Quantitative Genetic Modeling and Inference in the Presence of Nonignorable Missing Data

Abstract

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.

The genetic covariance between life cycle stages separated by metamorphosis

“…In our study, viability was the missing data process, as well as the focus of our investigations, hence viability selection was explicitly considered in our genetic analyses. For traits with low heritability, such as in our study (heritability , 0.25 for all traits), the bias in univaritate estimates of genetic variation caused by ignoring the missing data process can be relatively small [51]. However, our data and the field data of Steinsland et al [51] demonstrate that the genetic covariance associated with viability can be large.…”

“…For example, Mojica & Kelly [52] found that estimates of selection on flower size in Mimulus guttatus changed sign when the negative association between flower size and survival to maturity was included in their analyses. Similarly, Hadfield [50] and Steinsland et al [51] show that ignoring missing data when data are not missing at random can bias estimates of predicted breeding values and additive genetic variation. In our study, viability was the missing data process, as well as the focus of our investigations, hence viability selection was explicitly considered in our genetic analyses.…”

Sleep and vigilance linked to melanism in wild barn owls

“…genes passed on by the mother have different effects than when passed on by the father, Lawson et al ., ), which can also depend on offspring sex (the parent‐of‐offspring effect may differ between sons and daughters, Hager et al ., ). From an ultimate point of view, the sex‐specific association between sleep and plumage spottiness is in line with recent results showing that selection acting on this plumage trait is sex specific (Roulin et al ., ,b, ; Steinsland et al ., ). Selection on spottiness is positive in females but negative in males, implying that physiological traits such as sleep could be associated with plumage spottiness in a sex‐specific way as reported in the present study.…”

Heritability, selection, and the response to selection in the presence of phenotypic measurement error: Effects, cures, and the role of repeated measurements

“…; Charmantier and Reale ; Hadfield ) and problems arising from missing data (e.g., Steinsland et al. ; Wolak and Reid ). In contrast, although known for a long time (e.g., Price and Boag ), the effects of phenotypic measurement error on estimates of (co‐)variance components have received less attention (but see, e.g., Hoffmann ; Dohm ; Macgregor et al.…”