Searching for Recursive Causal Structures in Multivariate Quantitative Genetics Mixed Models

Abstract

Biology is characterized by complex interactions between phenotypes, such as recursive and simultaneous relationships between substrates and enzymes in biochemical systems. Structural equation models (SEMs) can be used to study such relationships in multivariate analyses, e.g., with multiple traits in a quantitative genetics context. Nonetheless, the number of different recursive causal structures that can be used for fitting a SEM to multivariate data can be huge, even when only a few traits are considered. In recent applications of SEMs in mixed-model quantitative genetics settings, causal structures were preselected on the basis of prior biological knowledge alone. Therefore, the wide range of possible causal structures has not been properly explored. Alternatively, causal structure spaces can be explored using algorithms that, using data-driven evidence, can search for structures that are compatible with the joint distribution of the variables under study. However, the search cannot be performed directly on the joint distribution of the phenotypes as it is possibly confounded by genetic covariance among traits. In this article we propose to search for recursive causal structures among phenotypes using the inductive causation (IC) algorithm after adjusting the data for genetic effects. A standard multiple-trait model is fitted using Bayesian methods to obtain a posterior covariance matrix of phenotypes conditional to unobservable additive genetic effects, which is then used as input for the IC algorithm. As an illustrative example, the proposed methodology was applied to simulated data related to multiple traits measured on a set of inbred lines.

Is Structural Equation Modeling Advantageous for the Genetic Improvement of Multiple Traits?

“…In most applications that followed Gianola and Sorensen (2004), causal structures among traits were assumed known on the basis of prior knowledge on how traits are biologically associated or according to temporal information. In the framework of these applications, the choice of causal structures could be aided by algorithms that explore spaces of acyclic graphs (Pearl 2000;Spirtes et al 2000;Valente et al 2010) driven by data.…”

“…where L is a t · t matrix filled with zeros, except for specific off-diagonal entries according to a causal structure (Valente et al 2010). These nonnull entries contain parameters called structural coefficients that represent the magnitude of each linear causal relationship between traits.…”

“…The likelihood equivalence between MTMs and SEMs was addressed by Varona et al (2007). As an attempt to tackle the problem of causal structure selection, Valente et al (2010) proposed an approach that adapted the inductive causation (IC) algorithm (Verma and Pearl 1990;Pearl 2000) to mixed-models scenarios, allowing searching for recursive causal structures in the presence of confounding resulting from additive genetic correlations between traits. The development and application of such methodologies are reviewed in Wu et al (2010) and Rosa et al (2011).…”

“…While these articles focus on inferences of structural coefficients and their causal interpretations, fitting a SEM and converting its genetic parameters to MTM parameters negates the advantages of using a causal model as a SEM for quantitative genetic analysis. Consequently, the application of the SEM loses its appeal, especially as this approach introduces additional complexities such as causal structure selection (Valente et al 2010) and parameter identifiability issues .…”

Desenvolvimento de modelos de causalidade com informações de QTLs para estudo do relacionamento de caracteres fenotípicos relativos à absorção de fósforo em milho

“…No melhoramento animal, os MEEs têm sido empregados para a inferência de redes de causalidade entre fenótipos relacionados à produção na ausência de dados genotípicos (VALENTE et al, 2010(VALENTE et al, , 2011MATURANA et al, 2009;BOWMAN et al, 2014). Em plantas, Mi et al (2010aMi et al ( , 2010b …”