1. Evolution by Natural Selection as a Syllogism
If individuals in a population vary with respect to a particular trait that has some genetic basis
AND
2. If the variants differ with respect to their abilities to survive and reproduce in the present environment
THEN
3. There will be an increase in the frequency of individuals having those traits that increased fitness in the next generation
Note, the content of this lecture and any figures were taken liberally from other sources….

2. The Syllogism Parallels the Breeder’s Equation
R = h2S
The breeder’s equation

3. Parallel between the Syllogism and the Breeder’s Equation
If individuals in a population vary with respect to a particular trait that has some genetic basis
AND
2. If the variants differ with respect to their abilities to survive and reproduce in the present environment
THEN
3. There will be an increase in the frequency of individuals having those traits that increased fitness in the next generation h2 S R

4. Selection on a Quantitative Trait
Consider a situation where there is a clear “selective event” within a generation
Response (R)
= mean Zoffspring – mean Zparents
Mean phenotypic trait in next generation
frequency
phenotype
Mean phenotypic trait value AFTER selection
Mean phenotypic trait value BEFORE selection
Selection differential (S)
= mean Zafter – mean Zbefore
The Breeder’s Equation predicts the mean phenotype of the next generation

5. Evolutionary Response to Selection on a Quantitative Trait
Offspring trait value
Slope = 1.0
h2 = 1.0
Mean of offspring of selected parents R
Population mean
When h2 = 1,
R = S
Parent trait value S
Mean
before
after

6. Evolutionary Response to Selection on a Quantitative Trait
Offspring trait value
Slope = 1.0
h2 = 1.0
Mean of offspring of selected parents R
Population mean
When h2 = 1,
R = S
Parent trait value S
Mean
before
after

7. Evolutionary Response to Selection on a Quantitative Trait
Offspring trait value
Slope = 0.5
h2 = 0.5
Mean of offspring of selected parents R
Population mean
When h2 < 1,
R < S
Parent trait value S
Mean
before
after

8. Evolutionary Response to Selection on a Quantitative Trait
The displacement of the mean of the character each generation is the response to selection
Given the same strength of selection, a larger heritability means a larger response.
If heritability doesn’t change, constant selection yields constant response
Across Multiple Generations R1 R2 R3 z0 _

9. So, What is Heritability?
Heritability describes the proportion of variation in trait that can respond to selection
Broad-sense Heritability (H2 = h2B = VG/VP)
could include dominance and epistatic variation
Narrow-sense Heritability (h2= VA/VP)
proportion of phenotypic variance that is due to additive genetic causes

10. Characterizing a Quantitative Trait
Mean (average)
# of individuals Z
Variance
(mean squared deviation from mean)

11. What Causes Phenotypic Variation Among Individuals
Genetics?
Environment?
Both? Z
# of individuals

12. Partitioning Variance
Total Phenotypic Variance (VP) VG VE
VG x E

13. classic experiments of Clausen, Keck and Hiesey (1948) on Achillea:
Plants from low elevation populations are taller than plants from high elevation. Is this difference between populations due only to the environment or are there genetic differences as well?
Note in each population there are a distribution of heights (the blue areas on each figure, turn your head sideways to view the distribution).
classic experiments of Clausen, Keck and Hiesey (1948) on Achillea:

14. Unspecified source population
Fig 8.26
Unspecified source population
The total phenotypic variation in a population can be viewed as a stick that can be decomposed into component parts: Vp = V genetic + Venvi + Vgxe.
The variance due to GxE is variation due to an interaction between genotype and the environment. In othe rwords, its variation due to the fact that not all genotypes respond to the environment in the same way. In the above figure, 7 genotypes were grown in one of 2 environments (Stanford = Low elevation, Mather = high elevation). Notice that the genotypes are ranked based on height when grown in the Stanford population. Even though on average the plants are taller when grown in the Stanford environment than in the Mather environment, not all genotypes responded to the change in environment in the same way. For example, genotype E was relatively less affected by the change in environment compared to genotype B—these sorts of differences are what make up the GxE component of variation.

15. Partitioning Variance
Total Phenotypic Variance (VP) VG VE
VG x E
VADD
VDOM
VEPI
Genetic Variance can be subdivided:
VADD= phenotypic variation due to the additive effects of alleles
VDOM = phenotypic variation due to dominance effects (when the effect of the allele depends on the identity of the other allele at that locus)
VEPI = phenotypic variation due to epistatic effects (when the effect of the allele depends on the identity of alleles at different loci)

16. Dominance and Epistasis
BBEE
BBee
Bbee
BBEe
bbee
BbEE
BbEe
bbEE
bbEe

17. Partitioning Variance
Total Phenotypic Variance (VP) VG VE
VG x E
VENV
Environmental Variance can be subdivided:
VEN V= phenotypic variation due to random environmental influences
VCOM = phenotypic variation due to common family influences
VCOM
VMAT
VMAT = phenotypic variation due to maternal influences

18. Plasticity in Guppy Offspring Size
Food stressed mothers produce larger offspring
David Reznick and undergrad at the time, Tony Yang showed that guppies exhibit plasticity in offspring size. And the form of that plasticity is really cool. In response to low food levels, mothers make a larger baby then when they have plenty of food. So they do produce fewer babies, but each one is larger.
What’s interesting is that this plastic response is on the same order of magnitude as the genetic difference between upstream and downstream sites.
And that made me wonder…
Reznick and Yang 1993

19. Partitioning Variance
Total Phenotypic Variance (VP) VG VE
VG x E
VDOM
VEPI
VADD
VENV
VCOM
VMAT
heritability (h2) = the proportion of phenotypic variation that is due to the additive effects of alleles [how much of VP is made up by VADD]
Total Phenotypic Variance (VP)
VADD

20. Why only Additive Genetic Variance?
The additive effects of alleles are responsible for the degree of similarity between parents and offspring
Additive effects
Dominant A2
a = the effect of substituting an A1 or A2 allele
Why is there spread around the phenotypic values of 6, 8, and 10 for each genotype? VE
  A2A2 A1A2 A1A1 a d
ADD only
w/ DOM

21. Why only Additive Genetic Variance?
The additive effects of alleles are responsible for the degree of similarity between parents and offspring
Additive effects
Dominant A2
A1A2 x A1A2
Parents = 8
Parents = 10
Offspring = .25(6)+.5(8)+.25(10) = 8
Offspring = .25(6)+.5(10)+.25(10) = 9
Dominance causes offspring phenotype to deviate from parental phenotype!

22. Measuring Heritability
Heritability is the slope of the regression between offspring and mid-parent phenotype
Mid-parent phenotypic trait value
Offspring phenotypic trait value
Slope = 0.89
h2= 0.89
Can look at other relatives too!
Slope(mom,daughter) = ½ h2
Slope(half-sibs) = ¼ h2