much by their environments and life histories?”
Heritability is NOT a fixed value. Again, it is population-specific: in a society where everyone has access to education, IQ will have a higher broad heritability (genetic component of IQ variation) than in a society where certain groups of people do not have equal access

28. Further partitioning the genetic component of phenotypic variance (VG):
VG = VA + VD + VI
VA = additive genetic variance
Predicts how much additive alleles contribute to phenotypic variation in the next generation. (E.g. g = 2cm, G = 4cm, GG = 8cm, Gg = 6cm, gg = 4cm)
VD = dominance variance
Predicts how much non-additive dominant alleles contribute to phenotypic variation in the next generation. (E.g. BB and Bb individuals might have the exact same phenotype. But Bb would create greater phenotypic variation than BB in the next generation; if the B trait is more desirable, BB individuals would be more useful to the breeder).
VI = interaction variance
Predicts how much epistasis contributes to phenotypic variation in the next generation (e.g. BBee, Bbee, bbee = all yellow labs).

29. Narrow-Sense Heritability
Recall that
And recall that VG = VA + VD + VI
But out of these, only VA (additive genetic variance) is under the direct control of natural selection
VD: cannot select e.g. BB over Bb
VI: cannot select e.g. BBee over bbee
Natural selection “selects” the next generation’s phenotype
We can use the VA part of VG to help us predict how similar a baby will be to its parents
it is used for breeding purposes, to help select phenotypes for the next generation
Narrow-sense heritability =

30. If narrow-sense heritability = 1
VP = VA
phenotypic selection for producing the best next generation should be 100% effective

31. It is possible…
that broad heritability = 1, but narrow heritability < 1
So this trait would be under strictly genetic control, but that does not mean phenotypic selection will be 100% effective
Recap:
broad heritability can tell us what proportion of the phenotypic variation in the population is due to variation in the genotypes
narrow heritability can tell us how much a baby will look like its parents