Joint Analysis of Binomial and Continuous Traits with a Recursive Model: A Case Study Using Mortality and Litter Size of Pigs

Abstract

This work presents a model for the joint analysis of a binomial and a Gaussian trait using a recursive parametrization that leads to a computationally efficient implementation. The model is illustrated in an analysis of mortality and litter size in two breeds of Danish pigs, Landrace and Yorkshire. Available evidence suggests that mortality of piglets increased partly as a result of successful selection for total number of piglets born. In recent years there has been a need to decrease the incidence of mortality in pig-breeding programs. We report estimates of genetic variation at the level of the logit of the probability of mortality and quantify how it is affected by the size of the litter. Several models for mortality are considered and the best fits are obtained by postulating linear and cubic relationships between the logit of the probability of mortality and litter size, for Landrace and Yorkshire, respectively. An interpretation of how the presence of genetic variation affects the probability of mortality in the population is provided and we discuss and quantify the prospects of selecting for reduced mortality, without affecting litter size.M IXED linear models (Henderson 1984) are broadly used in livestock and plant breeding and play an important role in evolutionary and theoretical quantitative genetics (Lande 1979;Cheverud 1984;Walsh 2003). The classical approach for a multiple-trait analysis is to use models posing that the nature of the correlation between response variables (phenotypes) is due to linear associations between unobservables, such as additive genetic values or nongenetic sources, like permanent or temporary environmental effects.Structural equation models represent an extension of the standard linear model to account for links (feedback and/or recursiveness) involving either the phenotypes directly or latent variables; they are well established in econometrics and sociology (Goldberger 1972;Jöreskog 1973;Duncan 1975). These models were discussed in the early genetics literature by Wright (1921) but this work has not received much attention in quantitative genetics. Xiong et al. (2004) proposed the use of structural equation models for modeling and identifying genetic networks. In a quantitative genetics context, Gianola and Sorensen (2004) studied the consequences of the existence of simultaneous and recursive relationships between phenotypes on genetic parameters and presented statistical methods for inference. An application to study the relationship between somatic cell score and milk yield in goats is in de los Campos et al. (2006). Varona et al. (2007) present a recursive model for the joint analysis of litter size and average litter weight in Danish pigs. These studies were concerned with normally distributed traits. Here the methodology is developed further for the joint analysis of a binomial and a continuous trait and it is shown that a computationally simple implementation can be arrived at by appropriate choice of the recursive specification. The method is illustrate...

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Heritable Environmental Variance Causes Nonlinear Relationships Between Traits: Application to Birth Weight and Stillbirth of Pigs

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A diallel of the mouse Collaborative Cross founders reveals strong strain-specific maternal effects on litter size

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