Judul: Studi untuk Mempertahankan Keragaman Genetik Tanaman Jagung Melalui Pembentukan Core Collection
Abstrak: The research and development in maize are immense, leading to hundreds of maize-improved varieties being released in Indonesia. In order to ensure the sustained availability of broad genetic diversity, the conservation of genetic resources is carried out through ex-situ conservation in the form of seed genebanks. The Agricultural Genebank under the Ministry of Agriculture is the largest genebank in Indonesia and conserves 12,000 accessions covering 40 plant species. However, the cross-pollinated genetic system of maize makes maize genetic resources in the genebank prone to experience inbreeding depression and needs specific treatment to maintain the genetic integrity of the accession. Thus, maize germplasm’s regeneration cost in the genebank is higher than self-pollinated species. The dissertation aimed to develop a maize core collection as one of the solutions to overcome the challenge of maize germplasm management in the genebank and assess how the core collection could preserve the existing genetic diversity in the whole set of maize collections. The study consists of 4 main stages of research activities: 1) getting to know, 2) constructing, 3) assessing, and 4) validating. The first research was to identify the structure of the whole set maize collection in the genebank and analyze its genetic diversity status. The result showed that a moderate to high genetic diversity based on kernel characters and passport data was identified. Two kernel characters, i.e. kernel type and color, were demonstrated as key characters that successfully differentiated all accessions into 10 clusters. The data of kernel characters for all accessions in the maize collection of the genebank was then used in the next research stage. The second research evaluated and identified which methods are appropriate for developing maize core collection. Five methods have been evaluated and based on the homogeneity of the frequency distribution of collection structure, the value of genetic diversity, and the value of summary statistics of core properties, Core Hunter 3 was determined as the appropriate method to select 150 accessions accounting of 11.7% of the whole set maize collection in the genebank. Core Hunter 3 demonstrated better diversity core properties, such as a low mean difference (MD) value, high variance difference (VD) and variable rate (VR) values, a coincidence rate (CR) value of >80%, and the highest coverage value. Moreover, it showed a homogeneity of the mean value of almost all kernel characters and a significantly higher variance value indicating an increased diversity compared to the whole set maize collection. The third research was conducted to assess the dynamics in maize core collection development in terms of entries and characters number used in the core construction process. Four core collections were developed from different datasets, i.e. 1 whole set (1,279 accessions) and 3 combination subset collection (560 accessions). The results showed that 7 accessions were conformally selected by the three cores which were developed from subset collection, representing the most diverse accessions of the whole set maize collection. It also observed that the entries number had more influence in maize core collection development compared to the characters number. The last research was conducted to ensure the prior developed maize core
Keyword: conservation, Core Hunter 3, genebank, genetic resources

Judul: Cluster Analysis for Creating a Core Collection of Cassava (Manihot esculenta C.) Germplasm
Abstrak: anihot esculenta C.) Germplasm. Advised by ASEP SAEFUDDIN dan SUTORO Cassava that are locally often called as tapioca, sampeu, cassava is Manihot esculenta Crantz species, from the family Euphorbiaceae, originally from Brazil, the Amazon region. The development of cassava needs upgrading to improve the productivity of cassava. Its productivity can be enhanced by the presence of plant breeding. Genetic variability of germplasm is needed to produce superior varieties. Although there is an increase in the number of germplasm accessions in gene bank, there is no corresponding increase in their use by crop improvement scientists, indicating that collection were not being used their full potential. This is due to the lack of funding for research and limited human resources. Therefore, to solve the problems, developing core collection is necessary. Core collection is a germplasm sample in the range that exists in the entire collection. Statistical methods used in the core collection are clustering and allocation sampling. Therefore breeders need same indicates for creating core collection. The first index refers to the average of absolute differences between variances across all of the characteristic in the core and entire collections relative to the means in entire collection, MD%. The other index is the average of the absolute differences between variances across all of the characteristic in the core and entire collections relative to the variances in entire collection, VD%. The result shows that the two allocation sampling methods are good enough to construct core collection. However, stratified random sampling always has higher value than two stage random sampling for all evaluation of parameters.
Keyword: core collection, cassava germplasm, cluster analysis, MD (%), VD (%)

Judul: Bifurkasi lokal pada titik tetap non-hiperbolik
Abstrak: Bifurkasi menggambarkan perubahan pada struktur orbit di sekitar titik tetap. Titik tetap dibagi menjadi dua yaitu titik tetap hiperbolik dan titik tetap non-hiperbolik. Titik tetap non-hiperbolik terjadi jika ada nilai eigen dengan bagian real sama dengan nol. Kestabilan dari titik tetap dapat diketahui dari nilai eigen yang diperoleh dari pelinearan medan vektor. Pada bifurkasi satu-dimensi ditemukan kasus-kasus untuk bifurkasi saddle-node, bifurkasi transcritical dan bifurkasi pitchfork. Bifurkasi saddle-node terjadi jika satu sisi dari nilai parameter tidak terdapat titik tetap dan pada sisi lain terdapat dua titik tetap, dimana yang satu stabil dan yang lainnya tak-stabil. Bifurkasi transcritical terjadi jika terdapat pertukaran kestabilan, yaitu dari titik tetap stabil menjadi titik tetap tak-stabil dan sebaliknya. Sedangkan bifurkasi pitchfork dibagi menjadi dua, yaitu: bifurkasi pitchfork supercritical dan bifurkasi pitchfork subcritical. Bifurkasi pitchfork supercritical terjadi jika satu titik tetap stabil berubah menjadi dua titik tetap stabil dan satu titik tetap tak-stabil, dan bifurkasi pitchfork subcritical terjadi jika satu titik tetap stabil dan dua titik tetap tak-stabil berubah menjadi satu titik tetap tak-stabil. Bifurkasi Hopf (bifurkasi dua-dimensi) terjadi jika terdapat orbit periodik pada struktur orbitnya yang berupa lingkaran dengan jari-jari konstan. Ada atau tidaknya orbit periodik dapat diketahui setelah sistem ditransformasikan ke dalam koordinat polar. Orbit periodik ini dapat bersifat stabil maupun tak-stabil. Model periklanan (advertising) Feichtinger merupakan salah satu contoh penerapan bifurkasi Hopf Model ini menghasilkan satu titik tetap dan orbit periodik yang bersifat stabil.
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