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  • Allele frequency  (2)
  • Genotype x environment interaction  (2)
  • Separability  (2)
  • Core subsets  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied genetics 77 (1989), S. 153-161 
    ISSN: 1432-2242
    Keywords: Seed regeneration ; Sample size ; Random genetic drift ; Effective population size ; Allele frequency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.
    Type of Medium: Electronic Resource
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  • 2
    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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  • 3
    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.
    Type of Medium: Electronic Resource
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and applied genetics 87 (1993), S. 409-415 
    ISSN: 1432-2242
    Keywords: Genotype x environment interaction ; Adaptation ; Stability ; Desirability index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (D i). Thus, D i is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. D i is equal to the mean of the i th genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large D i. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of D i was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of D i 's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on D i .
    Type of Medium: Electronic Resource
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