Transcript Mechanisms in variability

Variation and its inheritance
The foundation of inheritance is the laws of Mendelian
genetics. Mendel succeeded and understood particulate
(discontinuous or discrete) inheritance.
Darwin also undertook experiments on plant inheritance, but
failed to recognize the significance of his results.
Darwin studied inheritance
of flower form in Antirrhinum
(snapdragon). Most flowers
are asymmetric, but occasionally symmetric flowers occur.
This is discontinuous variation.
Darwin did the same thing as Mendel – he crossed
snapdragons that produced asymmetrical flowers (normal,
wild type) with plants that produced peloric (symmetrical)
flowers.
In the F1 generation, all plants had asymmetrical flowers.
He produced an F2 generation by self-pollination of F1
flowers. Among the F2s he found the following:
88/127: asymmetrical
2/127: intermediate
37/127: peloric
What would you say about this pattern of inheritance?
Darwin did not recognize what these numbers suggested.
Do we need to go over Mendelian one and two factor
inheritance?
The Law of Segregation?
The Law of Independent Assortment?
What Darwin had found was Mendelian inheritance of flower
shape. Such patterns are called heteromorphism.
The wild type parents were SS.
The peloric parent had the genoptype ss.
All F1s were heterozygous Ss.
Within tolerances, the F2s showed a 3:1 ratio of phenotypes,
and, most likely, a 1:2:1 ratio of genotypes.
Situations involving discontinuous traits like Mendel’s flower
colour (and other traits) in peas and Darwin’s flower shape in
snapdragons involve what are called major gene inheritance.
An only slightly more complicated example is a
polymorphism in white clover, Trifolium repens, with respect
to the production of cyanogenic glycosides and the release of
cyanide when leaves are damaged (as a defense). The
production of the glycoside is under the control of one locus,
and the presence of allele Ac.
The release of cyanide is under the control of a second locus.
Recessive homozygotes (li/li) do not produce the enzyme
linamarase required to release cyanide. Only plants with the Li
allele are cyanogenic.
Genes with discrete patterns of inheritance that are easily
scored, are often used as “marker genes” to track populations.
However, it was remarkable and statistically unlikely that
Mendel stumbled on 7 unlinked traits with discrete
inheritance. Most traits are polygenic, and are inherited with
continuous distributions of quantitative characteristics.
Discontinuous traits tend not to be strongly influenced by
environmental conditions.
Continuous traits are much more frequently affected by
environmental conditions.
The multiple loci involved in regulation of continuous traits
are not individually different from the loci Mendel studied. To
distinguish them, they are collectively and individually called
Quantitative Trait Loci (or QTLs).
Given that quantitative traits tend to respond to environmental
conditions, the way in which a quantitative trait responds to a
range of conditions is called the reaction norm, and the
variation in phenotype is called phenotypic plasticity. The
plasticity itself may have a heritable component.
Reaction norms of plant size for maternal
families of Abutilon theofrasti across a range
of soil nutrient conditions.
Note that the reaction norms are not identical. When
phenotypic differences between genotypes vary (differ)
between environments, we say there is a genotype x
environment interaction.
One example of this is the response of the plant world’s “lab
rat”, Arabidopsis thaliana, to cold treatment. Either seeds
were vernalized for 4 weeks, or rosettes of leaves were coldtreated for the same time.
The time to bolting (growing a flowering stalk) was measured
for different genotypic families. There was clear evidence of
considerable difference, ranging from little response to large
response, across the range of families studied…
In the last example there is clear evidence of both genetic and
environmental effect on the ‘bolting phenotype’. In it we know
the genotypes. In most situations involving quantitative
inheritance, we don’t know as much.
How do you separate the effects of genetic and environmental
variability on phenotypic variation?
One method is to remove environmental variation by growing
plants in a common garden. This was the approach of Clausen,
Keck and Hiesey (1948) in studying variation in yarrow from
the Pacific coast near Stanford University up the Sierra
Nevada mountains. In their native environments the plants
varied in size and stature. All grown in a common garden at
Stanford…
In the absence of environmental variation, the in plant
architecture observed among these populations of Achillea
lanulosa must be genetic.
The common garden is not a native habitat for any of those
populations. Another approach is a reciprocal transplant study.
Plants are moved between habitats where they differ (and as
control removed and replanted in the same habitat).
Differences in some phenotypic characteristic that persist
across habitats have a genetic component, and differences in
the variation between habitats demonstrates an environmental
component.
In general, we can, in theory, specify a phenotypic value (size,
height, leaf area, or whatever) as the sum of a genotypic value
and environmental deviation:
P=G+E
Maybe someday we’ll be able to specify the genotypic value
in an individual from DNA sequences. However, we can use
the population level variability to assess the contributions of
genes and environment to phenotypes:
The total phenotypic variation is the sum of contributions
from genetic and environmental causes ( and a covariance of
genes and environment):
VP = VG + VE + covGE
What fraction of the total variation is due to genetics?
VG/VP
This ratio is called the broad-sense heritability.
Genetic variation, to be thorough, should be subdivided. Only
a fraction of it is ‘available’ to selection. That portion is called
the additive component, VA.
There is also a component commonly called dominance
deviation. This refers to differences in phenotypic expression
due to the character of the other allele at the same locus.
And there is a third component due to epistasis, which is the
effect on the phenotypic expression of a gene due to the
characteristics of alleles at other loci.
The examples in the text show how dominance (box 6A) and
epistasis effect phenotypes:
Assume plant height is determined by a single diploid locus.
There are no environmental effects on height. Genotype AA
produces plants 100cm tall, aa plants 20cm tall.
If individuals with genotype Aa all have the intermediate
height (60cm), then the effects of alleles A and a are strictly
additive; there is no evidence of dominance or epistasis.
However, what would you find if the A allele is dominant to
a? (Remember that we don’t know what the parental or
offspring genotypes are; all we know is the measured height
of parents and offspring)
If both parents are AA, then all offspring will be 100cm tall.
If one parent is AA and one Aa, all offspring will be 100cm
tall.
If both parents are aa, then all offspring will be 20cm tall.
If both are Aa, then ¾ of the offspring will be 100cm tall, and
¼ will be 20cm. The average among offspring will be 80cm.
Difference from the parental average indicates dominance.
Epistasis: assume that these plants have two phenotypes for
leaf shape – lanceolate and ‘heart-shaped’ (cordate).
How would we explain differences in height that are effected
by leaf shape?
Plants with the AA genotype are 110cm tall with lanceolate
leaves, and 90cm with cordate leaves.
Plants with the aa genotype are 15cm with lanceolate leaves
and 25cm with cordate leaves.
The effects need not be opposite on the two genotypes, but the
only explanation is that there is an epistatic interaction
between the height determining locus and the leaf shape locus.
So, the complete equation is:
VP = VA + VD + VI + VE + VGxE + covGE
A quick reminder of the statistics you may have forgotten. The
variance of a characteristic is:


xi  x


s2 
n1
_
2
xi is a single measure of the characteristic
_
x is the mean of measurements of the characteristic
n is the number of measurements made (if only a sample of
individuals is measured. If all are measured then the proper
denominator is n.
When a plant can be cloned, you can sort out VE and get at the
components that way, having removed VG.
Another frequent question is how many genes are involved in
determining the quantitative trait under study? You can
determine that if you can create two different inbred
(homozygous) lines.
The two parental lines are genetically uniform, so all variation
in each line must be environmental. Now cross the two lines.
All offspring will be heterozygous at all involved loci. But
variance among individuals is still all environmental.
Now cross the F1 heterozygotes. The F2s will vary genetically
as well. The difference between variances in the F1s and F2s
estimates VG.
Here’s what the experiment looks like genetically:
F2 generation
Gene 1:
Gene 2:
Gene 3:
Gene 4:
A1/A1
Or
A1/A2
Or
A2/A2
B1/B1
Or
B1/B2
Or
B2/B2
C1/C1
Or
C1/C2
Or
C2/C2
D1/D1
Or
D1/D2
Or
D2/D2
– For these 4 loci, 3 X 3 X 3 X 3 = 81 different genotypes are
possible
The variation observed in these F2s includes both genetic
variation among the 81 different possible genotypes and the
environmental variance which should still be equal to that
seen in the parental and F1 generations. Now we can estimate
VG.
VG = variance in F2 – variance in F1
If we assume each locus has equal impact on the observed
phenotype, then the number of loci involved is estimated as:
n = (mean of line 1 – mean of line 2)2
4VG