What causes negative selection in quantitative trading

 Population Genetics and Quantitative Genetics

1. Population genetics
1.1. Genotype and allele frequencies
1.2. Chance mating and Hardy-Weinberg equilibrium
2. Quantitative Genetics
2.1. Features and variation
2.1.1. Polygenic, oligogenic inheritance
2.1.2. Environmental influences
2.1.3. Genotype-environment interaction
2.2. Heritability
2.2.1. Decomposition of the genotypic value
2.2.2. Types of heritability
2.2.3. Experimental methods of determining heritability
2.2.4. Heritability of individual features
2.3. Selection success
2.3.1. The observed selection success
2.3.2. The expected selection success
2.3.3. Selection intensity
3. Further reading

1. Population genetics

... deals with the processes that influence the genetic make-up of populations. By "population" is meant a group of plants that form a reproductive community. The plants in a population are linked by a common gene pool ("gene pool"), which is passed on to the offspring during reproduction. A population has a temporal continuity; it consists of successive generations.

1.1. Genotype and allele frequencies

A population can be described either by the relative frequencies of the genotypes (P, H, Q) or by the relative frequencies of the alleles (p, q). Allele frequencies change primarily through mutation or selection, which inevitably leads to a change in the genotype frequencies (a change in the genotype frequencies is also possible without the allele frequencies changing! (See Table 1)).

Table 1: Examples for calculating the genotype and allele frequencies, with the allele frequency remaining the same, but with a changed genotype frequency.

1.2. Chance mating and Hardy-Weinberg equilibrium

* P a n m i x i erandom mating’): Every pairing between two plants of a population is equally likely, e.g. rye field.

* H a r d y - W e i n b e r g G l e i h g e w i c h t :
(1) Genotype frequencies result from allele frequencies. The genotype frequencies of a random mating population are constant as long as the allele frequencies do not change.
(2) A constant composition of a population is achieved by a single generation of random mating.
(3) In the Hardy-Weinberg equilibrium the genotypes AA, Aa and aa have the frequencies p², 2pq and q².

Rare alleles (e.g. lethal genes) almost only occur in heterozygous genotypes under this equilibrium (homozygous genotypes are extremely rare, as effects become visible during inbreeding!).

Requirements for the validity of the Hardy-Weinberg equilibrium:
(1) large population,
(2) panmixie,
(3) no artificial or natural selection,
(4) no mutation,
(5) no introduction of genes from outside the population.

2. Quantitative Genetics

2.1. Features and variation

* Qualitative characteristics Þ discontinuous variation
* Quantitative characteristics Þ continuous variation

Table 2: Inheritance and variation of various interesting breeding traits

2.1.1. Polygenic, oligogenic inheritance

The Swede Hermann NILSSON-EHLE succeeded in proving polygenic inheritance for the first time. In a wheat cross between a red and white-grained variety, a split in the F2 was able to determine in five color gradations.

P.1 (red) x P2 (white) Þ F1 (pink) Þ F2 (five color gradations) 1: 4: 6: 4: 1

This split could be explained by two genes with two alleles each Þ the F2 follows a dihybrid cleavage. In the case of traits with several genes involved, the number of classes becomes so large that they can no longer be distinguished and the impression of continuous variation is created.

2.1.2. Environmental influences

The trait measured on a single plant or offspring is called the phenotypic value. It is made up of the genotypic value and the environmental effect. The genotypic value is the mean value of the plants of a genotype over all conceivable environmental conditions. The environmental effect can be positive or negative and leads to the phenotypic value being above or below the genotypic value.

Þ 1903: Wilhelm JOHANNSEN (first mention of the terms ‘gene’, ‘genotype’, phenotype ’): experiments on the inheritance of seed weight at Phaseolus-Bean Þ continuous variation is partly genetic, partly environmental. Beans are self-fertilizers, so the plants of a variety are homozygous Þ the descendants of a homozygous individual plant are genetically identical to one another and their variation is purely environmental-related Þ Pure line ’(‘pure line’) Þ Commercial grade‘Princess’It was evidently a mixture of different genotypes with genetic differences in the seed size Þ The first selection was therefore successful (Fig. 1).

Fig. 1: Johannsen experiment (1903): In the first selection step a the smallest and largest beans were selected and sown and the weight of the beans of the resulting plant was determined. In the event of b was a mean of 0.351 g, for b ' 0.643 g was found. So the first selection was successful, i.e. the variation between b and b ' can only be traced back to the genotype. In the second selection step (within the first progeny the smallest and largest beans were picked out and sown again) no variation between the individual subpopulations could be determined (b: 0.358 and 0.348 g; b ': 0.631 and 0.649 g), i.e. the variation within b and b ' or its two sub-populations was purely environmental.

2.1.3. Genotype-environment interaction

* Fixed factors: Environmental factors that are defined and known prior to cultivation, e.g. the climatic region and plant cultivation measures (sowing time, seed strength, fertilization level, etc.).

* Random factors: Environmental factors which show a random variation and which cannot be predicted, e.g. the annual weather.

Þ (1) It is hardly possible to draw general conclusions from a single experiment, and yield tests must always be carried out at several locations and over several years, (2) different locations can be differently suited as locations for a yield test, (3) different genotypes can be different have interactions of different sizes and genotypes can be selected in which these interactions are as low as possible.

Þ It is often of interest to make a general statement about how important interactions are in relation to the main effects. Such a statement is possible if we consider the variances, i.e. ask to what extent the occurring variation is based on differences in the genotypes, environmental conditions and / or interactions.

What is desired is a genotype that has as few interactions with the environment as possible. (Þ performance stability, yield security).

2.2. Heritability

Heritability ("heredity") records the relative importance of the genotype for the variability that occurs. Experimental determination, e.g. by estimating variance components: in this way the size of the genotypic variance can be determined and related to the size of the phenotypic variance; Selection experiments: the higher the heritability, the greater the success of a selection. The heritability in the starting population can therefore be inferred from an observed selection success.

2.2.1. Decomposition of the genotypic value

Þ Additive effect and deviation from dominance
Additive effect, Breeding value (A): Sum of the average effects of the alleles. Without dominance, the breeding values ​​are the same as the genotypic values. In the case of partial or complete dominance, the breeding value of the heterozygous genotype is lower than its genotypic value, since some of its offspring become homozygous for the unfavorable allele. The difference between the breeding value and the genotypic value is called Dominance deviation (D).

Þ epistasia
The genotypic value of an individual cannot always be understood simply as the sum of the genotypic values ​​of individual genes. It happens that two genes only show a particularly favorable or unfavorable effect when they are combined. Such an interaction between different genes is called Epistasia (I).

2.2.2. Types of heritability

Þ Heritability in the broader sense (‘broad sense heritability‘; h²b, H, H²)

Þ Heritability in the narrower sense (‘narrow sense heritability‘; h²n, h²)

Þ Heritability only indicates the proportion of the phenotype that can be traced back to the genotype; however, it says nothing about the number of genes involved, their location or gene products.

2.2.3. Experimental methods of determining heritability Heritability in cross-breeding populations

Idea: Estimation of the environmental variance in genetically homogeneous populations (parents, F1), Estimate of the total variance (VP.) at the F2-Population that contains all of the genetic variance, but is also subject to environmental fluctuations at the same time.

a) Mahmud & Kramer method

b) Weber's method

The methods of Mahmud & Kramer and Weber estimate heritability in the broader sense Þ VG is not disassembled.

c) Allard's method (backcrossing method): variances of parents, F1, F2 and the backcrosses of the F1 with both parents (B.1 and B2) allow the genetic variance V to be separatedG into components VA. and VD. and thus the estimate of heritability in the broader and narrower sense. V.F2, VB1, VB2 as well as VP1, VP2 and VF1 are determined from the experiment; the heritability is determined after calculating VA. and VD. determined by inserting the known values ​​into the equations of the expected values ​​and then solving the equations.

Expected values: (1)


Estimated values:

Heritability: Heritability through parent-offspring - regression

(b ..... regression of the offspring on the parents) Variance component method ("operative heritability“)

Example: field trial, 3 clones, 3 locations, analysis of variance for the dry matter yield characteristic.

The calculation of the heritability based on a series of field tests over several years and locations would be according to the formula

where G = genotypes, O = locations, J = years and R = repetitions. Realized heritability

Fig. 2: The heritability estimate based on the selection success R: In addition to the selection success R, the phenotypic standard deviation of the selected trait in the starting population sP. as well as the selection intensity i (standardized measure for the percentage of plants selected from the starting population). (for a complete understanding and for the calculation of R see 2.3)

2.2.4. Heritability of individual features

A possible selection order according to the heritability of individual characteristics in the breeding of self-fertilizing cereals:

HeritabilitycharacteristicStart of selection
highBest. Resistance properties, ripening time, cover, grain color, husk shapeF2 - F3
mediumGrain and ear characteristics, stability, quality characteristics, possibly the length of the stalkF4 - F5
lowIncome components, income potential, various physiol. propertiesF7 - F8

2.3. Selection success

The aim of a selection based on quantitative properties is to select superior genotypes Þ Shift the mean value of a population of genotypes in a desired direction. The change in the mean value of a population due to selection is called selection success, (‘response to selection’, R)

2.3.1. The observed selection success

Þ The phenotypic difference between the mean of the selected fraction and the mean of the entire population is called the selection differential S. The selection success is:

The relationship between R and S is called the realized heritability (see; Fig.2).

2.3.2. The expected selection success

Theoretical prediction of the selection gain based on the characteristics of a population. The success of the selection depends on three factors:
(a) how much genetic variation there is,
(b) how reliably this variation can be recognized and
(c) how strong is the selection.

corresponds to
An increase and maximization of the selection success is possible via each of the three factors involved.

2.3.3. Selection intensity

The selection intensity is a standardized coefficient that indicates how many standard deviations the mean of the selected plants is above the population mean.

Þ The sum of the genotype-environment interactions in all species is greater than the genotypic variance. When testing at only one location, the variance between the test members is equal to the sum of genotypic variance and interaction variance, so when testing at only one location, the genotypic variance is greatly overestimated.
Þ The heritability of the values ​​on which the selection is made is decisive for the success of the selection, i.e. the heritability of the mean values ​​over the environmental conditions and repetitions in which the test was carried out. One possibility to increase the heritability while maintaining the same scope of testing is to change the allocation of the test parcels, i.e. a better division of the available number of parcels into repetitions, years and locations.
Þ Heritability is not a biological constant, but depends very much on the type of breeding test. In the case of examinations at only one location, the heritability remains low even with a large number of repetitions, since the interactions are not recorded. Due to the genotype-year interaction, the maximum achievable heritability in one-year tests is limited and cannot be raised to the level of heritabilities in tests over several years, even with a very large number of locations.

Selection success with indirect selection with an auxiliary characteristic

Þ Since the correlation coefficient r can in the best case be one, but is normally below one, i ’and / or h’ for the auxiliary feature should be greater than i and h for the target feature. Auxiliary features are therefore of interest (a) if they can be determined quickly and easily in a large number of material, as this enables a higher selection intensity, (b) if they have a high heritability, and (c) if they also have a high level of heritability are sufficiently correlated with the breeding goal.

3. Further reading

Allard RW, 1960: Principles of Plant Breeding. John Wiley & Sons, Inc., New York.
Becker H, 1993: Plant Breeding. Publishing house Eugen Ulmer, Stuttgart.
Böhm H, Schuster W, 1985: Investigations into the heritability of maize (Zea mays L.). Plant Breeding Journal 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. Agronomy Journal 43: 605-609.

See also: selection