1. Lecture 7: Introduction to Selection
September 11, 2015

2. Last Time
Effects of inbreeding on heterozygosity and genetic diversity
Estimating inbreeding coefficients from pedigrees
Mixed mating systems
Inbreeding equilibrium

3. Today Inbreeding and selection: inbreeding depression
The basic selection model
Dominance and selection

4. Relatedness in Natural Populations
White-toothed shrew inbreeding (Crocidura russula) (Duarte et al. 2003, Evol. 57: )
Breeding pairs defend territory
Some female offspring disperse away from parents
How much inbreeding occurs?
12 microsatellite loci used to calculate relatedness in population and determine parentage
17% of matings from inbreeding
Number of matings
Relatedness
Parental Relatedness
Offspring Heterozygosity

5. What will be the long-term effects of inbreeding on this shrew population?

6. Inbreeding and allele frequency
Inbreeding alone does not alter allele frequencies
Yet in real populations, frequencies DO change when inbreeding occurs
What causes allele frequency change?
Why do so many adaptations exist to avoid inbreeding?

8. Natural Selection
Non-random and differential reproduction of genotypes
Preserve favorable variants
Exclude nonfavorable variants
Primary driving force behind adaptive evolution of quantitative traits

9. Fitness Very specific meaning in evolutionary biology:
Relative competitive ability of a given genotype
Usually quantified as the average number of surviving progeny of one genotype compared to a competing genotype, or the relative contribution of one genotype to the next generation
Heritable variation is the primary focus
Extremely difficult to measure in practice. Often look at fitness components
Consider only survival, assume fecundity is equal

10. Inbreeding, Heterozygosity, and Fitness
Inbreeding reduces heterozygosity on genome-wide scale
Heterozygosity of individual can be index of extent of inbreeding
Multilocus Heterozygosity:
Proportion of loci for which individual is heterozygous
Often shows relationship with fitness
Reed and Frankham 2003 Cons Biol 17:230
Correlation Between Heterozygosity and Fitness
Observed
Number of heterozygous loci
Deng and Fu 1998 Genetics 148:1333
Simulated

11. Inbreeding Depression
wikipedia
notexactlyrocketscience.wordpress.com
terrierman.com/inbredthinking.htm
Reduced fitness of inbred individuals compared to outcrossed individuals
Negative correlation between fitness and inbreeding coefficient observed in wide variety of organisms
Inbreeding depression often more prevalent under stressful conditions
Lynch and Walsh 1998

12. Mechanisms of Inbreeding Depression
Two major hypotheses: Partial Dominance and Overdominance
Partial Dominance (really a misnomer)
Inbreeding depression is due to exposure of recessive deleterious alleles
Overdominance
Inherent advantage of heterozygosity
Enhanced fitness of heterozygote due to pleiotropy (one gene affects multiple traits): differentiation of allele functions
Bypass homeostasis/regulation

13. What about long-term effects on the shrew?
Fecundity (measured by number of offspring weaned) was not affected by relatedness between mating pairs or heterozygosity of individuals
No evidence of inbreeding depression in this species
Why not?

14. How do we quantify the effects of natural selection on allele frequencies over time? Can we predict and model evolution?

15. Relative Fitness of Diploids And NM is the best-performing genotype
Consider a population of newborns with variable survival among three genotypes:
A1A1 A1A2 A2A2 N
Survival
New parameter: ω, relative fitness (assuming equal fecundity of genotypes in this case)
Define ω=1 for best performer; others are ratios relative to best performer:
Where N11s is number of A1A1 offspring surviving after selection in current generation
And NM is the best-performing genotype

16. Average Fitness
Use genotype frequencies to calculate weighted fitness for entire population
A1A1 A1A2 A2A2 ω
ω = D(ω11) + H(ω12) + R(ω22)
ω = (100/300)(1) + (100/300)(0.7) + (100/300)(0.5) = 0.733
When fitness varies among genotypes, average fitness of the population is less than 1

17. Frequency After Selection
D’ = D(ω11)/ω
H’ = H(ω12)/ω = (0.33)(0.7)/0.733 = 0.32
R’ = R(ω22)/ω = (0.33)(0.5)/0.733 = 0.23
= (0.33)(1)/0.733 = 0.45
Selection causes increase in more fit genotype and reduction in less fit genotypes
Allele Frequency Change:
q = (N22 + N12/2)/N = ( /2)/300 = 0.5
q’ = (40+56/2)/176 = 0.39
Δq = q’ – q = 0.39 – 0.5 = -0.11

18. Over time, what will happen to p and q in this population?
What is Δp in the previous example?

19. Starting from Allele Frequencies
A1A1 A1A2 A2A2
freq0 p2 2pq q2
ω ω11 ω12 ω22
freq1 p2 ω11/ω 2pq ω12/ω q2 ω22/ω
ω = p2(ω11) + 2pq(ω12) + q2(ω22)
q’ = q2ω22+pqω12 ω

20. Change in Allele Frequencies due to Selection (i.e., evolution)
q2ω22+pqω12 ω
q2ω22+pqω12 - qω ω
q’ - q =
- q =
Simplifies to:
Δq =pq[q(ω22- ω12) - p(ω11 – ω12)] ω
See p. 118 in your text for derivation
“The single most important equation in all of population genetics and evolution!”
Gillespie 2004, p. 62

21. Fitness effects of individual alleles
Δq =pq[q(ω22 – ω12) - p(ω11- ω12)] ω
Effects of substituting one allele for another
Conceptually, compare fitness of homozygote to heterozygote
Rate of change inversely proportional to mean fitness of population: allele frequencies don’t change much in a fit population!
Marginal fitness: the effects of an individual allele on fitness (the average fitness genotypes containing that allele)

22. Incorporating Selection and Dominance
Selection Coefficient (s)
Measure of the relative fitness of one homozygote compared to another.
ω11 = 1 and ω22 = 1-s
s ranges 0 to 1 in most cases (more fit allele always A1 by convention)
Heterozygous Effect (level of dominance) (h)
Measure of the fitness of the heterozygote relative to the selective difference between homozygotes
ω12 = 1 - hs

23. Relative Fitness (ω) ω11 ω12 ω22
Heterozygous Effect
A1A1 A1A2 A2A2
Relative Fitness (ω) ω11 ω12 ω22
Relative Fitness (hs) hs 1-s
h = 0, A1 dominant, A2 recessive
h = 1, A2 dominant, A1 recessive
0 < h < 1, incomplete dominance
h = 0.5, additivity
h < 0, overdominance
h > 1, underdominance

24. Putting it all together
A1A1 A1A2 A2A2
Relative Fitness (ω) ω11 ω12 ω22
Relative Fitness (hs) hs 1-s
Δq =pq[q(ω22 – ω12) - p(ω11- ω12)] ω
Reduces to:
Δq =-pqs[ph + q(1-h)]
1-2pqhs-q2s

25. Modes of Selection on Single Loci
Directional – One homozygous genotype has the highest fitness
Purifying selection AND Darwinian/positive/adaptive selection
Depends on your perspective!
0 ≤ h ≤ 1 ω
A1A1
A1A2
A2A2 ω
A1A1
A1A2
A2A2
Overdominance – Heterozygous genotype has the highest fitness (balancing selection)
h<0, 1-hs > 1
Underdominance – The heterozygous genotypes has the lowest fitness (diversifying selection)
h>1, (1-hs) < (1 – s) < 1 for s > 0 ω
A1A1
A1A2
A2A2

26. Directional Selection
Δq =-pqs[ph + q(1-h)]
1-2pqhs-q2s
0 ≤ h ≤ 1 1
0.5 Δq
h=0.5, s=0.1 q q
Time

27. Relative Fitness (ω) ω11 ω12 ω22 Relative Fitness (hs) 1 1-hs 1-s
Lethal Recessives
A1A1 A1A2 A2A2
Relative Fitness (ω) ω11 ω12 ω22
Relative Fitness (hs) hs 1-s
For completely recessive case, h=0
What is s for lethal alleles? ω
A1A1
A1A2
A2A2
0.2
0.4
0.6
0.8 1