Browsing by Subject "Gemischtes Modell"

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Biometrical tools for heterosis research
(2010) Schützenmeister, André; Piepho, Hans-Peter
Molecular biological technologies are frequently applied for heterosis research. Large datasets are generated, which are usually analyzed with linear models or linear mixed models. Both types of model make a number of assumptions, and it is important to ensure that the underlying theory applies for datasets at hand. Simultaneous violation of the normality and homoscedasticity assumptions in the linear model setup can produce highly misleading results of associated t- and F-tests. Linear mixed models assume multivariate normality of random effects and errors. These distributional assumptions enable (restricted) maximum likelihood based procedures for estimating variance components. Violations of these assumptions lead to results, which are unreliable and, thus, are potentially misleading. A simulation-based approach for the residual analysis of linear models is introduced, which is extended to linear mixed models. Based on simulation results, the concept of simultaneous tolerance bounds is developed, which facilitates assessing various diagnostic plots. This is exemplified by applying the approach to the residual analysis of different datasets, comparing results to those of other authors. It is shown that the approach is also beneficial, when applied to formal significance tests, which may be used for assessing model assumptions as well. This is supported by the results of a simulation study, where various alternative, non-normal distributions were used for generating data of various experimental designs of varying complexity. For linear mixed models, where studentized residuals are not pivotal quantities, as is the case for linear models, a simulation study is employed for assessing whether the nominal error rate under the null hypothesis complies with the expected nominal error rate. Furthermore, a novel step within the preprocessing pipeline of two-color cDNA microarray data is introduced. The additional step comprises spatial smoothing of microarray background intensities. It is investigated whether anisotropic correlation models need to be employed or isotropic models are sufficient. A self-versus-self dataset with superimposed sets of simulated, differentially expressed genes is used to demonstrate several beneficial features of background smoothing. In combination with background correction algorithms, which avoid negative intensities and which have already been shown to be superior, this additional step increases the power in finding differentially expressed genes, lowers the number of false positive results, and increases the accuracy of estimated fold changes.
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.
Modeling the influence of coastal vegetation on the 2004 tsunami wave impact
(2014) Laso Bayas, Juan Carlos; Cadisch, Georg
A tsunami causes several effects once it reaches inland. Infrastructure damage and casualties are two of its most severe consequences being mostly determined by seaquake intensity and offshore properties. Nevertheless, once on land, the energy of the wave is attenuated by gravity (elevation) and friction (land cover). Despite being promoted as ‘bio-shields’ against wave impact, proposed tree-belt effects lacked quantitative evidence of their performance in such extreme events, and have been criticized for creating a false sense of security. The current study analyzed some of the land uses in sites affected by the 2004 tsunami event, especially in coastal areas close to the coast of Indonesia, more specifically on the west coast of Aceh, Sumatra as well as on the Seychelles. Using transects perpendicular to the coast, the influence of coastal vegetation on the impact of the 2004 tsunami, particularly cultivated trees, was modeled. A spatial statistical model using a land cover roughness coefficient to account for the resistance offered by different land uses to the wave advance was developed. The coefficient was built using land cover maps, land use characteristics (stem diameter, height, and planting density), as well as a literature review. The spatial generalized linear mixed models used showed that while distance to coast was the dominant determinant of impact (casualties and infrastructure damage), the existing coastal vegetation in front of settlements also significantly reduced casualties, in the case of Aceh, by an average of 5%. Despite this positive effect of coastal vegetation in front of a settlement, it was also found that dense vegetation behind villages endangered human lives and increased structural damage in the same case, most likely due to debris carried by the backwash. The models initially developed in Aceh were adapted and tested for the effects that the same tsunami event caused in the Seychelles, where the intensity of the event was a tenth of that in Aceh. These new models suggested no direct effect of coastal vegetation, but they indicated that vegetation maintained dunes decreased the probability of structural damage. Additionally, using satellite imagery with higher resolution than that of the first study and/or from different years before the tsunami, corresponding land roughness coefficients were developed and tested with the existing models. The new models showed no signs of further increase of goodness of fit (AIC). Nevertheless, weather conditions at the acquisition dates as well as coverage and lack of image availability diminished the predictive power of these models. Overall, more than advocating for or against tree belts, a sustainable and effective coastal risk management should be promoted. This planning should acknowledge the location (relative to the sea) of settlements as the most important factor for future coastal arrangements. Nevertheless, it should also consider the possible direct and indirect roles of coastal vegetation, determined by its spatial arrangement as shown in the study models. Sustainability of these measures would only occur when coastal vegetation is regarded as a livelihood provider rather than just as a bio-shield. Practical examples could include, e.g. rubber plantations or home gardens in front of settlements, while leaving escape routes or grasslands and coconut plantations behind these. Therefore, the enforcement of educational programs, the setup and maintenance of effective warning systems and the adequate spatial allocation of coastal vegetation bringing tangible short and mid term benefits for local communities, as well as its adaption to local customs should be considered.