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Hello, welcome to the new lecture of the module Conservation and Sustainable Use of Animal Genetic Resources:

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Biodiversity analysis of animal genetic resources using pedigree data.

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The study of genetic diversity is possible based on two types of data:

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data obtained from the pedigree analysis, so-called genealogical data, and data obtained from molecular genetic analyses.

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This lecture will discuss genealogical data and working with them.

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Pedigree data can be recorded in different formats;

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here are various graphical representations of pedigrees and relationships between individuals.

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As can be seen, this type of pedigree may only sometimes be suitable for further processing.

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Therefore, the presented type of data record is most often used for work with pedigree data

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which is also suited for further "machine" processing of pedigrees.

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The so-called "three" column pedigree primarily contains the columns of individual,

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father, and mother. These columns are the basis of the whole pedigree file.

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However, the file may contain other necessary and important information, such as birth year and sex.

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Relationships are supported by the fact that each individual listed as a father or mother

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is simultaneously listed as an individual.

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If the pedigree is compiled correctly, the individual in the position of father or mother

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is always listed as an individual in one position before.

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It follows from the logic that an individual must first be born and then become a parents,

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as shown here for individual one. It may be that the relevant data for a given individual is unknown;

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for example, we do not know the individual's parents, the year of birth, or the sex.

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These unknown values are usually given as 0, as seen here.

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Inbreeding coefficient is one from the elementary genetic diversity indicators

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The basic parameter on which the inbreeding coefficient is based is Identity by descent (IBD). 

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This describes the state for copies of an allele that may be traced back through an arbitrary number of generations 

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without mutation to a common ancestor of the organisms that carry the copies. The opposite of IBD is 

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Identity by state - Identity by state (IBS), the coincidental possession of identical alleles (chemically similar). 

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Last but not least, we should mention the term "Autozygosity", 

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which is the state of the genotype where two alleles are identical by descent.

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As already mentioned, the most important indicators of genetic diversity is "Inbreeding coefficient". 

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Most commonly, the inbreeding coefficient is defined as "the probability 

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that two homologue genes in an individual are identical by descent".

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The female horse karyotype, which consists of 32 pairs of chromosomes, including XX chromosomes,

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is presented on the slide. As the picture shows, the chromosomes are coded by size. 

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For the following examples, we will select only loci on the first autosomal chromosome. 

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However, the patterns shown apply to an individual's entire genotype.

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This slide shows two parent pairs, with the male being identical in both cases. 

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The genotype of each individual is defined by a pair of chromosomes: one from the father, 

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shown in pink, and one from the mother, shown in orange. The parental generation is not an autozygous set, 

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as indicated by the different chromosome numbers that define the different founder individuals

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from which these chromosomes came, the so-called founders. In the generation of descendants of these parents, 

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the individuals are related because they have the same father. However, they are non-inbred individuals 

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because they have always obtained different parental chromosomes. 

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In the generation of grandchildren, that is in the second generation of offspring, 

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inbred individuals may already occur if they have inherited chromosomes identical by descent from their parents, 

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that is either chromosome 1 or chromosome 2 from both father and mother.

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This example can be made more concrete by marking certain alleles at a specific locus, 

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presented by a horizontal line. The slide shows that the female in the first generation 

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inherited identical pink-marked alleles from both father and mother. 

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Still, they come from different founders and are identical by state (IBS). 

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The male has kept different allele types from both father and mother, pink from the father and orange from the mother. 

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In the second generation of offspring, the following combinations occurred: 

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the first individual obtained identical alleles by state (IBS), the same colour variant, 

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but the alleles come from different founders. Thus, this is a non-inbred individual. 

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The second individual inherited different types of alleles, presented here by different colours, 

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so-called different by state (DBS) and different by descent (DBD), because both come from different founders. 

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Again, this is a non-inbred individual. The last individual inherited alleles identical by descent (IBD), 

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marked with the same colour and coming from the same founder. This individual is, therefore, inbred.

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As has already been said. The IBD value is "unobservable", so we use pedigree records to derive 

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the probability that two alleles at homologue genes in an individual are IBD. 

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Here in the figure above, individual X would only be inbred if he inherited either the A1 or A2 allele 

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from his father 1 or mother 3; in this case, the common ancestor would be his grandfather 

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or the B1 or B2 allele the common ancestor would be his grandmother. In other cases, 

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the individual would be non-inbred. The probability of individual X inheriting either the A1 or A2 allele 

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is shown by the red segments, and the probability of inheriting either the B1 or B2 allele 

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is shown by the blue segments. In both cases, the probability is one-half to three because there are three allele 

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transmission paths. And since both cases can occur, the two probabilities sum together.

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This slide shows a case where an individual can be inbred with a probability of 0.125. 

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In this case, the individual is Y. In the second cycle, for a given individual Y, the probability

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of transmitting the identical allele ‘A’ will no longer be 0.5 because with a probability 0.125 this individual is inbred, 

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it means that this animal has a probability 0.125 that his alleles are IBD, and it's means that 

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with this probability (0.125) it will transmit the identical allele A with 100% probability. 

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This fact must be considered in the estimation of the inbreeding coefficient of individual X. 

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This corresponds to the second part of the formula (1+FA), which takes this condition into account.

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Here, we have a similar example. The estimation of the inbreeding coefficient for individual X is shown. 

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Individual X has one common ancestor, ancestor D. The probability that he will get the IBD allele

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 from his parents from this ancestor is 0.5 to the fifth because there are five possible transmission paths. 

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It is also necessary to consider that individual D has a common ancestor, A, 

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and the inbreeding coefficient of individual D is 0.125. Considering all these facts, 

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the coefficient of inbreeding of individual X is equal to 0.0352 after rounding.

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Based on these facts, the overall formula for estimating the inbreeding coefficient is composed of these three parts,

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where the sum represents all possible combinations of alleles that can occur in an individual in the IBD state.

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To recap. The inbreeding coefficient can be defined in two ways. Either as "The probability that part of an individual's genome is autozygous (IBD)"

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or the other way, as "The probability that two randomly selected alleles at a single locus are autozygous."

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Another fundamental parameter defining the level of genetic diversity based on pedigree records is the relationship coefficient.

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The assessment of relationship assumes that two individuals are related if they share a chromosome,

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chromosome segment, allele, or point mutation that is identical by descent (IBD).

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It implies that two individuals must have a common ancestor.

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Again, several approaches are used to estimate the level of relationship between two individuals.

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The first is the so-called Kinship or Coancestry Coefficient.

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This coefficient is defined as the probability that an allele randomly selected in individual X

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is identical by descent to a randomly selected allele in individual Y.

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The coancestry coefficient can be estimated from the following relationship,

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where it is defined as the probability that an allele drawn at random from one individual X is identical by descent to a random allele from the other individual Y.

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In this case, individual Z inherited different alleles identical to descent.

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The relationship also shows that the coancestry coefficient of two individuals is the same 

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as the inbreeding coefficient of their hypothetical offspring.

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If we wanted to estimate the value of the coancestry coefficient between this male and female,

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we would get a value of 0.125. Because the only allele A is IBD. The other alleles are different by descent.

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For the individuals to be related, they must have the same allele, either A1 or A2.

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And since the probability that both the male and the female will inherit the A1 allele is 0.25 or that they will inherit the A2 allele is again 0.25.

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Thus, the probability of an individual inheriting either the allele A1 or the A2 allele from both the mother and the father is 0.5.

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Furthermore, the probability that the A1 allele acquired by an individual from both father and mother is identical by descent is 1.

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It is also true for the A2 allele. Therefore, the relationship between these individuals is equal to 0.125.

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Another indicator of the level of relationship between individuals is the Relationship Coefficient, according to Wright (1922).

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This coefficient is defined as the correlation of additive genetic value between two individuals.

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The relationship between the coancestry coefficient and the Wright's relationship coefficient is such that the Wright's relationship coefficient

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is equal to twice the coancestry coefficient, taking into account the coefficient of inbreeding of the two individuals.

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This slide shows that the relationship coefficient, according to Wright (1922), corresponds to twice the original coefficient.

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This is the same pedigree as in one of the previous slides. The estimate of the coefficient of relationship,

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according to Wright (1922), is 0.25, which corresponds exactly to twice the value of the coancestry coefficient.

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Last but not least, it is necessary to mention the additive relationship coefficient,

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which is based on constructing the additive relationship matrix.

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This coefficient expresses a quantitative measure of similarity between two individuals,

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which refers to the number of alleles shared between these individuals.

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This coefficient takes values from zero to two. The first value expresses zero relatedness between individuals.

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The last value, a value of two, may occur in an individual related to itself.

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One way to estimate the value of the additive relationship coefficient is to use the Tabular Method to construct an additive relationship matrix.

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In this matrix, the value of the inbreeding coefficient of the individual

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is expressed as the diagonal element of the additive relationship matrix for a given individual minus one,

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and the relationships between individuals are expressed on the off-diagonal element of the given additive relationship matrix.

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An example of an additive relationship matrix is shown in this slide.

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The first column and the first row in the matrix represent our individuals and their relationship to their parents.

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For example, individual 3 has parents 1 and 2, which are listed in brackets. Inside the matrix, the relationships are shown.

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The diagonal elements of the matrix show the values of the inbreeding coefficient + one.

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The matrix shows that only individual five has a higher value of the diagonal elements than one, it has a value of 1.25.

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This means that the value of the inbreeding coefficient of this individual equal to 0.25.

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The off-diagonal elements marked in green, or blue represent the relationships between individuals.

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This means that, for example, the relationship between individual 4 and 5 has a value of 0.75.

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As mentioned, the Wright’s relationship coefficient is twice the coancestry or additive relationship coefficients

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if the individual's parents are non-inbred. Otherwise, these different approaches give different values.

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It means that, if individuals X & Y are not inbred, relationship coefficient is then equal to the additive genetic relationship

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also, twice kinship coefficient of those two individuals

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as well as twice inbreeding coefficient of their potential offspring.

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Thank you for your attention, and I look forward on the next video.