Browsing by Subject "Biometrie"

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Biometrical approaches for analysing gene bank evaluation data on barley (Hordeum spec.)
(2007) Hartung, Karin; Piepho, Hans-Peter
This thesis explored methods to statistically analyse phenotypic data of gene banks. Traits of the barley data (Hordeum spp.) of the gene bank of the IPK-Gatersleben were evaluated. The data of years 1948-2002 were available. Within this period the ordinal scale changed from a 0-5 to a 1-9 scale after 1993. At most gene banks reproduction of accessions is currently done without any experimental design. With data of a single year only rarely do accessions have replications and there are only few replications of a single check for winter and summer barley. The data of 2002 were analysed separately for winter and summer barley using geostatistical methods. For the traits analysed four types of variogram model (linear, spherical, exponential and Gaussian) were fitted to the empirical variogram using non-linear regression. The spatial parameters obtained by non-linear regression for every variogram model then were implemented in a mixed model analysis and the four model fits compared using Akaike's Information Criterion (AIC). The approach to estimate the genetical parameter by Kriging can not be recommended. The first points of the empirical variogram should be explained well by the fitted theoretical variogram, as these represent most of the pairwise distances between plots and are most crucial for neighbour adjustments. The most common well-fitting geostatistical models were the spherical and the exponential model. A nugget effect was needed for nearly all traits. The small number of check plots for the available data made it difficult to accurately dissect the genetical effect from environmental effects. The threshold model allows for joint analysis of multi-year data from different rating scales, assuming a common latent scale for the different rating systems. The analysis suggests that a mixed model analysis which treats ordinal scores as metric data will yield meaningful results, but that the gain in efficiency is higher when using a threshold model. The threshold model may also be used when there is a metric scale underlying the observed ratings. The Laplace approximation as a numerical method to integrate the log-likelihood for random effects worked well, but it is recommended to increase the number of quadrature points until the change in parameter estimates becomes negligible. Three rating methods (1%, 5%, 9-point rating) were assessed by persons untrained (A) and experienced (B) in rating. Every person had to rate several pictograms of diseased leaves. The highest accuracy was found with Group B using the 1%-scale and with Group A using the 5%-scale. With a percentage scale Group A tended to use values that are multiples of 5%. For the time needed per leaf assessment the Group B was fastest when using the 5% rating scale. From a statistical point of view both percent ratings performed better than the ordinal rating scale and the possible error made by the rater is calculable and usually smaller than with ratings by rougher methods. So directly rating percentages whenever possible leads to smaller overall estimation errors, and with proper training accuracy and precision can be further improved. For gene banks augmented designs as proposed by Federer and by Lin et al. offer themselves, so an overview is given. The augmented designs proposed by Federer have the advantage of an unbiased error estimate. But the random allocation of checks is a problem. The augmented design by Lin et al. always places checks in the centre plot of every whole plot. But none of the methods is based on an explicit statistical model, so there is no well-founded decision criterion to select between them. Spatial analysis can be used to find an optimal field layout for an augmented design, i.e. a layout that yields small least significant differences. The average variance of a difference and the average squared LSD were used to compare competing designs, using a theoretical approach based on variations of two anisotropic models and different rotations of anisotropy axes towards field reference axes. Based on theoretical calculations, up to five checks per block are recommended. The nearly isotropic combinations led to designs with large quadratic blocks. With strongly anisotropic combinations the optimal design depends on degree of anisotropy and rotation of anisotropy axes: without rotation small elongated blocks are preferred; the closer the rotation is to 45° the more squarish blocks and the more checks are appropriate. The results presented in this thesis may be summarised as follows: Cultivation for regeneration of accessions should be based on a meaningful and statistically analysable experimental field design. The design needs to include checks and a random sample of accessions from the gene pool held at the gene bank. It is advisable to utilise metric or percentage rating scales. It can be expected that using a threshold model increases the quality of multivariate analysis and association mapping studies based on phenotypic gene bank data.
Improvement of breeding strategies for the trait vase life in cut carnations (Dianthus caryophyllus L.)
(2018) Boxriker, Maike; Piepho, Hans-Peter
Carnation (Dianthus caryophyllus L.) is one of the ten most famous cut flowers worldwide. A single big flower characterizes standard carnations, while mini car-nations possess multiple flowers per stem. Vase life (VL) is one of the most im-portant breeding objectives in carnations due to the need of long transportation times and direct influence on the costumers. But VL is a complex trait with several effects influencing it. Two-phase traits like VL are traits where the assessment is done in a second phase, in the laboratory and the plants are cultivated in the greenhouse, the first phase. Many experiments have a two-phase character, but little research has been conducted to develop experimental designs in the second phase. To improve breeding efficiency, molecular markers and genomic selection is used in agriculture science but it is so far not common in ornamental breeding. The goal of this thesis was the implementation of SNP-based molecular markers for the trait VL to improve selection of long-lasting, transportable cut carnations. For marker association, 1,500 carnation genotypes were screened for VL behav-ior in an experimental design in both phases. Response to selection was used to assess efficiency. The second-phase experimental design was more important for precise data analyses. This highlights the research need on this topic. Fur-thermore, it was possible to suggest row-column designs for VL trials. Row-column designs are more flexible in the case of positional effects compared with one-dimensional blocking and can be easily analyzed like an α-design. The easiest way to design the following phases are to apply the design one-to-one. The carnation types, mini and standard, showed an influence on VL. The mini carnations last 0.5 d longer than the standard carnations. The same conclusion was drawn based on the molecular data. Transcriptome data was generated with two different sequencing methods. By independent analysis of both carnation types, different results than via the analysis of the whole data set were found. This indicates that the analysis of carnations should be done separately for each carnation type. Association of the phenotypic and genotypic data was so far not possible. As an alternative to molecular markers, genetic correlations for the use as indirect selection for the trait VL and others for breeding relevant traits was calculated. For the first time, bivariate analysis was conducted in two-phase ex-periments. The genotypic correlation between VL and FD was high, but indirect selection would be less effective than direct selection. However, the information can provide an indication of the performance and the effort to measure FD is small. The calculated high heritability of VL and found differences in VL of up to 15 d between the best and worst genotypes showed the potential of improving the population mean by using improved selection strategies like marker-assisted selection or auxiliary traits and the use of statistical methods like experimental designs in all phases of the experiment. The influence of carnation type was shown with this thesis and indicates that the implementation of molecular markers must be done independently for each car-nation type. The importance of experimental designs in multi-phase experiments was highlighted and statistical analysis by mixed models and a bivariate analysis of different traits was performed. Until now, no molecular marker for VL was identified but in a further research project, this will be solved by generating more genotypic data and the construction of a genetic map.
Mixed modelling for phenotypic data from plant breeding
(2011) Möhring, Jens; Piepho, Hans-Peter
Phenotypic selection and genetic studies require an efficient and valid analysis of phenotypic plant breeding data. Therefore, the analysis must take the mating design, the field design and the genetic structure of tested genotypes into account. In Chapter 2 unbalanced multi-environment trials (METs) in maize using a factorial design are analysed. The dataset from 30 years is subdivided in periods of up to three years. Variance component estimates for general and specific combining ability are calculated for each period. While mean grain yield increased with ongoing inter-pool selection, no changes for the mean of dry matter yield or for variance component estimate ratios were found. The continuous preponderance of general combining ability variance allows a hybrid selection based on general combining effects. The analysis of large datasets is often performed in stage-wise fashion by analysing each trial or location separately and estimating adjusted genotype means per trial or location. These means are then submitted to a mixed model to calculate genotype main effects across trials or locations. Chapter 3 studies the influence of stage-wise analysis on genotype main effect estimates for models which take account of the typical genetic structure of genotype effects within plant breeding data. For comparison, the genetic effects were assumed both fixed and random. The performance of several weighting methods for the stage-wise analysis are analysed by correlating the two-stage estimates with results of one-stage analysis and by calculating the mean square error (MSE) between both types of estimate. In case of random genetic effects, the genetic structure is modelled in one of three ways, either by using the numerator relationship matrix, a marker-based kinship matrix or by using crossed and nested genetic effects. It was found that stage-wise analysis results in comparable genotype main effect estimates for all weighting methods and for the assumption of random or fixed genetic effect if the model for analysis is valid. In case of choosing invalid models, e.g., if the missing data pattern is informative, both analyses are invalid and the results can differ. Informative missing data pattern can result from ignoring information either used for selecting the analysed genotypes or for selecting the test environments of genotypes, if not all genotypes are tested in all environments. While correlated information from relatives is rarely directly used for analysis of plant breeding data, it is often used implicitly by the breeder for selection decisions, e.g. by looking at the performance of a genotype and the average performance of the underlying cross. Chapter 4 proposed a model with a joint variance-covariance structure for related genotypes in analysis of diallels. This model is compared to other diallel models based on assumptions regarding the inheritance of several independent genes, i.e. on genetic models with more restrictive assumptions on the relationship between relatives. The proposed diallel model using a joint variance-covariance structure for parents and parental effects in crosses is shown to be a general model subsuming other more specialized diallel models, as these latter models can be obtained from the general model by adding restrictions on the variance-covariance structure. If no a priori information about the genetic model is available the proposed general model can outperform the more restrictive models. Using restrictive models can result in biased variance component estimates, if restrictions are not fulfilled by the data analysed. Chapter 5 evaluates, whether a subdivision of 21 triticale genotypes into heterotic pools is preferable. Subdividing genotypes into heterotic pools implies a factorial mating design between heterotic pools and a diallel mating design within each heterotic pool. For two (or more) heterotic pools the model is extended by assuming a joint variance-covariance structure for parental effects and general combing ability effects within the diallel and within the factorials. It is shown that a model with two heterotic pools has the best model fit. The variance component estimates for the general combing ability decrease within the heterotic pools and increase between heterotic pools. The results in Chapter 2 to 5 show, that an efficient and valid analysis of phenotypic plant breeding data is an essential part of the plant breeding process. The analysis can be performed in one or two stages. The used mixed models recognizing the field and mating design and the genetic structure can be used for answering questions about the genetic variance in cultivar populations under selection and of the number of heterotic pools. The proposed general diallel model using a joint variance-covariance structure between related effects can further be modified for factorials and other mating designs with related genotypes.
Optimizing the prediction of genotypic values accounting for spatial trend andpopulation structure
(2010) Müller, Bettina Ulrike; Piepho, Hans-Peter
Different effects, like the design of the field trial, agricultural practice, competition between neighboured plots, climate as well as the spatial trend, have an influence on the non-genotypic variation of the genotype. This effects influence the prediction of the genotypic value by the non-genotypic variation. The error, which results from the influence of the non-genotypic variation, can be separated from the phenotypic value by field design and statistical models. The integration of different information, like spatial trend or marker, can lead to an improved prediction of genotypic values. The present work consists of four studies from the area of plant breeding and crop science, in which the prediction of the genotypic values was optimized with inclusion of the above mentioned aspects. Goals of the work were: (1) to compare the different spatial models and to find one model, which is applicable as routine in plant breeding analysis, (2) to optimize the analysis of unreplicated trials of plant breeding experiments by improving the allocation of replicated check genotypes, (3) to improve the analysis of intercropping experiments by using spatial models and to detect the neighbour effect between the different cultivars, and (4) to optimize the calculation of the genome-wide error rate in association mapping experiments by using an approach which regards the population structure. Different spatial models and a baseline model, which reflects the randomization of the field trial, were compared in three of the four studies. In one study the models were compared on basis of different efficiency criteria with the goal to find a model, which is applicable as routine in plant breeding experiments. In the second study the different spatial models and the baseline model were compared on unreplicated trials, which are used in the early generation of the plant breeding process. Adjacent to the comparison of the models in this study different designs were compared with the goal to see if a non-systematic allocation of check genotypes is more preferable than a systematic allocation of check genotypes. In the third study these different models were tested for intercropping experiments. In this study it should be tested, if an improvement is expectable for these non randomized or restricted randomized trials by using a spatial analysis. The results of the three studies are that no spatial model could be found, which is preferable over all other spatial models. In a lot of cases the baseline model, which regards only the randomization, but no spatial trend, was better than the spatial models, also for the restricted or non-randomized intercropping trials. In all three studies the basic principle was followed to start first with the baseline model, which is based on the randomization theory, and then to extend it by spatial trend, if the model fit can be improved. In the second study the systematic and non-systematic allocation of check plots in unreplicated trials were compared to solve the question if a non-systematic allocation leads to more efficient estimates of genotypes as the systematic allocation. The non-systematic allocation of check plots led to an unbiased estimation in three of four uniformity trials. As well as in the third study an analysis was done, if the border plots of the different cultivars are influenced by the neighboured cultivar and if there are significant differences to the inner plot. The position of the cultivars, border plot or inner plot, had a significant influence of the yield. If maize was cultivated adjacent to pea, the yield of the border plot of maize was much higher than the inner plot of maize. When wheat was cultivated behind maize, there were no significant differences in the yield, if the plot was a border plot or inner plot. In addition to optimizing the field design for unreplicated trials and the extension of the models by spatial trend the marker information was integrated in a fourth study. An approach was proposed in this study, which calculates the genome wide error for association mapping experiments and accounts for the population structure. Advantages of this approach in contrast to previously published approaches are that the approach on the one hand is not too conservative and on the other hand accounts the population structure. The adherence of the genome wide error rate was tested on three datasets, which were provided by different plant breeding companies. The results of these studies, which were obtained in this thesis, show that by the different extensions, like integration of spatial trend and marker information, and modifications of the field design, an improved prediction of the genotypic values can be achieved.