Natural selection is typically exerted at some specific life stages. If natural selection takes place before a trait can be measured, using conventional models can cause wrong inference about population parameters. When the missing data process relates to the trait of interest, a valid inference requires explicit modeling of the missing process. We propose a joint modeling approach, a shared parameter model, to account for nonrandom missing data. It consists of an animal model for the phenotypic data and a logistic model for the missing process, linked by the additive genetic effects. A Bayesian approach is taken and inference is made using integrated nested Laplace approximations. From a simulation study we find that wrongly assuming that missing data are missing at random can result in severely biased estimates of additive genetic variance. Using real data from a wild population of Swiss barn owls Tyto alba, our model indicates that the missing individuals would display large black spots; and we conclude that genes affecting this trait are already under selection before it is expressed. Our model is a tool to correctly estimate the magnitude of both natural selection and additive genetic variance. K E Y W O R D S : Animal model, missing not at random, sex-linked inheritance, shared parameter model, Tyto alba.It is emphasized in a recent review that a number of key issues in ecology and evolutionary biology can be only tackled using data collected in populations over many years (Clutton-Brock and Sheldon 2010). For instance, long-term studies in the common tern (Sterna hirundo) have identified traits that are naturally selected in an age-specific manner (e.g., Rebke et al. 2010), which can then explain patterns of population dynamics (e.g., Ezard et al. 2007). Selection is typically exerted at different intensities throughout life, and identifying the life stages when selection is maximally exerted on a given phenotype will bring essential information on its adaptive function. This is however not an easy task because gathering information at all life stages can be logistically difficult. This is a problem because failing to collect data in the life stage * These are senior authors of this work.

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 ( and ). 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.

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The long-term hydropower scheduling problem is inherently stochastic due to uncertainty in future reservoir inflow.We use Stochastic Dual Dynamic Programming (SDDP) to solve this problem. This work evaluate and compare three scenario reduction methods used to construct a multistage scenario tree which represents the underlying stochastic inflow process in the SDDP model. A case study is carried out to numerically assess the performance of the different scenario reduction methods.The performance is measured using out-of-sample simulation, simulating the solution strategies obtain with the various scenario models on an exogenously given set of inflow scenarios. Our results show that the choice of scenario reduction method impacts the solution to a hydropower operation planning problem substantially.