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Hello everyone, I welcome you to another lecture from the Animal Genetics module,

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the topic of which is: Genetics of quantitative traits. 

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In the lecture, we will introduce qualitative and quantitative traits and the decomposition of phenotypic variance.

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If we are talking about the performance of an individual, we are talking about the so-called phenotype. 

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The phenotype is a set of traits observed on individual and is a function of genotype and environment. 

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It is therefore a set of all the traits of an individual that are of interest to us from the point of view of animal genetics.

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We expertly divide these observed traits into qualitative or qualitative traits. 

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When we talk about qualitative traits, we are talking about traits with a clear distinction between phenotypes,

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i.e., clearly determined categories (e.g., colour of individual, presence of horns, ...). 

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These traits are influenced by a few genes with large effects so call major genes or oligogenes. 

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The influence of the external environment on the given traits is negligible. 

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Because if we consider, for example, an individual's colour, 

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whether the individual is in a comfortable environment or a non-comfortable environment, it always have the same colour. 

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Qualitative traits show so-called alternative variability: animals are either black or white,

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nothing in between - for example, in the qualitative traits we can include: animal colour, genetic diseases, and more. 

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Quantitative traits are traits with a continuous distribution of performance.

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Many genes of small effect so-call minor genes or polygenes influence quantitative traits. 

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The influence of the external environment contributes to the individual's performance in different proportions for different traits. 

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It means that if the animal is in a comfortable environment, it will perform differently than in an uncomfortable environment. 

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In the quantitative traits we can includ for example dairy performance, daily gain, and meat productions.

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And quantitative traits show a normal distributions,

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We will present the relationship between genotype and phenotype for qualitative and quantitative traits. 

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For qualitative traits, the genotype is directly reflected in the phenotype. On the contrary, in the case of quantitative traits, 

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the genotype with developmental factors, which may include, for example, the upbringing of the individual, the disease experienced, create so-called potential ability, 

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which is further influenced by environmental conditions and only then manifests itself in the phenotype.

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These figure shows a normal distribution for a person's height, the so-called Gaussian curve.

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In animal genetics, variability is the most important parameter. Based on variability, we can choose and select individuals. 

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If there was no variability in the population, it is impossible to select the best individual as the parent of the following population. 

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In this picture, we will imagine the essence of genetic variability and the transition between quantitative and qualitative traits. 

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Suppose we were to consider that the colour of an individual is controlled by only one gene pair, and it would be an incomplete dominance. 

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In that case, the population will have three possible colour combinations - brown, orange and yellow, as shown in the picture on the left above. 

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If the colour were affected by two genes at two loci, there would already be five colour combinations, as shown in the left belove figure. 

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If we were to consider genes on three loci, the population would have seven colour variants, as in the picture at the top right. 

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But assuming many genes, we will already reach the so-called continuous variable, as shown on the lower right.

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If we consider only one gene, we are talking about the so-called "Mendelian genetics"; 

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if we think of many genes, we are already talking about the so-called "Quantitative genetic" or "Biometric genetics". 

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Which are subsequently describe using population statistical parameters.

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Basic population parameters include arithmetic mean and variance. The arithmetic mean indicates the mean or average value of a given population. 

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For example, the average milk productivity value of Holstein cattle in the Czech Republic in 2022 was 10,440 kg. 

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The formula for obtaining the arithmetic mean is shown in the upper left image. Other, and from the point of view of animal genetics, 

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more important parameters are the variance and standard deviation, which are used to evaluate the variability of the population. 

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The standard deviation represents the average deviation in the performance of all individuals in the population from the mean of the given population. 

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For example, the standard deviation for milk productivity of Holstein cattle in the Czech Republic in 2022 of 600 kg of milk. 

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It means that, on average, each dairy cow deviates by 600 kg of milk from the average value of the population. 

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Some dairy cows deviate higher and some lower, but they all vary by 600 kilograms on average. 

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We cannot calculate the standard deviation directly because we always get a value of 0 if we add all the deviations from the population mean. 

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Therefore, we get the standard deviation as the square root of the variance. The variance represents the mean square of the deviations from the mean. 

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And as already follows from the description, the square of the deviations is always a positive number that mostly deviates from zero.

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If we use the basic definition of the phenotype. The phenotype is always defined as a function of the genotype and the environment. 

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We can define the phenotype as the sum of the level of the genotype, the environment and the relationship or interaction between the genotype and the environment.

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If we convert this relationship into phenotypic variance, then phenotypic variance is influenced by genetic variance and environmental variance. 

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Genetic variance can be divided into variance influenced by the additive component of the genotype,

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variance influenced by the dominance component and variance influenced by the component of gene interactions or epistasis. 

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Environmental variability can be divided into variance influenced by the permanent,

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so-call systematic, or temporary environment, so-call nonsystematic environment.
 
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This slide will explain the terms additivity, dominance and interaction. The concept of additivity can be explained as follows. 

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Each gene has some effect. It is generally assumed that the dominant allele shows a higher performance value

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(e.g. 5 kg on average) than the recessive allele (e.g. 2 kg on average). 

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The genetic value of the given individual for which we are considering the given genotype, affected only by the additivity effect, is 38 Kg. 

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We obtained this value by summing the individual effects of individual genes.

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Conversely, dominance represents the relationship of two genes, or two allels, at one locus. 

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For example: If it exists, let's call it over-dominance. That is, if the alleles at one locus are heterozygous,

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there is an increase in productivity by, for example, 10 kg. 

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The genetic value of the given genotype affected only by the dominance effect (D) is, therefore,

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20 kg since it contains only two gene pairs in the heterozygous state. 

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And interaction, or epistasis, represents the relationship between two genes at different loci.

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Suppose there is a relationship between the dominant allele A and the dominant allele B, and this relationship increases performance by 10 kg. 

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Therefore, in the genotype we are considering, the interaction effect will increase productivity or prerfomance by 20 kg,

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 because the genotype contains only dominant allele A and two dominant alleles B. 

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By summing the effects of additivity, and dominance of the interaction,

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we get the total genetic value, which is 78 kg for the genotype we are considering.

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We are able divide the effect of the environment into systematic or permanent effects and non-systematic or temporary effects. 

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Systematic effects affect the whole group of animals in the same direction and magnitude, which allows them to be corrected. 

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And that by both the calculation procedure and the standardization of the environment. These effects include, for example, age, litter frequency, economy, year, season, and others. 

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On the contrary, non-systematic effects can affect only one individual in an unknown size and direction.

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Because we do not know the size or direction of the effect, 

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it is impossible to eliminate these effects. It includes, for example, the so-called residual error, which introduces inaccuracies into most genetic estimates.

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In this lecture, we introduced the fundamental difference between qualitative and quantitative traits and restructured the phenotype and phenotypic variance concept. 

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Thank you for your attention, and I look forward to meeting you at the following lecture.