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Hello, welcome to another video from the module Conservation and Sustainable Use of Animal Genetic Resources,

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where we will show the basic operations with pedigree records.

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It is important to understand at the beginning the basic difference between the terms:

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inbreeding coefficient and relationship coefficient. The relationships coefficient represents the probability that

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two related individuals have inherited an allele of the same locus from a common ancestor (the so-called IBD allele - "identical by descent").

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In contrast, the Inbreeding Coefficient - Fx, represents the probability that two homologous alleles of an individual

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are identical by descent (IBD - autozygous).

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First, we will look at the inbreeding coefficient.  Several approaches can be used to estimate the level of the inbreeding coefficient.

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The two basic approaches are shown here on the slide. One is the Wright's inbreeding coefficient,

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and the other is the inbreeding coefficient based on the additive relationship matrix.

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We have already discussed both approaches in the lecture video.

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The method of constructing the additive relatedness matrix is discussed in detail in the lecture module

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"Animal Breeding" - the topic "Genetic value of the individual".

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Several examples will then be given to illustrate the different approaches.

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We want to estimate the level of the coefficient of inbreeding for the individual Rek I.

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There is one common ancestor in this pedigree, the individual Baronka. This individual is in the second generation of ancestors,

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which implies that the number of free generations from the father's side (Kazan) is equal to 1

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and the number of free generations from the mother's side (Poly) is also equal to 1.

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If we put this information into the appropriate formula for estimating the inbreeding coefficient according to Wright,

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where n1 and n2 is the number of free generations from the sire's and dam's side to the common ancestor,

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where the number of these free generations from the sire's and dam's sides was equal to 1 in both cases,

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we obtain a value of the inbreeding coefficient corresponding to 0.125, or, as shown here, 12,5 %.

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7)We obtain the same value if we use the additive relatedness matrix to find values of inbreeding coefficients.

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The inbreeding coefficient is shown here on the diagonal and for the Rek I individual it represents the value 1.125 - 1.

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This means that the value of the inbreeding coefficient is equal 0.125.

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As the additive relationship matrix shows, the coefficient of inbreeding of an individual corresponds

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to half of the additive relationship between the parents of that individual.

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The additive relationship of the parents of individual Rek I, which is Kazan and Poly, takes the value of 0.25. Shown here in red.

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Here on the slide, we will show a situation when we want to predict the value of the inbreeding coefficient of a future offspring of an individual Rek I and Poly.

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Note that Poly is the mother of individual Rek I. Therefore, the closest common ancestor in this case is Poly.

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The number of free generations from the parents to the common ancestor is equal to 1 from the father (Rek I)

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and equal to 0 from the mother (Poly), because it is the mother (Poly) who is the common ancestor.

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Therefore, the value of the expected coefficient of inbreeding for a future offspring between Rek I and Poly is equal to 0.3125, i.e. 31.25%.

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Again, if we use the additive relationship matrix to predict the value of the inbreeding coefficient of individual X,

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resulting from the mating of Rek I and Poly, we obtain a value of 0.3125, similar to the previous slide.

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The additive relationship matrix further shows that the relationship coefficient between individual Rek I and Poly is equal to 0.625.

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Again, the inbreeding coefficient corresponds to half of the relationship between the father Rek I and the mother Poly,

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in this case, as already indicated, to a value of 0.3125.

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But because sometimes in breeding more complicated combinations occur in the following examples we will show more complex relationships.

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Here we have one of the more complicated pedigrees.

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This slide shows all possible common ancestors in that pedigree.

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These are the Dan individual, the Jiskra individual, the Kim individual, and the Orka individual.

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If we wanted to select all the inbred individuals in this pedigree, these would be the following individuals:

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Dan, who has a inbreeding coefficient equal to 0.125 and has a common ancestor in Ziki.

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Bára, who has a inbreeding coefficient equal to 0.0625 and her common ancestor is the individual Kim.

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And Alan, who has a inbreeding coefficient of 0.1953, with Dan and Kim as common ancestors.

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This slide shows an estimate of the inbreeding coefficient according to Wright (1922) for the individual "Alan".

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The overall value of the inbreeding coefficient for Alan is approximately equal to 20%.

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Alan has several common ancestors on both his sire's and dam's side

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One of them, for example, is Dan, who is even inbred himself and his inbreeding coefficient is equal to 0.125.

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Dan contributes 14% to the total inbreeding coefficient. Another common ancestor for the individual Alan is the individual Jiskra.

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Jiskra contributes 3% to the Alan's total inbreeding coefficient.

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Another common ancestor is the individual Kim, which contributes 1.56% to the total inbreeding coefficient for Alan.

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And the last common ancestor for the individual Alan is Orka.

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Which contributes 0.78% to the total inbreeding coefficient for Alan.

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If we sum up all these contributions we get approximately the allredy mentioned value of 20%.

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Which corresponds to the total coefficient of inbreeding for the individual Alan.

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The above example begins to be complicated, and therefore it is very easy to overlook any relationship

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between the two individuals of a given pedigree.

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For this reason, it is preferable to use an additive genetic relationship matrix for more complicated relationships.

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As it follows from the additive relatedness matrix, the estimate of the inbreeding coefficient for the individual Alana

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has the same values as in the previous calculation. Minor inaccuracies are due to rounding errors.

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In addition, from the additive relationship matrix it is possible to directly obtain the inbreeding coefficients for all individuals

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in the pedigree and possible relationships between individuals.

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Finally, let's take a few cases for consideration. Everyone should try to find the right answer to each question and be able to justify it.

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There are no exact answers to these questions.  The first question, when a breeder resorts to inbreeding, may be answered, for example,

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that the breeder is trying to establish some breed-specific traits or variables. But there are several other correct answers.

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To the second question whether inbreeding is bad, there is no clear answer because as the name suggests inbreeding

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can be neither bad nor good but depends on the context. For example, if the breeder is trying to fix some important breeding traits or variables,

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as already mentioned, this is a good or positive approach.

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Conversely, if bad and undesirable traits are being fixed and so-called inbreeding depression is occurring,

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this is a bad situation or a bad part of breeding.

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At the end of this video, I would like to thank you for your attention and I look forward to seeing you again for the next videos.