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In this thesis we describe the results of a number of quantitative techniques that were used to understand the genetics of yield in pepper as an example of complex trait measured in a number of environments. Main objectives were; i) to propose a number of mixed models to detect QTLs for multiple traits and multiple environments, ii) to extend the multi-trait QTL models to a multi-trait genomic prediction model, iii) to study how well the complex trait yield can be indirectly predicted from its component traits, and iv) to understand the ‘causal’ relationships between the target trait yield and its component traits. The thesis is part of an EU-FP7 project “ S mart tools for P rediction and I mprovements of C rop Y ield” (SPICY- http://www.spicyweb.eu/). This project generated phenotypic data from four environments using 149 individuals from the sixth generation of recombinant inbred lines obtained from intraspecific cross between large – fruited inbred pepper cultivar ‘Yolo Wonder’ (YW) and the hot pepper cultivar ‘Criollo de Morelos 334’ (CM 334). A total of 16 physiological traits were evaluated across the four trials and various types of genetic parameters were estimated. In a first analysis, the traits were univariately analyzed using linear mixed model. Trait heritabilities were generally large (ranging between 0.43 – 0.96 with an average of 0.86) and mostly comparable across trials while many of the traits displayed heterosis and transgression. The same QTLs were detected across the four trials, though QTL magnitude differed for many of the traits. We also found that some QTLs affected more than one trait, suggesting QTL pleiotropy (a QTL region affecting more than one trait). We discussed our results in the light of previously reported QTLs for these and similar traits in pepper. We addressed the presence of genotype-by-environment interaction (GEI) in yield and the other traits through a multi-environment (ME) mixed model methodology with terms for QTL-by-environment interaction (QEI). We opined that yield would benefit from joint analysis with other traits and so deployed two other mixed model based multi-response QTL approaches: a multi-trait approach (MT) and a multi-trait multi-environment approach (MTME). For yield as well as the other traits, MTME was superior to ME and MT in the number of QTLs, the explained variance and accuracy of predictions. Many of the detected QTLs were pleiotropic and showed quantitative QEI. The results confirmed the feasibility and strengths of novel mixed model QTL methodology to study the architecture of complex traits. The QTL methods considered thus far are not well suited for prediction purposes as only a limited set of QTL-related markers are used. Since the main interest of this research includes improvement of yield prediction, we explored both single-trait and multi-trait versions of genomic prediction (GP) models as alternatives to the QTL-based prediction (QP) models. This was termed direct prediction. The methods differed in their predictive accuracies with GP methods outperforming QP methods in both single and multi-traits situations. We borrowed ideas from crop growth model (CGM) to dissect complex trait yield into a number of its component traits. Here, we integrated QTL/genomic prediction and CGM approaches and showed that the target trait yield can be predicted via its component traits together with environmental covariables. This was termed indirect prediction. The CGM approach seemed to work well at first sight, but this is especially due to the fact that yield appeared to be strongly driven by just one of its components, the partitioning to fruit. An alternative representation of the biological knowledge of a complex target trait such as yield is provided by network type models. We constructed both conditional and unconditional networks across the four environments to understand the ‘causal’ relationships between target trait yield and its component traits. The final networks for each environment from both conditional and unconditional methods were used in a structural equation model to assess the causal relationships. Conditioning QTL mapping on network structure improved detection of refined genetic architecture by distinguishing between QTL with direct and indirect effects, thereby removing non-significant effects found in the unconditional network and resolving QTL pleiotropy. Similar to the CGM topology, yield was established to be downstream to its component traits, indicating that yield can be studied and predicted from its component traits. Thus, the genetic improvements of yield would benefit from improvements on the component traits. Finally, complex trait prediction can be enhanced by a full integration of the methods described in the different chapters. Recent research efforts have been channelled to incorporating both multivariate whole genome prediction models and crop growth models. Further research is required, but we hope that the present thesis presents useful steps towards better prediction models for complex traits exhibiting genotype by environment interaction.

Background Measurement error in exposure variables is an important issue in epidemiological studies that relate exposures to health outcomes. Such studies, however, usually pay limited attention to the quantitative effects of exposure measurement error on estimated exposure-outcome associations. Therefore, the estimators for exposure-outcome associations are prone to bias. Existing methods to adjust for the bias in the associations require a validation study with multiple replicates of a reference measurement. Validation studies with multiple replicates are quite costly and therefore, in some cases only a single–replicate validation study is conducted besides the main study. For a study that does not include an internal validation study, the challenge in dealing with exposure measurement error is even bigger. The challenge is how to use external data from other similar validation studies to adjust for the bias in the exposure-outcome association. In accelerometry research, various accelerometer models have currently been developed. However, some of these new accelerometer models have not been properly validated in field situations. Despite the widely recognized measurement error in the accelerometer, some accelerometers have been used to validate other instruments, such as physical activity questionnaires, in measuring physical activity. Consequently, if an instrument is validated against the accelerometer, and the accelerometer itself has considerable measurement error, the observed validity in the instrument being validated will misrepresent the true validity. Methodology In this thesis, we adapted regression calibration to adjust for exposure measurement error for a single-replicate validation study with zero-inflated reference measurements and assessed the adequacy of the adapted method in a simulation study. For the case where there is no internal validation study, we showed how to combine external data on validity for self-report instruments with the observed questionnaire data to adjust for the bias in the associations caused by measurement error in correlated exposures. In the last part, we applied a measurement error model to assess the measurement error in physical activity as measured by an accelerometer in free-living individuals in a recently concluded validation study. Results The performance of the proposed two-part model was sensitive to the form of continuous independent variables and was minimally influenced by the correlation between the probability of a non-zero response and the actual non-zero response values. Reducing the number of covariates in the model seemed beneficial, but was not critical in large-sample studies. We showed that if the confounder is strongly linked with the outcome, measurement error in the confounder can be more influential than measurement error in the exposure in causing the bias in the exposure-outcome association, and that the bias can be in any direction. We further showed that when accelerometers are used to monitor the level of physical activity in free-living individuals, the mean level of physical activity would be underestimated, the associations between physical activity and health outcomes would be biased, and there would be loss of statistical power to detect associations. Conclusion The following remarks were made from the work in this thesis. First, when only a single-replicate validation study with zero-inflated reference measurements is available, a correctly specified regression calibration can be used to adjust for the bias in the exposure-outcome associations. The performance of the proposed calibration model is influenced more by the assumption made on the form of the continuous covariates than the form of the response distribution. Second, in the absence of an internal validation study, carefully extracted validation data that is transportable to the main study can be used to adjust for the bias in the associations. The proposed method is also useful in conducting sensitivity analyses on the effect of measurement errors. Lastly, when “reference” instruments are themselves marred by substantial bias, the effect of measurement error in an instrument being validated can be seriously underestimated.