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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



(2) Quantitative traits → continous variation

S Pearce et al (2011) Baron et al. (2012)



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



Homework

Work out the segregation of the cross R1R1r2r2 × r1r1R2R2



Transgression


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


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


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


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.


→ 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




→ 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).



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)


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


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


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.


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


HERITABILITY

Calculations

Parent-offspring correlation

𝒉²𝒃 =𝒓𝒐𝒃𝒔𝒆𝒓𝒗𝒆𝒅𝒓𝒆𝒙𝒑𝒆𝒄𝒕𝒆𝒅

Parent-offspring regression

𝒉²𝒃 = 𝒃

Example: milk yield of cows


Wray & Visscher (2008) Estimating trait heritability. Nature Education 1(1)

http://www.nature.com/scitable/topicpage/estimating-trait-heritability-46889


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


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


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


RESPONSE TO SELECTION

𝑺 = 𝒙 𝒑𝒓𝒐𝒈𝒆𝒏𝒚 − 𝒙 𝒑𝒂𝒓𝒆𝒏𝒕𝒂𝒍

𝑺 = 𝒊 × 𝒔𝑷

𝑹 = 𝒉² × 𝒊 × 𝒔𝑷

𝒉 ² =𝑹

𝒊 × 𝒔𝑷=𝑹

𝑺



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.



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.



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.

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