Genomische Selektion ist ein Routine-Verfahren bei verschiedenen Nutztierarten, aber noch nicht bei der Honigbiene wegen der Besonderheiten dieser Spezies. Für die Zuchtwertschätzung bei der Honigbiene ist eine spezielle genetische Verwandtschaftsmatrix erforderlich, da die Paarungsbiologie dieser Spezies ungesicherte Vaterschaft, diploide Königinnen und haploide Drohnen umfasst. Die Arbeit präsentiert einen neu-entwickelten Algorithmus zur effizienten Berechnung der Inversen der genetischen Verwandtschaftsmatrix und der Inzuchtkoeffizienten auf großen Datensätzen. Die Methode wurde zur Voraussage von genomischen und Stammbaum-basierten Zuchtwerten in einer Simulationsstudie genutzt. Die Genauigkeit und die Verzerrung der geschätzten Zuchtwerte wurden ausgewertet unter Berücksichtigung verschiedener Größen der Referenzpopulation. Außerdem wurde der Zuchtfortschritt im ersten Durchlauf von Zuchtprogrammen ausgewertet, die Zuchtschemata mit genomischer oder Stammbaum-basierter Selektion nutzten. Ein erheblich größerer Zuchtfortschritt als bei Stammbaum-basierter Selektion wurde mit genomischer Vorselektion erzielt, für die junge Königinnen genotypisiert wurden, und nur die Kandidaten mit den höchsten genomischen Zuchtwerten zur Anpaarung oder Leistungsprüfung zugelassen wurden. Für einen realen Datensatz von ungefähr 3000 genotypisierten Königinnen wurden Stammbaum-basierte und genomische Zuchtwerte für sechs wirtschaftlich bedeutende Merkmale vorhergesagt. Drei Merkmale zeigten eine signifikant höhere Vorhersagegenauigkeit bei genomischer Zuchtwertschätzung gegenüber Stammbaum-basierten Verfahren und die Unterschiede zwischen allen sechs Merkmalen konnten im Wesentlichen aus den genetischen Parametern der Merkmale und der begrenzten Größe der Referenzpopulation erklärt werden. Damit zeigt die Arbeit, dass die genomische Selektion bei der Honigbiene genutzt werden kann, den Zuchtfortschritt zu erhöhen. / Genomic selection is a routine practice for several important livestock species but not yet in honey bees, due to the peculiarities of this species. For honey bees, a specialized genetic relationship matrix is required for the prediction of breeding values, since their mating biology involves uncertain paternity, diploid queens, and haploid drones. The thesis presents a novel algorithm for the efficient computation of the inverse of the numerator relationship matrix and the coefficients of inbreeding on large data sets. The method was used to estimate genomic and pedigree-based breeding values in a simulation study. The accuracy and bias of the estimated breeding values were evaluated and various sizes of the reference population were considered. Subsequently, the genetic gain in the initial cycle of breeding programs was evaluated for several breeding schemes employing genomic or pedigree-based selection. A considerably higher genetic gain than with pedigree-based selection was achieved with genomic preselection, for which queens were genotyped early in life, and only the candidates of high genomic breeding value were admitted for mating or phenotyping. On a real data set of about 3000 genotyped queens, pedigree-based and genomic breeding values were predicted for six economically relevant traits. Three traits showed significantly higher prediction accuracy with genomic compared to pedigree-based methods, and the differences between all the six traits could be explained mainly from their genetic parameters and the limited size of the reference population. The results show that genomic selection can be applied in honey bees, and the thesis provides appropriate breeding schemes and mathematical methods for its implementation.

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The study sought to determine, first, what the rules of the Hananwa family law were and, second, whether those rules were compatible with the Constitution. First, it documented the rules of the official family law. The problem that the study countenanced is that customary law is "corrupted, inauthentic and lacking authority".1 Second, it established and documented the rules of the Hananwa family law. The problem that the study countenanced in respect of Hananwa law was that it was difficult to ascertain the content of the rules of the "living" Hananwa law in order to determine their compatibility with the provisions of the Bill of Rights. Moreover, the traditional Hananwa community is inegalitarian and patriarchal. Section 9 of the Constitution provides that everyone is equal before the law and enjoys equal and full protection and benefit of the law. The study found that the Hananwas still observe their system of customary law. However, there are visible changes. For instance, nowadays the spousal consent is a validity requirement for all customary marriages. A parent or legal guardian must consent to a customary marriage of a minor. The individual spouses, not their families, are parties to their own customary marriages. African women enjoy equal status. This development is consistent with section 9 of the Constitution read with section 6 of the Recognition of Customary Marriages Act 120 of 1998. According to the Constitutional Court, in MM v MN and Another 2013 4 SA 415 (CC), the first wife must consent to her husband's customary marriage to another woman in addition to her customary marriage to him. However, some rules of the Hananwa law do not comply with the provisions of the Bill of Rights. For instance, according to the Hananwa law, extramarital children do not enjoy equal inheritance rights and maintenance rights yet. This discrimination is inconsistent with the constitutional right to equality and the provisions of the Reform of Customary Laws of Succession and Regulations of Related Matters Act 11 of 2009.The Constitution puts common law and customary law on a par. However, the courts have often replaced customary law dispute resolution rules with the common law rules. For instance, the Constitutional Court in Bhe and Others v Magistrate, Khayelitsha and Others; Shibi v Sithole and South African Human Rights Commission and Another v President of the Republic of South Africa and Another 2005 1 SA 580 (CC) and the High Court in Maluleke v Minister of Home Affairs 2008 JDR 0426 (W) substituted the rules of common law for those of customary law in order to resolve customary law disputes. The legislature could not be outdone. A meticulous study of the Recognition of Customary Marriages Act 120 of 1998 and the Reform of Customary Laws of Succession and Regulations of Related Matters Act 11 of 2009 reveals that their provisions almost appropriately reflect the common law marriage and intestate succession rules respectively. The Recognition of Customary Marriages Act has, furthermore, adopted the provisions of the Divorce Act of 1979. Section 28 of the Constitution read with the Children's Act 38 of 2005 has generally substituted the fundamental human rights for the unequal rights provided by the customary law of parent and child. The Maintenance Act 99 of 1998 has substituted the communal form of maintenance under customary law. / Public, Constitutional, & International Law / LLD (International and Constitutional Law)

The study sought to determine, first, what the rules of the Hananwa family law were and, second, whether those rules were compatible with the Constitution. First, it documented the rules of the official family law. The problem that the study countenanced is that customary law is "corrupted, inauthentic and lacking authority".1 Second, it established and documented the rules of the Hananwa family law. The problem that the study countenanced in respect of Hananwa law was that it was difficult to ascertain the content of the rules of the "living" Hananwa law in order to determine their compatibility with the provisions of the Bill of Rights. Moreover, the traditional Hananwa community is inegalitarian and patriarchal. Section 9 of the Constitution provides that everyone is equal before the law and enjoys equal and full protection and benefit of the law. The study found that the Hananwas still observe their system of customary law. However, there are visible changes. For instance, nowadays the spousal consent is a validity requirement for all customary marriages. A parent or legal guardian must consent to a customary marriage of a minor. The individual spouses, not their families, are parties to their own customary marriages. African women enjoy equal status. This development is consistent with section 9 of the Constitution read with section 6 of the Recognition of Customary Marriages Act 120 of 1998. According to the Constitutional Court, in MM v MN and Another 2013 4 SA 415 (CC), the first wife must consent to her husband's customary marriage to another woman in addition to her customary marriage to him. However, some rules of the Hananwa law do not comply with the provisions of the Bill of Rights. For instance, according to the Hananwa law, extramarital children do not enjoy equal inheritance rights and maintenance rights yet. This discrimination is inconsistent with the constitutional right to equality and the provisions of the Reform of Customary Laws of Succession and Regulations of Related Matters Act 11 of 2009.The Constitution puts common law and customary law on a par. However, the courts have often replaced customary law dispute resolution rules with the common law rules. For instance, the Constitutional Court in Bhe and Others v Magistrate, Khayelitsha and Others; Shibi v Sithole and South African Human Rights Commission and Another v President of the Republic of South Africa and Another 2005 1 SA 580 (CC) and the High Court in Maluleke v Minister of Home Affairs 2008 JDR 0426 (W) substituted the rules of common law for those of customary law in order to resolve customary law disputes. The legislature could not be outdone. A meticulous study of the Recognition of Customary Marriages Act 120 of 1998 and the Reform of Customary Laws of Succession and Regulations of Related Matters Act 11 of 2009 reveals that their provisions almost appropriately reflect the common law marriage and intestate succession rules respectively. The Recognition of Customary Marriages Act has, furthermore, adopted the provisions of the Divorce Act of 1979. Section 28 of the Constitution read with the Children's Act 38 of 2005 has generally substituted the fundamental human rights for the unequal rights provided by the customary law of parent and child. The Maintenance Act 99 of 1998 has substituted the communal form of maintenance under customary law. / Public, Constitutional, and International Law / LLD (International and Constitutional Law)