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Quantitative Genetics:Traits controlled my many loci
So far in our discussions, we have focused onunderstanding how selection works on a small number ofloci (1 or 2).
However in many cases, evolutionary biologists askquestions about traits or phenotypes (for example…)
Many factors may affect a trait, including the action ofalleles at one or more loci, and the environment in whichan individual exists.
Quantitative genetics provides the framework forunderstanding how evolutionary forces act on complextraits.
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Quantitative Genetics I:Traits controlled my many loci
Learning Objectives:
1. To describe how segregation at multiple loci can produce apattern of quantitative variation in a trait.
2. To define the breeding value (A) and relate it to the averageeffects of alleles.
3. To define and differentiate broad and narrow sense heritability.
4. To describe the components of trait (phenotypic) variation anddescribe how and why additive genetic variation is the keycomponent of variation relevant to narrow sense heritability andthe response to selection.
Readings: Chapter 9 in Freeman
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Quantitative genetics vs.population genetics
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Sir Ronald Fisher (1890-1962):Linking quantitative traits
variation and Mendelian genetics
• In 1918, Fisher showed that a large number of Mendelianfactors (genes) influencing a trait would cause a nearlycontinuous distribution of trait values. Therefore, mendeliangenetics can lead to an approximately normal distribution
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This figure showsmeasured phenotypes in apopulation of F2 plantsfrom parents that differin kernel colour.We can see that morethan two or threephenotypes are seen inthe F2. This pattern isexplained by the action ofthree loci.
Wheat kernelcolour variation
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Wheat kernelcolour variation
With three loci, eachwith two alleles, sixphenotypic classes areobtained, and thedistribution ofphenotypes begins tolook like a normalcurve.
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Population genetics
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What are the conditions that will lead to a shiftin the mean value of a trait under selection?
Quantitative genetics
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Human Height: An example of a quantitative trait
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Breeder’s equation
Breeder’s equation: R = h2S
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The first big question inquantitative genetics:
• How much phenotypic variation amongindividuals is due to the presence andinteraction of different alleles, and howmuch is due to differences in theenvironment?
• Answers to this question will determinethe degree to which traits can respondto selection.
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Building a Quantitative GeneticsModel: lessons from agriculture
In quantitative genetics, the phenotypic value (P) of anindividual (e.g. height) is attributed to the genotype ofthe individual and to its environment:
P = G + EThe genotypic value (G) reflects the influence of everygene carried by the individual on the phenotypic value.The environmental deviation (E) is a measure of theinfluence of the environment of the phenotypic value ofan individual.We can see how these components are estimated in anexample from crop yield in wheat.
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Average Yield of three wheat strains overa ten year period (bushels/acre)
43.4952.1845.63Mean
53.565.153.11995
39.853.241.71994
48.862.958.21993
41.549.046.61992
55.471.060.31991
0.00.00.01990
60.566.561.61989
28.425.723.11988
59.572.563.81987
47.555.947.91986
AgassizSewardRoughriderYear
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Average Yield of three wheat strains overa ten year period (bushels/acre)
43.4952.1845.63Mean
53.565.153.11995
39.853.241.71994
48.862.958.21993
41.549.046.61992
55.471.060.31991
0.00.00.01990
60.566.561.61989
28.425.723.11988
59.572.563.81987
47.555.947.91986
AgassizSewardRoughriderYear
Genetic values (G)
Environmental values (E)
63.8 - 45.63 = 18.17
49.0 - 52.18 = -3.18
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Using Genetic values in breeding:The Breeding Value
Genetic value of a parent(80 bushels/acre)
Mean yield of population(60 bushels/acre)
Expected genetic value of offspring (70 bushels/acre)
The genetic value of a genotype reflects the sum totaleffect of all alleles at the loci that affect the trait ofinterest.Given that a parent in a sexual species passes half ofits alleles to the offspring, what is the expectedgenetic value of the offspring? (assume a randomlychosen mate) 336-9 16
Using Genetic values in breeding:The Breeding Value
Genetic value of a parent(80 bushels/acre)
Mean yield of population(60 bushels/acre)
Actual genetic value of offspring (67 bushels/acre)
In reality, the yield of the offspring may differ fromthat predicted on the basis of the genetic value of theparent.Why? - Dominance (interactions among alleles at a locus) - Epistasis (interactions among alleles at different loci)
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Using Genetic values in breeding:The Breeding Value
Breeding Value (A) of the parent genotype(74 bushels/acre)
Mean yield of population(60 bushels/acre)
Actual genetic value of offspring (67 bushels/acre)
The breeding value of a genotype (A) is obtained byadding twice the deviation of the mean (d) of theoffspring from the population mean.
d d
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Breeding Value Example 1
To increase milk yield, dairy farmers estimate thebreeding value of bulls from the average dairyproduction of each bull’s daughters.When a particular bull is mated to several cows,his daughters produce an average of 100 liters ofmilk per day, in a herd with an averageproduction of 75 liters.In terms of dairy production,...what is the breeding value (A) of the bull?(125)...what is the phenotypic value of the bull? (!!)
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Breeding Value Example 2Now say that a particular cow produces 100 liters of milk
per day, compared to a herd average of 75 liters perday.
When mated to different bulls, this cow’s daughtersproduce an average of 80 liters of milk per day.
In terms of dairy production,...what is the breeding value (A) of the cow? (85)...what is the phenotypic value of the cow? (100)What contributes to this difference (assuming no
environmental effects)?If alleles at some loci affect traits differently
depending on the rest of the genotype (Interactions)Dominance (D) (interactions at the same locus)Epistasis (I) (interactions at different loci) 336-9 20
Effects of Dominance
Dominance relationships among alleles at a locus affectthe way in which a trait is transmitted to theoffspring.
A parent that is homozygous (e.g. BB) at a locus thataffects a trait cannot transmit this condition to itsoffspring.
If B is recessive to b, a high fitness BB parent mated toa low fitness bb parent produces only Bb (low fitness)offspring.
Such dominance effects have an impact on traitexpression of the offspring from any cross.
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Effects of Gene Interactions/Epistasis
Similarly, good interaction among the alleles at differentloci are not faithfully transmitted, as illustrated in thesecard hands. Even though Mom and Dad have goodcombinations, they may not combine well in the offspring.
6
!
4
"
A
#
A
$
A
"
5
"
6
"
7
"
8
"
9
"
6
!
4
"
7
"
A
$
9
"
Mom Dad
Offspring 336-9 22
Average Allele Effect
Because of dominance and epistasis, a given allele may notalways have the same effect of the phenotype.
The average effect of an allele accounts for thedifference in the effect of an allele paired with anyother alleles /genes currently found within the population(e.g., accounting for the chance that it is found in aheterozygote or homozygote, in any particular geneticbackground).
The breeding value of an individual (A) represents theaverage effects of all of his/her alleles.
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Expanding the basic quantitativegenetics equation
We earlier described the relationship,
P = G + E,
Which describe the factors that determine an individual’sphenotype, but we now understand that the component G can befurther broken down into:
G= A + D + I,
to describe the components of Genetic effects on the phenotypeattributed to Additive genetic effects (as measured by heBreeding value), Dominance effects and Interaction effects(Epistasis).
Our description of the Breeding value (A) showed that thephenotype of an individual’s offspring is mainly determined by thebreeding value of its parents.
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From individuals to populations:patterns of phenotypic variation
With an understanding of factorsthat determine the phenotype of anindividual, we can move back up tothe level of the population todevelop our understanding of how toestimate the genetic component ofquantitative trait variation.
Q: How much of the phenotypicvariation that we observe is due togenetic variation?How much of this genetic variationcontributes to the response toselection?
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From individuals to populations:patterns of phenotypic variation
The phenotypic variance (VP)measures the extent to whichindividuals vary in phenotype for aparticular trait.
The phenotypic variance within apopulation may be due to geneticand/or environmental differencesamong individuals:
VP = VG + VE
(Ignoring interactions betweengenes & environment)
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From individuals to populations:patterns of phenotypic variation
VP = VG + VE
The genetic variance (VG) can befurther broken down into additive,dominance and interactioncomponents, analogous to thoseused to describe an individualphenotype:
VG = VA + VD + VI
The additive genetic variance (VA)equals the variance in breedingvalues within a population andmeasures the degree to whichoffspring resemble their parents.
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Calculating phenotypic andadditive genetic variances
Example: Milk yield in cows
Variance:
_
Vx= !i (Xi – X)2
---------------
(n – 1)
75mean
10010
799
488
1007
436
825
834
523
882
751
yieldCow
VP = (75-75)2 + (88-75)2 +…n-1
= 425.6
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Calculating phenotypic andadditive genetic variances
Example: Milk yield in cows
Variance:
_
Vx= !i (Xi – X)2
---------------
(n – 1)
78
79.5
64.5
84
66
78.5
79
65.5
81.5
74.5
OffspringYield
75mean
10010
799
488
1007
436
825
834
523
882
751
yieldCow A = (offspring-mean) X 2 + mean
A = 83
A = 93
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Calculating Phenotypic andAdditive Genetic Variance
Example: Milk yield in cows
Variance:
_
Vx= !i (Xi – X)2
---------------
(n – 1)
75.2
81
84
54
93
57
82
83
56
88
74
A
78
79.5
64.5
84
66
78.5
79
65.5
81.5
74.5
OffspringYield
75mean
10010
799
488
1007
436
825
834
523
882
751
yieldCow
VP = 425.6
VA = 205.5
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Calculating Phenotypic andAdditive Genetic Variance
Knowledge of the phenotypicvariance and additive geneticvariance allows us to predicthow similar we expect thephenotypes of parents andoffspring to be.
It will also allow us topredict the magnitude of theresponse to selection whenindividuals with differentphenotypic means havedifferent probabilities ofsurvival or reproduction.
VP = 425.6
VA = 205.5
In the previous example,nearly half of thephenotypic variance wasthe result of additivegenetic variance.
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Narrow-Sense Heritabilityh2 = VA / VP
h2 = VA / (VA + VD + VI + VE)
Heritability can be low due to:
Narrow sense heritability describes theproportion of phenotypic variance due toadditive genetic variance among individuals, orthe extent to which variation in phenotype iscaused by genes transmitted from parents.
Conversely, h2 will be 1 only if there is novariation due to dominance, epistasis, orenvironmental effects. When h2 = 1, P = G = A. 336-9 32
Broad-Sense HeritabilityH2 = VG / VP
H2 = VG / VP
Broad sense heritability describes theproportion of phenotypic variance due to totalgenetic variance among individuals.
Broad-sense heritability will be 1 if all of the phenotypicvariation within a population is due to genotypicdifferences among individuals (VG = VP).Broad-sense heritability will be 0 if all of the phenotypicvariation is caused by environmental differences.
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Important points aboutheritability
1. When we use the term ‘heritability’, we are almostalways referring to narrow sense heritability.
2. Estimates of heritability are not transferable. Theyare specific to the population and the environmentin which they are estimated.
3. Heritability estimates are for populations, notindividuals
4. Heritability does not indicate the degree to which atrait is genetically based. Rather, it measures theproportion of the phenotypic variance that is theresult of genetic factors.
