Hierarchical modeling of haplotype effects based on a phylogeny

Abstract

This paper introduces a hierarchical model to estimate haplotype effects based on phylogenetic relationships between haplotypes and their association with observed phenotypes. In a population there are usually many, but not all possible, distinct haplotypes and few observations per haplotype. Further, haplotype frequencies tend to vary substantially -few haplotypes have high frequency and many haplotypes have low frequency. Such data structure challenge estimation of haplotype effects. However, haplotypes often differ only due to few mutations and leveraging these similarities can improve the estimation of haplotype effects. There is extensive literature on this topic. Here we build on these observations and develop an autoregressive model of order one that hierarchically models haplotype effects by leveraging phylogenetic relationships between the haplotypes described with a directed acyclic graph. The phylogenetic relationships can be either in a form of a tree or a network and we therefore refer to the model as the haplotype network model. The haplotype network model can be included as a component in a phenotype model to estimate associations between haplotypes and phenotypes. The key contribution of this work is that by leveraging the haplotype network structure we obtain a sparse model and by using hierarchical autoregression the flow of information between similar haplotypes is estimated from the data. We show with a simulation study that the hierarchical model can improve estimates of haplotype effects compared to an independent haplotype model, especially when there are few observations for a specific haplotype.We also compared it to a mutation model and observed comparable performance, though the haplotype model has the potential to capture background specific effects. We demonstrate the model with a case study of modeling the effect of mitochondrial haplotypes on milk yield in cattle.

Tree-based QTL mapping with expected local genetic relatedness matrices

“…IBD mapping, in turn, can be seen as a generalization of linkage mapping that uses IBD among pairs of people who are not closely related rather than only among close relatives. Our method is also closely related to haplotype mapping, and in particular approaches to haplotype mapping that estimate tree-like structures to describe relatedness among sets of haplotypes (Liu et al, 2001;Morris, 2005;Selle et al, 2021). Finally, our method adds to a tradition of methods for identifying trait-involved loci that are explicitly tree-based (Templeton et al, 1987;McPeek and Strahs, 1999;Larribe et al, 2002;Morris et al, 2002;Zöllner and Pritchard, 2005;Minichiello and Durbin, 2006;Mailund et al, 2006;Tachmazidou et al, 2007;Kimmel et al, 2008;Wu, 2008;Besenbacher et al, 2009;Zhang et al, 2012;Burkett et al, 2013;Thompson and Kubatko, 2013;Thompson et al, 2016).…”

“…Tree-based approaches to quantitative trait locus (QTL) mapping-in which a trait is tested for association with a tree or set of trees describing genetic variation in a region-have been proposed several times and shown to provide some advantages (Templeton et al, 1987;McPeek and Strahs, 1999;Larribe et al, 2002;Morris et al, 2002;Zöllner and Pritchard, 2005;Minichiello and Durbin, 2006;Mailund et al, 2006;Tachmazidou et al, 2007;Kimmel et al, 2008;Wu, 2008;Besenbacher et al, 2009;Zhang et al, 2012;Burkett et al, 2013;Thompson and Kubatko, 2013;Thompson et al, 2016), as have approaches to haplotype-based mapping that leverage awareness of tree-like relatedness patterns among sets of haplotypes (Liu et al, 2001;Morris, 2005;Selle et al, 2021). At the same time, explicitly tree-based approaches have until recently been limited by difficulties in estimating locus-level trees at scale.…”

Spatial modelling improves genetic evaluation in smallholder breeding programs

“…It uses the same key underlying linear algebra routines as standard genetic evaluation software [25,[71][72][73], and enables both full Bayesian analysis with fast and very accurate approximate algorithm [74] or even faster empirical Bayesian analysis. We have used the R-INLA package extensively for standard quantitative genetic studies [75][76][77], accounting for selection [78], spatial modelling of plant and tree trials [79] and for modelling of phenotypes on phylogeny [80]. While the R-INLA package is fast for models with a sparse structure (time-series, spatial regions or points and pedigree), it does not fare well for genomic models that have dense a structure [32,33].…”

Inferring the Allelic Series at QTL in Multiparental Populations

“…It would also still be subject to computational constraints on the number of haplotypes and, in the case of the tree-informed prior, to caveats about local phylogeny in recombinant systems. Nonetheless, it would be interesting to apply our allele-based inference approach to QTL in non-experimental populations and to compare it with emerging haplotype-based, phylogeny-informed association approaches designed for these populations (Selle et al 2020). This allelic perspective may provide new insight into the genetic architecture of QTL that is not revealed by the variant-based approaches commonly used in non-experimental populations.…”

“…This defines a prior distribution over the allelic series that is informed by a tree, p(M|T). In this way, our approach is similar to other models that include phylogenetic information; for example, by modeling distributional "changepoints" on a tree (Azim Ansari and Didelot 2016), or by using phylogenetic distance as an input for a distance-dependent CRP (Cybis et al 2018), among others (Zhang et al 2012;Thompson and Kubatko 2013;Behr et al 2020;Selle et al 2020). In particular, Azim Ansari and Didelot (2016) specify a prior distribution over the allelic series by defining the prior probability that each branch of a tree is functionally mutated with respect to a phenotype (in their case, a categorical trait).…”