On estimation and identifiability issues of sex-linked inheritance with a case study of pigmentation in Swiss barn owl (Tyto alba)

Genetic evaluation using animal models or pedigree-based models generally assume only autosomal inheritance. Bayesian animal models provide a flexible framework for genetic evaluation, and we show how the model readily can accommodate situations where the trait of interest is influenced by both autosomal and sex-linked inheritance. This allows for simultaneous calculation of autosomal and sex-chromosomal additive genetic effects. Inferences were performed using integrated nested Laplace approximations (INLA), a nonsampling-based Bayesian inference methodology. We provide a detailed description of how to calculate the inverse of the X- or Z-chromosomal additive genetic relationship matrix, needed for inference. The case study of eumelanic spot diameter in a Swiss barn owl (Tyto alba) population shows that this trait is substantially influenced by variation in genes on the Z-chromosome (sigma(2)(z) = 0.2719 and sigma(2)(a) = 0.4405). Further, a simulation study for this study system shows that the animal model accounting for both autosomal and sex-chromosome-linked inheritance is identifiable, that is, the two effects can be distinguished, and provides accurate inference on the variance components.

The application of trend surface models to the analysis of time factors in Swiss cancer mortality.

To study different temporal components on cancer mortality (age, period and cohort) methods of graphic representation were applied to Swiss mortality data from 1950 to 1984. Maps using continuous slopes ("contour maps") and based on eight tones of grey according to the absolute distribution of rates were used to represent the surfaces defined by the matrix of various age-specific rates. Further, progressively more complex regression surface equations were defined, on the basis of two independent variables (age/cohort) and a dependent one (each age-specific mortality rate). General patterns of trends in cancer mortality were thus identified, permitting definition of important cohort (e.g., upwards for lung and other tobacco-related neoplasms, or downwards for stomach) or period (e.g., downwards for intestines or thyroid cancers) effects, besides the major underlying age component. For most cancer sites, even the lower order (1st to 3rd) models utilised provided excellent fitting, allowing immediate identification of the residuals (e.g., high or low mortality points) as well as estimates of first-order interactions between the three factors, although the parameters of the main effects remained still undetermined. Thus, the method should be essentially used as summary guide to illustrate and understand the general patterns of age, period and cohort effects in (cancer) mortality, although they cannot conceptually solve the inherent problem of identifiability of the three components.