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Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber
957.321
Heinrich Grausgruber Department of Crop Sciences
Division of Plant Breeding
Konrad-Lorenz-Str. 24
3430 Tulln Sources: Nespolo (2003); Le Rouzic et al. (2007)
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 2
TRAITS AND VARIATION
(1) Qualitative traits → discontinous variation
VK Shumny B. Steffenson X Chang
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 3
TRAITS AND VARIATION
(2) Quantitative traits → continous variation
S Pearce et al (2011) Baron et al. (2012)
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 4
TRAITS AND VARIATION
Polygenic/oligogenic inheritance
1909: H. Nilssohn-Ehle → wheat seed colour
R1R1R2R2 (very dark red) × r1r1r2r2 (white)
↓
R1r1R2r2
↓
1 : 2 : 2 : 1 : 4 : 1 : 2 : 2 : 1
R1R1R2R2 : R1R1R2r2 : R1r1R2R2 : R1R1r2r2 : R1r1R2r2 : r1r1R2R2 : R1r1r2r2 : r1r1R2r2 : r1r1r2r2
1 : 4 : 6 : 4 : 1
very dark red : dark red : medium red : light red : white
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 5
TRAITS AND VARIATION
Homework
Work out the segregation of the cross R1R1r2r2 × r1r1R2R2
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 6
TRAITS AND VARIATION
Transgression
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 7
TRAITS AND VARIATION
Transgression
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 8
ENVIRONMENTAL INFLUENCE
Traits measured on individual plants or on progenies are called PHENOTYPE. The
phenotype is the result of the GENOTYPE modified by the ENVIRONMENT.
The genotypic value is the mean phenotype of the plants of one genotype across all
possible environments. The environmental influence can be positive or negative and
results in a phenotypic value above or below the genotypic value.
P = G + E
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 9
ENVIRONMENTAL INFLUENCE
1903: Wilhelm JOHANNSEN
First time usage of the terms ‘gene’, ‘genotype’, ‘phenotype’
Experiment on the inheritance of the seed weight of Phaseolus bean
→ continous variation ist partly genetically, partly environmentally determined. Garden
bean is a self pollinating crop, hence, the plants of one variety are homozygous →
progenies of a homozygous plant are genetically identical and the observed variation is
caused only by the environment
→ ‘pure line’ → variety ‘Princess’ was obviously a mixture of different genotypes with
genetically determined differences with respect to seed weight → first selection was
successful
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 10
ENVIRONMENTAL
INFLUENCE
1903: Wilhelm JOHANNSEN No 19 No 1
0.351 g 0.6426 g
0.358 g 0.348 g 0.631 g 0.649 g
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 11
GENOTYPE BY ENVIRONMENT INTERACTION
Fixed effects
Environmental factors which are fixed already before sowing of the experiment, e.g.
climate region, agronomic factors (sowing time, seed density, fertilization rates etc.)
Random effects
Environmental factors which influenced by random variaiton and, therefore, can‘t be
predicted before trial set up, e.g. climatic conditions during the vegetation period,
breeding lines which present a random sample of the whole population, etc.
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 12
→ one single experiment doesn‘t allow general conclusions, therefore, experiments on
quantitative traits have always to be carried out over multiple sites and years
→ METs: multi-environment trials; multiple sites account for differences in climate and
soil conditions, multiple years for climate changes over time
→ different genotypes can exhibit different interaction patterns and sizes; genotypes
with minimal interaction can be selected
GENOTYPE BY ENVIRONMENT INTERACTION
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 13
GENOTYPE BY ENVIRONMENT INTERACTION
→ first it is of interest to check how important the genotype by environment interaction
is in comparison to the main effects (genotype, environment) → analysis of variance
²𝑷 = ²𝑮 + ²𝑬 + ²𝑮𝑬 → 𝒔²𝑷 = 𝒔²𝑮+ 𝒔²𝑬+ 𝒔²𝑮𝑬
The desirable genotype should show minimum interaction with the environment (↑
phenotypic stability, broad adaptation, yield stability).
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 14
GENOTYPE BY ENVIRONMENT INTERACTION
Quantitative variation can be the result of
many genes (polygenic inheritance) with or
without environmental influence or one/few
genes with strong environmental influence Source: Becker (1993)
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 15
HERITABILITY
Heritability is the relative impact of the genotype on the observed variation. Heritability
is determined by e.g. the estimation of variance components. Thereby the genotypic
variance is calculated and related to the phenotypic variance.
Selection experiments: the higher the heritability, the higher is the response to
selection. Therefore, the heritability of the original population can be calculated based
upon the response to selection.
Breakdown of the genotypic value:
𝒔²𝑮 = 𝒔²𝑨+ 𝒔²𝑫+ 𝒔²𝑰
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 16
HERITABILITY
Additive effects and dominance
Additive effects, breeding value (A): sum of the average effects of alleles. Without dominance the
breeding value is equivalent to the genotypic values. If partial or full dominance is present, the
breeding value of a heterozygous genotype is lower as its genotypic value as a part of the progenies
will segregate homozygous for the unfavourable allele. The difference between breeding value and
genotypic value is called dominance deviation (D).
Epistasis
The genotypic value of an individual is not always the sum of the genotypic values of single genes.
It happens that two genes exhibit a negative or positive effect on one trait not before they are
appearing in combination. Such an interaction between genes is called epistasis (I).
𝒔²𝑷 = 𝒔²𝑨+ 𝒔²𝑫+ 𝒔²𝑰+ 𝒔²𝑬+ 𝒔²𝑮𝑬
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 17
HERITABILITY
Broad sense heritability, h²b
𝒉²𝒃 =𝒔²𝑮𝒔²𝑷
Narrow sense heritability, h²n
𝒉²𝒏 =𝒔²𝑨𝒔²𝑷
Heritability is the ratio of the phenotype which can be explained by the genotype; heritability, however, provides no
information on the es no information on the number of involved genes, nor their localistion or gene products.
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 18
HERITABILITY
Types of calculation in segregating populations
Idea: Estimation of the environmental variance on genetically homogenous populations (parents, F1),
Estimation of the total phenotypic variation (s²P) on the segregating F2-generation, which represents
the total possible genetic variance but includes also the environmental influence.
Mahmud & Kramer
𝒉²𝒃 =𝒔²𝑭𝟐− 𝒔²𝑷𝟏× 𝒔²𝑷𝟐
𝒔²𝑭𝟐
Example: plant height wheat
Weber
𝒉²𝒃 =𝒔²𝑭𝟐 − 𝒔²𝑷𝟏 × 𝒔²𝑷𝟐 × 𝒔²𝑭𝟏
𝟑
𝒔²𝑭𝟐
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 19
HERITABILITY
Calculations
Parent-offspring correlation
𝒉²𝒃 =𝒓𝒐𝒃𝒔𝒆𝒓𝒗𝒆𝒅𝒓𝒆𝒙𝒑𝒆𝒄𝒕𝒆𝒅
Parent-offspring regression
𝒉²𝒃 = 𝒃
Example: milk yield of cows
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 20
Wray & Visscher (2008) Estimating trait heritability. Nature Education 1(1)
http://www.nature.com/scitable/topicpage/estimating-trait-heritability-46889
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 21
HERITABILITY
Calculations
Method according to Allard (Backcross-method): variances of parents F1, F2 and back-crosses of F1 to both parents
(BC1 and BC2) allow the breakdown of the genetic variance s²G to the components s²A and s²D and, therefore, the
estimation of broad and narrow sense heritability. s²F2, s²BC1, s²BC2 as well as s²P1, s²P2 and s²F1 are determined from
the experiment
Expected values
𝒔²𝑭𝟐 =𝒔²𝑨𝟐
+𝒔²𝑫𝟒
+ 𝒔²𝑬
𝒔²𝑩𝑪𝟏+ 𝒔²𝑩𝑪𝟐 = 𝒔²𝑨𝟐
+𝒔²𝑫𝟐
+ 𝟐𝒔²𝑬
Estimated values
𝒔²𝑬 =𝒔²𝑷𝟏+ 𝒔²𝑷𝟐+ 𝒔²𝑭𝟏
𝟑
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 22
HERITABILITY
Calculations
Operative heritability (variance component method):
Variance components will be calculated from a series of field experiments and heritability is cacluated according to
𝒉² =𝒔²𝑮
𝒔²𝑮+𝒔²𝑮𝑳𝑵𝑳
+𝒔²𝑮𝒀𝑵𝒀
+𝒔²𝑮𝑳𝒀𝑵𝑳𝒀
+𝒔²𝑹𝒆𝒔𝒊𝒅𝒖𝒂𝒍𝑵𝑳𝒀𝑹
where G = genotypes, L = locations, Y = years and R = replications; Ni = number of the respective factor
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 23
HERITABILITY
Calculations
Realised heritability:
Aim of selection is to select superior genotypes with respect to a certain trait
⇒ mean of a population of genotypes is shifted to the favourable direction.
The difference in the population mean between original and offspring generation is called the RESPONSE TO
SELECTION (R). Die phenotypic difference between the mean of the selected fraction and the mean of the original
population is called selection differential (S).
For the estimation of heritability based on the response to selection R you need the phenotypic standard deviation of
the selected part of the original population sP as well as the selection intensity i (standardised value for the
percentage of selected plants).
𝑹 = 𝒉² × 𝑺
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 24
RESPONSE TO SELECTION
𝑺 = 𝒙 𝒑𝒓𝒐𝒈𝒆𝒏𝒚 − 𝒙 𝒑𝒂𝒓𝒆𝒏𝒕𝒂𝒍
𝑺 = 𝒊 × 𝒔𝑷
𝑹 = 𝒉² × 𝒊 × 𝒔𝑷
𝒉 ² =𝑹
𝒊 × 𝒔𝑷=𝑹
𝑺
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 25
RESPONSE TO SELECTION
Proportion Intensity Proportion Intensity Proportion Intensity
of plants i of plants i of plants i
----------------------- ----------------------- ----------------------
1.00 0.00
0.90 0.20 0.09 1.80 0.008 2.74
0.80 0.35 0.08 1.85 0.006 2.83
0.70 0.50 0.07 1.91 0.004 2.96
0.60 0.64 0.06 1.98 0.002 3.17
0.50 0.80 0.05 2.06 0.001 3.38
0.40 0.97 0.04 2.15 0.0008 3.43
0.30 1.14 0.03 2.27 0.0006 3.51
0.20 1.40 0.02 2.42 0.0004 3.61
0.10 1.76 0.01 2.67 0.0002 3.79
Selection intensity i as a function of the % of selected individuals (a)
The selection intensity i is a standardised coefficient which indicates the number of phenotypic standard
deviation units that the mean of the selected fraction is superior to the mean of the original population.
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 26
RESPONSE TO SELECTION
The response to selection is dependent on:
(a) genotypic variation
(b) reliability of the evaluation of the genotypic variation
(c) selection intensity
An increase and maximisation of the response to selection is possible via each of these three factors.
𝑹 = 𝒉² × 𝒊 × 𝒔𝑷 ≡ 𝒉 × 𝒊 × 𝒔𝑮
Heritability is no biological constant, but largely dependent on the type of breeding experiment. If the
experiment is carried out at only one location, heritibility will be low even if multiple replications are
included, as the interaction can‘t be measured. Due to the genotype by year interaction, heritability based
on one year experiments are limited and can‘t be improved to values derived from multi-year trials by
increasing the number of test sites.
Zuchtmethodik & Quantitative Genetik UX / 957.321 / Heinrich Grausgruber 27
RESPONSE TO SELECTION
The response to selection in case of indirect selection is calculated by
𝑹′ = 𝒉²′ × 𝒊′ × 𝒓 × 𝒔𝑷′
As the correlation coefficient r between direct and indirect trait is maximum 1, i’ (selection intensity of indirect trait)
and/or h²’ (heritability for indirect trait) should be higher than i and/or h for the direct trait. Indirect traits are helpful
for selection if (a) they can be determined easier and faster than the direct trait, (b) heritability is high (higher than for
the direct trait), and (c) they are highly correlated to the direct trait.
Further reading:
Allard RW, 1960: Principles of plant breeding. John Wiley & Sons, Inc., New York.
Becker H, 1993: Pflanzenzüchtung. Verlag Eugen Ulmer, Stuttgart.
Böhm H, Schuster W, 1985: Untersuchungen zur Heritabilität bei Mais (Zea mays L.). Z Pflanzenzüchtg 95:125-134.
Bos I, Caligari P, 1995: Selection methods in plant breeding. Chapman & Hall, London.
Gallais A, 1990: Théorie de la sélection en amélioration des plantes. Masson, Paris.
Mahmud I, Kramer HH, 1951: Segregation for yield, height and maturity following a soybean cross. Agron J 43:605-609.