13 Quantitative Selection - Division of Physical...

Lecture 13 Selection on quantitative characters

Selection on quantitative characters

What is a quantitative (continuous) character?

Selection on quantitative characters

What is a quantitative character?

• quantitative characters exhibit continuous variation among individuals.

Selection on quantitative characters

What is a quantitative character?

• quantitative characters exhibit continuous variation among individuals.

• unlike discrete characters, it is not possible to assign phenotypes to discrete groups.

Examples of discrete characters

Example of a continuous character

Height

Two characteristics of quantitative traits:

Two characteristics of quantitative traits:

1. Controlled by many genetic loci

Two characteristics of quantitative traits:

1. Controlled by many genetic loci

2. Exhibit variation due to both genetic and environmental effects

Two characteristics of quantitative traits:

1. Controlled by many genetic loci

2. Exhibit variation due to both genetic and environmental effects

• the genes that influence quantitative traits are now called quantitative trait loci or QTLs.

Quantitative characters can be controlled by small numbers of genes

What are QTLs?

What are QTLs?

• QTLs possess possess multiple alleles, exhibit varying degrees of dominance, and experience selection and drift.

What are QTLs?

• QTLs possess multiple alleles, exhibit varying degrees of dominance, and experience selection and drift.

• some QTLs exhibit stronger effects than others – these are called major effect and minor effect genes, respectively.

What are QTLs?

• QTLs possess multiple alleles, exhibit varying degrees of dominance, and experience selection and drift.

• some QTLs exhibit stronger effects than others – these are called major effect and minor effect genes, respectively.

• the number and relative contributions of major effect and minor effect genes underlies the genetic architecture of the trait.

What are QTLs?

• QTLs possess multiple alleles, exhibit varying degrees of dominance, and experience selection and drift.

• some QTLs exhibit stronger effects than others – these are called major effect and minor effect genes, respectively.

• the number and relative contributions of major effect and minor effect genes underlies the genetic architecture of the trait.

• mapping QTLs is expensive, labor intensive, and fraught with statistical problems!

Mimulus phylogeny

F2 progeny from Mimulus cardinalis x M. lewisii F1 hybrids

Heritability

- heritability does not mean “heritable” or “inherited”!!

- heritability represents the degree to which the trait is determined by genetic and not by environmental effects.

Beans:

Average is 404 mg. Select the top 10% of the population for next years crop (new mean 692 mg). - the mean of the crop from the selected group is 609 mg. - the average seed size has thus increased by 51% over one generation.

Heritability

1. What would have occurred if the variation in bean size was entirely due to environmental effects?

the mean bean size would have remained unchanged (at about 404 mg).

2. What if all of the variation was controlled by genetic factors? the mean bean size in generation 1 would have been about 692 mg.

Heritability Selection differential, S = the “strength” of selection = mean (selected) - mean (whole pop.) = 692 - 404 = 288

Response differential, R = the change in average phenotype due to selection = mean (whole pop. in gen. 1) - mean (whole pop. in gen. 0) = 609 - 404 = 205

Realized heritability, h^2 = R/S = 205/288 = 0.71

- a heritability of 0.71 means that 71% of the variation in bean size in the starting population was due to genetic factors and 29% was caused by the environmental factors

- knowing the heritability of a trait allows us to predict its response to selection.

- (Realized heritability, h^2 = R/S) - the equation above can be rearranged to: Response differential, R = h^2 . S

- this means that the response of the trait to selection is determined by its heritability and by the intensity of selection.

- strong selection acting on a trait with a low heritability will be ineffective!

Heritability

trait h^2

fingerprint 0.98 (# of ridges) head width 0.95 height 0.84 blood pressure 0.70 IQ 0.55 twinning 0.52 handedness 0.32 body weight 0.05

Heritability

What is heritability?

What is heritability?

• heritability is the proportion of the total phenotypic variation controlled by genetic rather than environmental factors.

What is heritability?

• heritability is the proportion of the total phenotypic variation controlled by genetic rather than environmental factors.

The total phenotypic variance may be decomposed:

VP = total phenotypic variance

The total phenotypic variance may be decomposed:

VP = total phenotypic variance VG = total genetic variance

The total phenotypic variance may be decomposed:

VP = total phenotypic variance VG = total genetic variance VE = environmental variance

The total phenotypic variance may be decomposed:

VP = total phenotypic variance VG = total genetic variance VE = environmental variance

VP = VG + VE

The total phenotypic variance may be decomposed:

VP = total phenotypic variance VG = total genetic variance VE = environmental variance

heritability = VG/VP (broad-sense)

The total genetic variance (VG) may be decomposed:

The total genetic variance (VG) may be decomposed:

VA = additive genetic variance

The total genetic variance (VG) may be decomposed:

VA = additive genetic variance VD = dominance genetic variance

The total genetic variance (VG) may be decomposed:

VA = additive genetic variance VD = dominance genetic variance VI = epistatic (interactive) genetic variance

The total genetic variance (VG) may be decomposed:

VA = additive genetic variance VD = dominance genetic variance VI = epistatic (interactive) genetic variance

VG = VA + VD + VI

The total genetic variance (VG) may be decomposed:

VA = additive genetic variance VD = dominance genetic variance VI = epistatic (interactive) genetic variance

heritability = h2 = VA/VP (narrow sense)

What is additive gene action?

What is additive gene action?

Consider 2 genes:

B1B1 B1B2 B2B2

A1A1

A1A2

A2A2

What is additive gene action?

Consider 2 genes:

B1B1 B1B2 B2B2

A1A1 0 1 2

A1A2 2 3 4

A2A2 4 5 6

Estimating heritability

Estimating heritability

• one common approach is to compare phenotypic scores of parents and their offspring:

Estimating heritability

• one common approach is to compare phenotypic scores of parents and their offspring:

Junco tarsus length (cm)

Cross Midparent value Offspring value

Estimating heritability

• one common approach is to compare phenotypic scores of parents and their offspring:

Junco tarsus length (cm)

Cross Midparent value Offspring value

F1 x M1 4.34 4.73

Estimating heritability

• one common approach is to compare phenotypic scores of parents and their offspring:

Junco tarsus length (cm)

Cross Midparent value Offspring value

F1 x M1 4.34 4.73

F2 x M2 5.56 5.31

Estimating heritability

• one common approach is to compare phenotypic scores of parents and their offspring:

Junco tarsus length (cm)

Cross Midparent value Offspring value

F1 x M1 4.34 4.73

F2 x M2 5.56 5.31

F3 x M3 3.88 4.02

← Slope = h2

Regress offspring value on midparent value

Heritability estimates from other regression analyses

Comparison Slope

Heritability estimates from other regression analyses

Comparison Slope Midparent-offspring h2

Heritability estimates from other regression analyses

Comparison Slope Midparent-offspring h2

Parent-offspring 1/2h2

Heritability estimates from other regression analyses

Comparison Slope Midparent-offspring h2

Parent-offspring 1/2h2

Half-sibs 1/4h2

Heritability estimates from other regression analyses

Comparison Slope Midparent-offspring h2

Parent-offspring 1/2h2

Half-sibs 1/4h2

First cousins 1/8h2

Heritability estimates from other regression analyses

Comparison Slope Midparent-offspring h2

Parent-offspring 1/2h2

Half-sibs 1/4h2

First cousins 1/8h2

• as the groups become less related, the precision of the h2 estimate is reduced.

Heritabilities vary between 0 and 1

Heritability estimates from other regression analyses

Comparison Slope Midparent-offspring h2

Parent-offspring 1/2h2

Half-sibs 1/4h2

First cousins 1/8h2

• as the groups become less related, the precision of the h2 estimate is reduced.

Cross-fostering is a common approach

Q: Why is knowing heritability important?

Q: Why is knowing heritability important?

A: Because it allows us to predict a trait’s response to selection

Q: Why is knowing heritability important?

A: Because it allows us to predict a trait’s response to selection

Let S = selection differential

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm S = 10.11 – 8.82 = 1.29 mm

Q: Why is knowing heritability important?

A: Because it allows us to predict a trait’s response to selection

Let S = selection differential

Let h2 = heritability

Q: Why is knowing heritability important?

A: Because it allows us to predict a trait’s response to selection

Let S = selection differential

Let h2 = heritability

Let R = response to selection

Q: Why is knowing heritability important?

A: Because it allows us to predict a trait’s response to selection

Let S = selection differential

Let h2 = heritability

Let R = response to selection

R = h2S

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm S = 10.11 – 8.82 = 1.29 mm

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm S = 10.11 – 8.82 = 1.29 mm

h2 = 0.72

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm S = 10.11 – 8.82 = 1.29 mm

h2 = 0.72 R = h2S = (1.29)(0.72) = 0.93 mm

Predicting the response to selection

Example: the large ground finch, Geospiza magnirostris

Mean beak depth of survivors = 10.11 mm

Mean beak depth of initial pop = 8.82 mm S = 10.11 – 8.82 = 1.29

h2 = 0.72 R = h2S = (1.29)(0.72) = 0.93

Beak depth next generation = 8.82 + 0.93 = 9.75 mm

The selective differential and the selective gradient

The selective differential and the selective gradient

The selective differential and the selective gradient

Selective gradient = β = Selective differential (S) Variance

What are heritability estimates in nature?

What are heritability estimates in nature?

Medium Character Ground finch

Body weight 0.91 Wing length 0.84 Tarsus length 0.71 Bill length 0.65 Bill depth 0.79 Bill width 0.90

• data from Boag (1983)

What are heritability estimates in nature?

Medium Song Character Ground finch Sparrow

Body weight 0.91 0.04 Wing length 0.84 0.13 Tarsus length 0.71 0.32 Bill length 0.65 0.33 Bill depth 0.79 0.51 Bill width 0.90 0.50

• data from Boag (1983) and Smith & Zach (1979)

What are heritability estimates in nature?

What are heritability estimates in nature?

Trait Sample size Mean h2 Std. Error

What are heritability estimates in nature?

Trait Sample size Mean h2 Std. error

Life history 341 0.262 0.012

What are heritability estimates in nature?

Trait Sample size Mean h2 Std. error

Life history 341 0.262 0.012

Physiological 104 0.330 0.027

What are heritability estimates in nature?

Trait Sample size Mean h2 Std. error

Life history 341 0.262 0.012

Physiological 104 0.330 0.027

Behavioral 105 0.302 0.023

What are heritability estimates in nature?

Trait Sample size Mean h2 Std. error

Life history 341 0.262 0.012

Physiological 104 0.330 0.027

Behavioral 105 0.302 0.023

Morphological 570 0.461 0.004

• data from Mousseau and Roff (1983)

1.  Directional selection

2. Stabilizing selection

3. Disruptive selection

Natural selection at the phenotypic level

1.  Directional selection

a form of selection favoring individuals at above or below the mean.

-  this type of selection causes the trait to either increase or decrease in magnitude and, as a result, reduces the population variance.

- example: cranial capacity in early hominid evolution.

Natural selection at the phenotypic level

After selection

During selection N

umbe

r of i

ndiv

idua

ls

Before selection

Normal distribution

Directional selection changes the average value of a trait.

Value of a trait

Body size class

Perc

enta

ge o

f bird

s

40 35

30

25

20

15

10

5

0

40

35

30

25

20

15

10

5

0

Difference in average

1 2 3 4 5 7 8 9 10 11 12 6

Survivors N = 1027

Nonsurvivors N = 1853

For example, directional selection caused overall body size to increase in a cliff swallow population

2. Stabilizing selection

a form of selection favoring intermediate phenotypes.

-  this form of selection reduces variation but does not change the trait’s mean.

- example: birth weight in humans.

Natural selection at the phenotypic level

Normal distribution

High fitness

Value of a trait

Num

ber o

f ind

ivid

uals

After selection

During selection

Before selection

Stabilizing selection reduces the amount of variation in a trait.

20

15

10

5

0 1 2 3 4 5 6 7 8 9 10 11

2

3

5

7

10

20

30

50

70

100

Birthweight (pounds)

Percentage of mortality

Perc

enta

ge o

f Pop

ulat

ion

Heavy mortality on extremes

Mortality

For example, very small and very large babies are most likely to die, leaving a narrower distribution of birthweights.

3.  Disruptive selection

a form of selection favoring both extremes of the phenotypic distribution.

-  this causes the variation of the trait to increase in the population.

- example: beak length in African seedcracker finches.

Natural selection at the phenotypic level

Value of a trait

Low fitness

Normal distribution

Before selection

During selection

After selection

Num

ber o

f ind

ivid

uals

Disruptive selection increases the amount of variation in a trait.

6 7 11 10 8 9

Beak length (mm)

10

0

20

30

Num

ber o

f ind

ivid

uals

For example, only juvenile blackbellied seedcrackers with very long or very short beaks survived long enough to breed.

- the three forms of selection outlined above occur on what are called quantitative or polygenic traits.

- quantitative traits differ from discrete traits in that it is not possible to assign individuals into distinct classes.

Selection on quantitative traits

1.  vary in a continuous fashion among individuals

2. are controlled by many genetic loci.

3. are affected by both genetic and environmental factors.

- to understand and predict the evolution of quantitative characters, we must define an important parameter called heritability.

Selection on quantitative traits

Modes of selection on quantitative traits

Modes of selection on quantitative traits

Directional selection on oil content in corn

Modes of selection on quantitative traits

Stabilizing selection on gall size

Modes of selection on quantitative traits

Disruptive selection in black-bellied seedcracker finches