Evolution at Multiple Loci:Quantitative Genetics

I. Rediscovery of Mendel and Challenges to Natural Selection

• Do traits that exhibit continuous variation have a genetic basis?

• If the only traits which have genetic variation are controlled by one or two loci then natural selection not as important as mutation

• Darwin envisioned evolution to be a continuous process of selection acting on limitless genetic variation, with small changes occurring in any one generation, but large changes occurring over long periods.

Why the normal distribution: Central Limit Theorem

Mendelian genetics can explain quantitative traits

Ex. 1: NILSSON-EHLE: Red and White Kernel Color in Wheat (red dominant, white recessive)

Ex. 2:East’s workwith tobacco

Quantitative traits are influenced by the environment as well as genotype

Yarrow plant

1. Fisher’s prediction

Mutation Effect

Prob

abili

ty o

f Fix

atio

n

2. Kimura’s modification

3. Orr’s modification

II. Neo Darwinian SynthesisTheoretical models that support vs. contend the Darwinian model

Typical results

Corolla Width (mm)

F2

BC

F1M. micranthus M. guttatus

F1

F2

Fenster & Ritland 1994

Testing the Models:

No filter

Filtered image—“bumblevision”

SegregationOf floral typesDemonstrateGenetic basisOf trait Differences

Convergent evolution??

Yosemite Sam thinks so

in the F2 generation

MC Qc

ML QL

ML QL

MC Qc

x

MC Qc

ML QL

If the map distance is 5 cm then there is a 95% chance that the marker will be associated with the QTL in the F2:

1- r(MQ)

MC1 Qc MC2

MC1 Qc MC2

x

If the map distance between markers and QTL are 5 cm then there is a 99.5% chance that one of the markers will be associated with the QTL in the F2:

1-2 r(M1Q)(QM2)

ML1 QL ML2

ML1 QL ML2

MC1 Qc MC2

ML1 QL ML2

xx

1. Fisher’s prediction

Mutation Effect

Prob

abili

ty o

f Fix

atio

n

2. Kimura’s modification

3. Orr’s modification

Theoretical models that support or contend with the Darwinian model

Alleles with a distribution of effect sizes contribute to adaptations

III. Measuring Selection and Response to Selection on Continuous Traits

A. Heritability

Song sparrows

Galapagos finches

58 60 62 64 66 68 70 72 74Femal eHt

0

0. 05

0. 1Density

90 105 120 135 150 165 180 195 210Femal eWt

0

0. 005

0. 01

0. 015Density

Class Data

Female Wt

Female HT

100 125 150 175 200 225 250 275Mal eWt

0

0. 005

0. 01

0. 015Density

62. 5 65. 0 67. 5 70. 0 72. 5 75. 0 77. 5Mal eHt

0

0. 05

0. 1

0. 15

Density

Male Wt

Male Ht

Model Equat i onFemal eWt = 91. 1457 + 0. 2807 Mot her Wt

100 150 200 250Mot her Wt

100

150

200

FemaleWt

Heritability of Female Wt

Model Equat i onFemal eWt = 75. 0179 + 0. 3094 Fat her Wt

150 200 250 300Fat her Wt

100

150

200

FemaleWt

Heritability of Female Wt

Model Equat i onFemal eWt = 57. 2357 + 0. 4499 Mi dPar ent Wt

150 200 250Mi dPar ent Wt

100

150

200

FemaleWt

Heritability of Female Wt

Model Equat i onFemal eHt = 48. 4108 + 0. 2592 Mot her Ht

55 60 65 70 75Mot her Ht

60

65

70FemaleHt

Heritability of Female Ht

Model Equat i onFemal eHt = 26. 1514 + 0. 5575 Fat her Ht

65 70 75Fat her Ht

60

65

70FemaleHt

Heritability of Female Ht

Model Equat i onFemal eHt = 23. 3220 + 0. 6198 Mi dpar ent Ht

62 64 66 68 70 72Mi dpar ent Ht

60

65

70FemaleHt

Heritability of Female Ht

Model Equat i onMal eWt = 137. 452 + 0. 1867 Mot her Wt

100 150 200Mot her Wt

150

200

250

MaleWt

Heritability of Male Wt

Model Equat i onMal eWt = 107. 950 + 0. 2951 Fat her Wt

150 200 250 300Fat her Wt

150

200

250

MaleWt

Heritability of Male Wt

Model Equat i onMal eWt = 99. 5721 + 0. 3870 Mi dPar ent Wt

150 200 250Mi dPar ent Wt

150

200

250

MaleWt

Heritability of Male Wt

Model Equat i onMal eHt = 29. 1168 + 0. 6420 Mot her Ht

60 65 70Mot her Ht

65

70

75

MaleHt

Heritability of Male Ht

Model Equat i onMal eHt = 31. 2457 + 0. 5623 Fat her Ht

65 70 75Fat her Ht

65

70

75

MaleHt

Heritability of Male Ht

Model Equat i onMal eHt = 14. 7069 + 0. 8275 Mi dpar ent Ht

62 64 66 68 70 72Mi dpar ent Ht

65

70

75

MaleHt

Heritability of Male Ht

Conclusions from class data:

Distributions of Wts and Hts are roughly normal

Distribution indicates that Wts and Hts are likely controlledby many loci, = many loci are segregating alleles that contribute to wt and ht differences among individuals

Heritabilities for Ht >> WT 50% >> 30%

Interpretation for other human traits??

Red

Red

Black

B. Selection

Functional significance of trait variation

S=

S= t* - t

t

t*

C. Response to Selection

The “2” term is meaningless, just an historical artifact of the derivation

The slope of the best-fit line is 0.13

Stabilizing selection on a gall-making fly

Disruptive selection on bill size in the black-bellied seedcracker

IV. Phenotypic Plasticity

Inducible defenses in Daphnia

Genetic by Environment Interaction

in yarrow

Low Altitude Site (Stanford)

High Altitude Site, Mather California

Plasticity can evolve

Conclusion• Continuous traits are common• Continuous traits can be heritable• Continuous traits can respond to

selection• Darwin’s notion of natural selection

acting on continuous variation is consistent with evidence

• Genetic x Environment interactions may be important

• G x E is a trait that can evolve