Quantitative Inheritance - Pt.2
Chapter 8
1
Offspringparent
regression for
height in
humans (and
why it’s
called
regression)
(Fig. 8.11d)
2
Assumptions of offpring-parent regression as
an estimate of heritability
• The most important assumption being made
in these analyses is that the only cause of
resemblance between offspring and parents
is shared genes
• This assumption may be violated if parents
and offspring share the same environment
and if environment has strong effects on the
trait
3
“Cross-fostering” and heritability of beak
length in song sparrows (Fig. 8.12) - 1
4
“Cross-fostering” and heritability of beak
length in song sparrows (Fig. 8.12) - 2
5
Estimating heritability from twin studies (Fig. 8.14)
If heritability is high both
monzygotic and dizygotic
twins should resemble each
other, but monzygotic twins
should resemble each other
more closely than dizygotic
twins (because the former
share all their genes, while
the latter share only half
their genes)
If heritability is low, then
neither type of twin should
show close resemblance
6
The heritability (H2 ?) of “general cognitive ability” as measured in a
study of Swedish twins is about 0.62 (Fig. 8.1c)
7
Estimating heritability from crosses between inbred lines:
Corolla height in longflower tobacco (see Fig. 8.3)
• F1 individuals all
have same
heterozygous
genotype.
Therefore F1
variance = VE
• F2 individuals have
variable genotypes
(homozygotes and
heterozygotes).
Therefore, F2
variance = VG + VE
• VG = (F2 variance)
minus (F1 variance)
8
Measuring the strength of directional selection (Fig. 8.15)
Selection for increased tail length in mice
9
Selection differential and selection gradient
• The directional selection differential, S, is the
difference between the mean phenotype of the
selected parents (t* in the previous slide), and the
mean phenotype of the entire population from
which the parents were selected (t “bar” in the
previous slide). It allows us to predict the
evolutionary response of a population to selection.
• The selection gradient is the relationship between
relative fitness and the phenotypic value. It shows
how strongly phenotypic variation affects fitness.
10
Fitness
Two-trait analysis of selection on Geospiza fortis on Daphne
Major during the drought of 1976-77 (Fig. 8.16)
Beak width
11
Two-trait analysis of antipredator defenses in garter snakes
(Brodie 1992)
For striped snakes, the
best survival strategy
is straight-line escape.
For unstriped or
spotted snakes, the best
survival strategy is to
reverse direction many
times
12
The evolutionary response to
directional selection
• Evolutionary response (in generation t + 1)
to a directional selection episode (in
generation t), R = h2S
• R is the change in the mean phenotype of
the population over one (or more)
generation(s)
• Note: if h2 = 0, the population will not
evolve
13
Response to directional selection, R = h2S
14
Response to selection for increased tail-length in
mice
• Di Masso et al. (1991) selected for longer tails in mice for
18 consecutive generations.
• Average tail length increased by about 10%
– This is a rather modest selection response
– It suggests that the heritability of tail length in this population of
mice was low, or that the intensity of selection, S, was low, or both.
– A selection response, R, indicates that a trait is heritable, h2 = R/S,
and that there is additive genetic variance for the trait (in this case
tail length)
– Closer analysis showed that long-tailed mice had more vertebrae in
their tails (28 vs. 26-27 in controls)
– Therefore, what was actually heritable (had additive genetic
variance) was number of tail vertebrae
15
Selection response in Geospiza fortis,
revisited
From the figure at left,
R = 9.7 - 8.9 = 0.8 mm
Average beak depth of
the survivors of the
drought was ~ 10.1 mm:
S = 10.1 - 8.9 = 1.1 mm
Therefore, the realized
heritability of beak
length is:
h2 = R/S = 0.8/1.1 = 0.73
16
Heritability and natural selection on flower size in alpine
skypilots (Candace Galen 1989, 1996)
•
•
•
•
•
A perennial Rocky Mountain wildflower
Flowers are about 12% larger in tundra populations vs.
timberline populations
Tundra populations are pollinated almost exclusively by
bumblebees
Timberline populations are pollinated by a variety of
insects
Questions:
1) Is flower size in skypilots heritable?
2) Do bumblebees select for larger flowers?
17
Is flower size in skypilots heritable?
• Offspring- single parent regression
– Measure diameters of 144 parents from small-flowered timberline
population
– Collect seeds from parents and germinate 617 seedlings in
laboratory
– Transplant seedlings to random locations in same habitat as parents
– Measure flower size in 58 surviving offspring seven years later
• The estimate of heritability was h2 = 1, but this has low
precision. With more confidence, Galen concluded that
0.2 ≤ h2 ≤ 1
18
Estimating the heritability of flower size in alpline
skypilots (Fig. 8.20)
The slope of the regression line
is about 0.5
Since this is offspring - single
parent regression, h2 = twice
the slope, or about 1.0
19
Do bumblebees select for larger flowers?
• Large screen-enclosed cage at study site with 98
transplanted skypilots + bumblebees (but no other
pollinators)
• Measured flowers and later collected seeds
• Germinated seeds in lab then planted seedlings at random
locations in natural habitat
• Six years later counted all the surviving offspring (=
fitness) that had been produced by each of the original
caged parents
• Calculated selection gradient on parents (relative fitness vs
flower size)
20
The selection gradient on flower size in alpine
skypilots (Fig. 8.21)
The slope of the line
(the selection
gradient) is about
0.13
This corresponds to a
selection differential,
S = 5%
(S = VP x selection
gradient)
21
Response to selection on flower size in alpine
skypilots
• Using the relationship R = h2S, and an estimate of
S = 5%, the single-generation response to
selection would be 1% (h2 = 0.2) to 5% (h2 = 1.0)
• Therefore, it would not take very many
generations for selection by bumblebees to
produce the 12% difference in flower size seen
between tundra and timberline populations of
skypilots
22
Selection on flower size in alpine sky pilots – two
questions
• How do we know that bumblebees are doing the
selecting? Maybe plants with bigger flowers
produce more offspring even without bumblebees
– Galen (1989) previously documented that plants with
larger flowers attract more bumblebees and plants that
attract more bumblebees produce more seeds
– Experimental controls: when plants are hand pollinated
or pollinated by other insects, there is no relationship
between flower size and fitness
• If bumblebees are constantly selecting for larger
flowers, why aren’t flowers getting bigger and
bigger?
23
Modes of selection
(Fig. 8.23)
24
Modes of selection and genetic variance
• Long-term directional phenotypic selection tends to reduce
phenotypic and genetic variance (it results in fixation of
alleles, as in our one-locus genetic models of selection)
• Long-term stabilizing selection also tends to reduce
phenotypic and genetic variance (it is not like single-locus
overdominant selection, which tends to preserve genetic
variation)
• Disruptive selection increases phenotypic variance in the
short-term. However, it is generally thought to be
uncommon because it will be unstable in a random mating
population (similar to single-locus underdominance), or
will favor reproductive isolation between alternative
phenotypes
25
Stabilizing selection on gall size in a gall-making fly
(Weis and Abramson, 1986)
• Fly larva (Eurosta solidaginis) induces host plant
goldenrod (Solidago altissima) to make a gall,
inside of which the larva develops
• Parasitic wasps attack fly larvae in small galls
• Birds eat larvae in large galls
• Larvae in medium size galls have highest survival
rate
26
Stabilizing selection on a
gall-making fly (Fig. 8.24)
27
Disruptive selection
on beak size in the
black-bellied seed
cracker (Smith 1993)
(Fig. 8.25)
• Adult birds have
either large or
small beaks
• Birds in the two
groups
specialize on
different kinds
of seeds
• Figure shows
survival of
juveniles in
relation to beak
size
28
Misunderstanding and misusing quantitative genetics – 1
• h2 = 0 means only that none of the phenotypic variation among
individuals is due to genetic differences among individuals
• h2 = 0 does not mean that genes do not “determine” the phenotype
• To understand this, consider the example that we have used of
inheritance of corolla height in longflower tobacco
• In a true-breeding (homozygous) parental line, all individuals have the
same genotype and the heritability of corolla height is zero within that
parental line
• However, the experiment also demonstrates that corolla length is under
genetic “control” and that the parental lines have genes that influence
corolla height
– The two parental lines have consistently different corolla heights when
grown in the same environment
– The F2 plants have increased phenotypic variance relative to the
genetically uniform F1 and the homozygous and genetically uniform
parental lines
– Starting with the F2, subsequent generations show a response to selection
29
Corolla
height in
longflower
tobacco (Fig.
8.3)
30
Misunderstanding and misusing quantitative genetics – 2
• Estimates of genetic variance and heritability apply only to the group or
population in which they are made
• Knowing that a trait has high heritability tells us nothing about the
causes of differences in mean phenotypes between groups or
populations
• Several studies indicate that the heritability of IQ score is ≥ 0.30
• On comparable IQ tests, Japanese children score, on average, about 10
points higher than white Americans
• Are Japanese genetically “smarter” than Americans?
• What other factors might explain the difference in average IQ scores?
• Can you design an experiment to test your hypothesis?
• Aside from the obvious ethical issues, what problems might such an
experiment encounter?
31
All of the difference
in average plant
height between these
two genetically
identical
“populations” of
Achillea is due to
environmenal effects
(Clausen, Keck and
Heisey) (Fig. 8.26)
Mather is in the foothills of the
Sierra Nevada mountains
Stanford is low altitude and near
the Pacific coast
32
Populations of Achillea at different elevations are genetically
different - but the direction of difference depends on the
elevation of the “common garden” (Fig. 8.29)
Our conclusion about which population
is genetically “programmed” to have
plants with more stems will depend on
where we chose to do the experiment.
This is an example of genotype by
environment interaction
33