Download Evolution at Multiple Loci

Heritability – “the fraction of the total variation in a trait that
is due to variation in genes.” (Freeman and Herron, 2007)
Typically, this variation is considered as the phenotypic
variation.
Vp – the total variance in the phenotypic trait of a population.
VP = VG + VE
VG = Genetic variation
VE = Environmental variation
Broad Sense Heritability
ℎ2
=
2
h
or
2
H
𝑉𝐺
𝑉𝑃
𝑉
𝐺
2
ℎ =
𝑉𝐺 + 𝑉𝐸
The problem?
VG represents all of the genetic variation as a single value.
Real genetic variation is complicated.
V𝐺 = V 𝐴 + V𝐷 + V𝐼
VA = additive genetic variance
VD = dominance genetic variance
VI = variance due to epistatic interactions
Additive Variation –VA
V𝐺 = V𝐴 + V𝐷 + V𝐼
• Important because it is why relatives resemble each
other.
• Alleles act independently.
• The phenotype of an organism is the sum of the
effect of each allele, hence additive.
• Additive alleles are not affected by the presence of
other alleles.
• The effect of additive alleles allow biologists to follow
evolution in a predictable way.
Additive Variation –VA
V𝐺 = V𝐴 + V𝐷 + V𝐼
A1 = 0.5, A2 = 0.5
Note: The best fit line (far right) explains all of the genetic variation. VG = VA.
Dominance Variation –VD
V𝐺 = V𝐴 + V𝐷 + V𝐼
• The addition of alleles is not additive.
• Dominance is one type of variation where alleles interact
(between sister alleles on other chromosome).
• The effect of an allele depends upon what it is paired with.
• Because of this dependence, the outcome of dominance
variation is not entirely predictable - it is context dependent.
• This context disappears every generation because of
meiosis. The pairing of an allele with a sister allele on
another chromosome in forming a zygote is unpredictable.
• Because of this , the effects of dominance variation change
every generation, and are not predictable.
Dominance Variation –VD
V𝐺 = V𝐴 + V𝐷 + V𝐼
A1 = 0.5, A2 = 0.5
Note: Adding a second copy of A2 does not change the phenotype. The
Dominance Variation (VD) does not explain all of the Genetic Variation (VG).
VG = VA + VD
Epistatic Effects –VI
V𝐺 = V𝐴 + V𝐷 + V𝐼
• The effect of an allele at a locus is dependent the presence of
an allele at another locus.
• The phenotype is dependent upon the allele at one locus
interacting with an allele at another locus. Not a predictable
outcome.
• Allele X may affect the phenotype one way in the presence of
allele A, and affect the phenotype another way in the
presence of allele B.
• Because of this dependence, the outcome of epistasis is not
entirely predictable - it is context dependent.
• This context disappears every generation because of meiosis.
When chromosomes independently assort and recombine, the
pairings of alleles change.
• Because of this , the effects of epistasis change every
generation, and are not predictable.
Narrow-Sense Heritability
ℎ2
=
2
h
or
2
H
𝑉𝐴
𝑉𝑃
𝑉
𝐴
2
ℎ =
𝑉𝐺 + 𝑉𝐸
𝑉
𝐴
2
ℎ =
𝑉𝐴 + 𝑉𝐷 + 𝑉𝐼 + 𝑉𝐸
In determining heritability, only narrow-sense heritability is used,
because only the variation due to additive effects permits
predictions due to selection.
Heritability Determination
How to determine heritability
Heritability is considered in the narrow sense.
Compare the best fit line of
mid-parent trait to midoffspring (mean) trait.
ℎ2
=
𝑉𝐴
𝑉𝐺 + 𝑉𝐸
Heritability Determination
Very important in agricutlure
Heritability Determination
But also useful in humans.
Selection of Quantitative Traits - Breeder’s eq. (R = h2S)
 Evolutionary Response (R = h2S)
Allows us to predict how a trait will change over each generation
R - the response to selection
h2 – heritability (the superscript is symbolic, not functional)
S – selection differential
Bottom-line: Allows us to predict whether selection on a trait will
cause a population to
evolve
Selection of Quantitative Traits - Breeder’s eq. (R = h2S)
 Need to determine differences in Reproductive Success and
Survival
 Strength of Selection is the difference between selected
individuals and the entire population
• Selection Differential (S): Difference between mean of
selected individuals and the mean of entire
population
Selection for longer tails in a
fictitious mouse population.
Selected
individuals
Non-breeders
Entire population
Selection of Quantitative Traits - Breeder’s eq. (R = h2S)
h2 – heritability – in the narrow sense – the fraction of the total phenotypic variation
in the population that is due to the additive effects of genes.
1) Slope of the best fit line between the mid-parent value (x- axis) and the midoffspring (mean) value (y- axis).
2) The rise over the run
Values on the x & y axes are the same as those in the body of the graph.
Selection of Quantitative Traits - Breeder’s eq. (R = h2S)
Selection gradient - A measure of the strength of selection
– related to the selection differential.
𝑺
𝒗𝒂𝒓 (𝒕𝒓𝒂𝒊𝒕)
What is the variance? (see Phenotypic and Genetic variation in
𝑦2
2
Brassica – Part I & II) 𝑠 =
𝑛
Selection of Quantitative Traits - Breeder’s eq. (R = h2S)
Selection gradient - A measure of the strength of selection
Two ways to determine
𝑷𝒔 −𝑷
1)
where Ps = Mean of breeders and P = whole
𝒗𝒂𝒓 (𝑷)
original population .
2) Slope of the line between the relative fitness of the breeders
and the non-breeders.
Breeders have a fitness = 1 (n = 10)
Non-breeders have a fitness = 0 (n = 20)
Mean fitness of 30 mice = 0.33
Relative fitness is =
𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑓𝑖𝑡𝑛𝑒𝑠𝑠
𝑚𝑒𝑎𝑛 𝑓𝑖𝑡𝑛𝑒𝑠𝑠
For breeding mice-
1
0.33
=3
Selection of Quantitative Traits - Breeder’s eq. (R = h2S)
Directional: Fitness increases (or decreases) with value of trait
Stabilizing: Intermediate individuals have the highest Fitness
Disruptive: Extreme individuals have the highest Fitness