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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied genetics 85 (1993), S. 577-586 
    ISSN: 1432-2242
    Keywords: Genotype-environment interaction ; Crossover interaction ; Separability ; Shifted multiplicative model ; Distance measure ; Cluster analysis ; Zea mays L
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The shifted multiplicative model (SHMM) is used with a cluster method to identify subsets of sites in an international maize (Zea mays L.) trial without genotypic rank-change. For cluster analysis, distance between two sites is defined as the residual sum of squares after fitting SHMM with one multiplicative term (SHMM1) if SHMM1 does not show genotypic rank-change. However, if SHMM1 does show genotypic rank-change, the distance between two sites is defined as the smaller of the sums of squares owing to genotypes within each of the two sites. Calculation of distance between two sites is facilitated by using the site regression model with one multiplicative term (SREG1), which can be reparameterized as SHMM1 when only two sites are considered. The dichotomous splitting procedure, used on the dendrogram obtained from cluster analysis, will first perform SHMM analyses on each of the last two cluster groups to join (end of the dendrogram). If SHMM1 does not give an adequate fit, the next step is to move down the branches of the tree until groups of sites (clusters) are found to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign. Five final groups of sites to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign were obtained. The procedure appears to be useful in identifying subsets of sites in which genotypic rank-change interactions are negligible.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied genetics 86 (1993), S. 673-678 
    ISSN: 1432-2242
    Keywords: Genetic resources conservation ; Sample size ; Allele frequency ; Probability models ; Core subsets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract One objective of the regeneration of genetic populations is to maintain at least one copy of each allele present in the original population. Genetic diversity within populations depends on the number and frequency of alleles across all loci. The objectives of this study on outbreeding crops are: (1) to use probability models to determine optimal sample sizes for the regeneration for a number of alleles at independent loci; and (2) to examine theoretical considerations in choosing core subsets of a collection. If we assume that k-1 alleles occur at an identical low frequency of p0 and that the kth allele occurs at a frequency of 1-[(k-1)p0], for loci with two, three, or four alleles, each with a p0 of 0.05, 89–110 additional individuals are required if at least one allele at each of 10 loci is to be retained with a 90% probability; if 100 loci are involved, 134–155 individuals are required. For two, three, or four alleles, when p0 is 0.03 at each of 10 loci, the sample size required to include at least one of the alleles from each class in each locus is 150–186 individuals; if 100 loci are involved, 75 additional individuals are required. Sample sizes of 160–210 plants are required to capture alleles at frequencies of 0.05 or higher in each of 150 loci, with a 90–95% probability. For rare alleles widespread throughout the collection, most alleles with frequencies of 0.03 and 0.05 per locus will be included in a core subset of 25–100 accessions.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied genetics 84 (1992), S. 161-172 
    ISSN: 1432-2242
    Keywords: Genotype x environment interaction ; Shifted multiplicative model ; Separability ; Concurrent regression model ; Crossover interaction ; Qualitative interaction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The shifted multiplicative model (SHMM) is used in an exploratory step-down method for identifying subsets of environments in which genotypic effects are “separable” from environmental effects. Subsets of environments are chosen on the basis of a SHMM analysis of the entire data set. SHMM analyses of the subsets may indicate a need for further subdivision and/or suggest that a different subdivision at the previous stage should be tried. The process continues until SHMM analysis indicates that a SHMM with only one multiplicative term and its “point of concurrence” outside (left or right) of the cluster of data points adequately fits the data in all subsets. The method is first illustrated with a simple example using a small data set from the statistical literature. Then results obtained in an international maize (Zea mays L.) yield trial with 20 sites and nine cultivars is presented and discussed.
    Type of Medium: Electronic Resource
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