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5 Degree of dominance = d/a No dominance: d/a = 0 Partial dominance: 0 1 The reference level in the metric model is the level c. This c is the average genotypic value of all possible homozygotes (nota bene: not the population mean !). Full homozygosity is reached only after a number of n = generations of selfing, hence, the models were termed F -model or better, F -metric. ( In some texts, the reference level is chosen as the average genotypic value of a F 2 -equilibrium population, leading to a somewhat different metric. In this case the metric is analogously termed F 2 -metric. )

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6 Schön, C.C., 1993 AA-genotypes aa-genotypes +a -a High Resistance Low

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7 Schön, C.C., 1993 a d

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10 UMC33UMC128 Schön, C.C., 1993

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12 It is of great importance whether a population (the per- formance of which is e.g ) changes its performance without (selection, mu- tation, drift etc., it means without) any reason. This is contradictory to the DUS critera (distinct- ness, uniformity, sta- bility; the reason here is EPISTASIS)

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13 Albina-Locus Xantha-Locus Albina-Locus Xantha-Locus

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19 2–loci-Model für n loci: n Locus....EeddCCBbAA Any genotype Genotypic value: - (aa) 14 + (ad) (da) 23 - (da) 24 + (dd) a 1 + d 2 + a 3 – a 4 + d (ad) 12 + (aa) 13 cG i = From the single parameters a, d, (aa), (ad), (da) and (dd), a summation parameter can be built by simple addition. Here, we will elucidate the parameter system, the metric, based on several numerical examples and by experimental data sets. The genotypic values are ordered in the standard matrix form: aabbaaBbaaBB Aabb AaBb AaBB AAbbAABbAABB

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25 Schierholt, Antje, 2000: Hoher Ölsäuregehalt (C18:1) im Samenöl: genetische Charakterisierung von Mutan- ten im Winterraps (Brassica napus L.). Dissertaion, Universität Göttingen.

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26 Schierholt, Antje, 2000: Hoher Ölsäuregehalt (C18:1) im Samenöl: genetische Charakterisierung von Mutan-ten im Winterraps (Brassica napus L.). Dissertaion, Universität Göttingen. Example F 2 - ½(B 1 +B 2 )= ¼(aa) 12 i.e., 70.5 – ½ ( ) = 1.6 thus,

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28 (F-metric), no linkage F

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Yield performance (t/ha) Ertragsleistung (t/ha) Inbreeding coefficient, Inzuchtkoeffizient Paren- tal mean; F F1-hybrid F2- mean; BC1-mean F3-generation mean Any difference of F and the parental mean shows additiv-additiv - epistatic effects Any deviation from this linearity is indicative for epistasis. The type(s) of epistasis depend(s) on the actual non-linearity.

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Genotypic trait value of offspring families Genotypic trait value of parents 2 =1.554 = = = =2.901 =1.703 = 3.406/2 h²=0.50 h²=0.37 ² G = ² A = A = ² D = Gentoypic variance; 100 loci; a=d=0.5; p(A)=0.634 Genotypic variance; 100 loci; a=0.5; d=0; p(A)=0.634 Random mating Value of AA = 1 Value of aa = 0 WHY ?

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33 COV frequency (p) of the favourable allele when allowing for different degrees of dominance.

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36 α 1 - α 2 = α =[a- (p-q)d] α i s sometimes called average effect of a gene substitution

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45 t Syn generation (t) Expected performance ( t ) of a synthetic population in the first generations of multiplicaitons 4

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