PBG 650 Advanced Plant Breeding Module 4: Quantitative Genetics –Components of phenotypes...
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Transcript of PBG 650 Advanced Plant Breeding Module 4: Quantitative Genetics –Components of phenotypes...
PBG 650 Advanced Plant Breeding
Module 4: Quantitative Genetics– Components of phenotypes– Genotypic values– Average effect of a gene– Breeding values
Definition:
“Statistical branch of genetics based upon fundamental Mendelian principles extended to polygenic characters”
Primary goal:
To provide us with a mechanistic understanding of the evolutionary process
What is Quantitative Genetics?
Lynch and Walsh, Chapter 1
• How much of the observed phenotypic variation is due to genetic vs environmental factors?
• How much of the genetic variation is additive (can be passed on from parent to offspring)?
• What is the breeding value of the available germplasm?
• Are there genotype by environment interactions?
• What are the consequences of inbreeding and outcrossing? What are the underlying causes?
• Are there genetic correlations among traits?
Questions of relevance to breeders
• Answers to these questions will influence
– response to selection
– choice of breeding methods
– choice of parents
– optimal type of variety (pureline, hybrid, synthetic, etc.)
– strategies for developing varieties adapted to target environments
Questions of relevance to breeders
Phenotypic Value
P = phenotypic value
G = genotypic value
E = environmental deviation
Bernardo, Chapt. 3; Falconer & Mackay, Chapt. 7; Lynch & Walsh, Chapt. 4
P = G + E
For the population as a whole:E(E) = 0
= E(P) = E(G)
Cov(G, E) = 0
Components of an individual’s Phenotypic Value
For individual k withgenotype AiAj
P(ij)k = + gij + e(ij)k
Single locus model
A1A1A2A2 A1A2
-a 0 d a
degree of dominance = a
d
no dominance d = 0partial dominance 0 < d < +a or 0 > d > –a complete dominance d = +a or –aoverdominance d > +a or d < –a
z z+a+d z+2a GenotypicValue
CodedGenotypic Value
The origin ( ) is midway between the two homozygotesP
a-P dP aP P
Single locus model
Different scales have been used in the literature
0 (1+k)a 2a
A1A1A2A2 A1A2
Lynch & Walsh
-a 0 d a
Conversions can be readily made
Falconer
0 au a
0 a 2a+d
Comstock and Robinson (1948)
Hill (1971)
Population mean
FrequencyGenotypic
valueFrequency
x value
A1A1 p2 a p2a
A1A2 2pq d 2pqd
A2A2 q2 –a –q2a
M = p2a + 2pqd – q2a= a(p2 – q2) + 2pqd= a(p + q)(p - q) + 2pqd= a(p - q) + 2pqd
contribution from homozygotes and heterozygotes
Mean on coded scale(centered around zero)
This is a weighted average
Mean on original scale
Population mean
M = a(p - q) + 2pqd
When there is no dominance a(p - q) When A1 is fixed aWhen A2 is fixed -aPotential range 2a
If the effects at different loci are additive (independent), then
M = Σa(p - q) + 2Σpqd
= P + a(p - q) + 2pqd
Means of breeding populations
= P + a(p - q) + 2pqd
In an F2 population, p = q = 0.5
F2 = P + (1/2)d
In a BC1 crossed to the favorable parent, p = 0.75,so after random mating
BC1(A1A1) = P + (1/2)a + (3/8)d
In a BC1 crossed to the unfavorable parent, p = 0.25,so after random mating
BC1(A2A2) = P - (1/2)a + (3/8)d
For ½ A1A1, ½ A1A2
= P + ½(a + d)
For ½ A1A2, ½ A2A2
= P + ½(d - a)
Average effects
• We have defined the mean in terms of genotypic values
• Genes (alleles), not genotypes, are passed from parent to offspring
• Average effect of a gene (i)
– mean deviation from the population mean of individuals who received that gene from their parents (the other gene taken at random from the population)
Gamete
A1A1
aA1A2
dA2A2
-a Freq x valueAverage effect
of a gene
A1 p q pa + qd 1=q[a+d(q-p)]
A2 p q pd - qa 2=-p[a+d(q-p)]
subtract M = a(p - q) + 2pqd
Average effect of a gene substitution
• a and d are intrinsic properties of genotypes
1, 2, and are joint properties of alleles and the populations in which they occur (they vary with gene frequencies)
Average effect of changing from A2 to A1
= 1 - 2
q[a+d(q-p)] – (-p)[a+d(q-p)]
= a+d(q-p)Average effect of changing from A1 to A2 = -
Relating this to the average effects of alleles:
1 = q 2 = -p
Breeding Value
Breeding value of individual Aij = i + j
Breeding Value
GenotypeAverage effect of a
geneAverage effect of a gene substitution
A1A1 21 2qA1A2 1 + 2 (q - p)A2A2 22 -2p
• For a population in H-W equilibrium, the mean breeding value = 0
• The expected breeding value of an individual is the average of the breeding value of its two parents
• For an individual mated at random to a number of individuals in a population, its breeding value is 2 x the mean deviation of its progeny from the population mean.
Regression of breeding value on genotype
Breeding values
• can be measured
• provide information about genetic values
• lead to predictions about genotypic and phenotypic values of progeny
Additive genetic variance• variance in breeding values
• variance due to regression of genotypic values on genotype (number of alleles)
● genotypic value○ breeding value
Genotypic values
• Genotypic values have been expressed as deviations from a midparent
• To calculate genetic variances and covariances, they must be expressed as a deviation from the population mean, which depends on gene frequencies
Genotypic values Genotype Scaled Adjusted for mean
A1A1 a 2q(a-pd) 2q(-qd)A1A2 d a(q-p)+d(1-2pq) (q-p)+2pqdA2A2 -a -2p(a+qd) -2p(+pd)
subtract M = a(p - q) + 2pqd
Remember = a + d(q - p) Substitute a = - d(q - p)
Dominance deviation
Components of an individual’s Phenotypic Value P = G + E
G = A + D
• In terms of statistics, D represents – within-locus interactions– deviations from additive effects of genes
• Arises from dominance between alleles at a locus– dependent on gene frequencies– not solely a function of degree of dominance– (a locus with completely dominant gene action contributes
substantially to additive genetic variance)
Gij = + i + j + ij
Partitioning Genotypic Value
GenotypeGenotypic Value (adj. for mean)
Breeding Value(additive effects)
Dominance Deviation
A1A1 2q(-qd) 2q -2q2dA1A2 (q-p)+2pqd (q - p) +2pqdA2A2 -2p(+pd) -2p -2p2d
When p = q = 0.5 (as in a biparental cross between inbred lines)
Genotype Genotypic Value Breeding Value Dominance
A1A1 -(1/2)d -(1/2)dA1A2 (1/2)d 0 (1/2)dA2A2 --(1/2)d - -(1/2)d
Dominance deviations from regression
-2p2d
2pqd
-2q2dGenotypic Value
A1A1 2q - 2q2d
A1A2 (q-p)+2pqd
A2A2 -2p - 2p2d
Interaction deviation
• Components of an individual’s Phenotypic Value
P = G + E
P = A + D + E• When more than one locus is considered, there may also be
interactions between loci (epistasis)
G = A + D + I
P = A + D + I + E• ‘I’ is expressed as a deviation from the population mean and
depends on gene frequencies
• For a population in H-W equilibrium, the mean ‘I’ = 0