Lecture 7: Introduction to

SelectionSeptember 11, 2015

Last Time Effects of inbreeding on

heterozygosity and genetic diversity

Estimating inbreeding coefficients from pedigrees

Mixed mating systems

Inbreeding equilibrium

Today Inbreeding and selection:

inbreeding depression

The basic selection model

Dominance and selection

Relatedness in Natural Populations White-toothed shrew

inbreeding (Crocidura russula) (Duarte et al. 2003, Evol. 57:638-645)

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

Nu

mb

er

of

mati

ng

s

Relatedness

Parental Relatedness

Off

sp

rin

g

Hete

rozyg

osit

y

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

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?

Natural Selection Non-random and differential

reproduction of genotypes

Preserve favorable variants

Exclude nonfavorable variants

Primary driving force behind adaptive evolution of quantitative traits

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

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

Number of heterozygous loci

Deng and Fu 1998 Genetics 148:1333

Simulated

Reed and Frankham 2003 Cons Biol 17:230

Correlation Between Heterozygosity and Fitness

Observed

Inbreeding Depression

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

wikipediawww.myrmecos.net/

notexactlyrocketscience.wordpress.com

terrierman.com/inbredthinking.htm

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 heterozygosityEnhanced fitness of heterozygote due to

pleiotropy (one gene affects multiple traits): differentiation of allele functions

Bypass homeostasis/regulation

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?

How do we quantify the effects of natural selection on allele frequencies over time?

Can we predict and model evolution?

Relative Fitness of Diploids Consider a population of newborns with

variable survival among three genotypes:

A1A1 A1A2 A2A2

N 100 100 100

Survival 80 56 40 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:

1

1008010080

11

11

11

M

Ms

s

N

NN

N

Where N11s is number of A1A1

offspring surviving after selection in current generation

And NM is the best-performing genotype

5.0

1008010040

22

22

22

M

Ms

s

N

NN

N

Average Fitness Use genotype frequencies to calculate weighted fitness for entire

population

A1A1 A1A2 A2A2

ω 1 0.7 0.5

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

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

Selection causes increase in more fit genotype and reduction in less fit genotypes

Allele Frequency Change:

q = (N22 + N12/2)/N = (100 + 100/2)/300 = 0.5

q ’ = (40+56/2)/176 = 0.39

Δq = q ’ – q = 0.39 – 0.5 = -0.11

= (0.33)(1)/0.733 = 0.45

Over time, what will happen to p and q in

this population?

What is Δp in the previous example?

Starting from Allele FrequenciesA1A1 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

Change in Allele Frequencies due to Selection (i.e.,

evolution)q2ω22+pqω12

ω

Simplifies to:

Δq =pq[q(ω22- ω12) - p(ω11 – ω12)]

ω

“The single most important equation in all of population genetics and

evolution!”Gillespie 2004, p. 62

See p. 118 in your text for derivation

q2ω22+pqω12 - qω

ω- q =q ’ - q =

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)

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

Heterozygous Effect

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

A1A1 A1A2

A2A2

Relative Fitness (ω) ω11 ω12

ω22

Relative Fitness (hs) 1 1-hs 1-s

Putting it all together A1A1 A1A2

A2A2

Relative Fitness (ω) ω11 ω12

ω22

Relative Fitness (hs) 1 1-hs 1-s

Δq =pq[q(ω22 – ω12) - p(ω11- ω12)]

ωReduces to:

Δq =-pqs[ph + q(1-h)]

1-2pqhs-q2s

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

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

0

0.2

0.4

0.6

0.8

1

AA Aa aa

ω

A1A1 A1A2 A2A2

0

0.2

0.4

0.6

0.8

1

AA Aa aa

ω

A1A1 A1A2 A2A2

0

0.2

0.4

0.6

0.8

1

AA Aa aa

ω

A1A1 A1A2 A2A2

Directional Selection Δq =-pqs[ph + q(1-h)]

1-2pqhs-q2s

0 ≤ h ≤ 1

q

Time10 0.5

Δq

h=0.5, s=0.1q

Lethal Recessives

For completely recessive case, h=0

What is s for lethal alleles?

ω

A1A1 A1A2 A2A2

0

0.2

0.4

0.6

0.8

1

A1A1 A1A2 A2A2A1A1 A1A2 A2A2

A1A1 A1A2

A2A2

Relative Fitness (ω) ω11 ω12

ω22

Relative Fitness (hs) 1 1-hs 1-s