On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo.

For various species, high quality sequences and complete genomes are nowadays available for many individuals. This makes data analysis challenging, as methods need not only to be accurate, but also time efficient given the tremendous amount of data to process. In this article, we introduce an efficient method to infer the evolutionary history of individuals under the multispecies coalescent model in networks (MSNC). Phylogenetic networks are an extension of phylogenetic trees that can contain reticulate nodes, which allow to model complex biological events such as horizontal gene transfer, hybridization and introgression. We present a novel way to compute the likelihood of biallelic markers sampled along genomes whose evolution involved such events. This likelihood computation is at the heart of a Bayesian network inference method called SnappNet, as it extends the Snapp method inferring evolutionary trees under the multispecies coalescent model, to networks. SnappNet is available as a package of the well-known beast 2 software. Recently, the MCMC_BiMarkers method, implemented in PhyloNet, also extended Snapp to networks. Both methods take biallelic markers as input, rely on the same model of evolution and sample networks in a Bayesian framework, though using different methods for computing priors. However, SnappNet relies on algorithms that are exponentially more time-efficient on non-trivial networks. Using simulations, we compare performances of SnappNet and MCMC_BiMarkers. We show that both methods enjoy similar abilities to recover simple networks, but SnappNet is more accurate than MCMC_BiMarkers on more complex network scenarios. Also, on complex networks, SnappNet is found to be extremely faster than MCMC_BiMarkers in terms of time required for the likelihood computation. We finally illustrate SnappNet performances on a rice data set. SnappNet infers a scenario that is consistent with previous results and provides additional understanding of rice evolution.

Training set optimization of genomic prediction by means of EthAcc.

Genomic prediction is a useful tool for plant and animal breeding programs and is starting to be used to predict human diseases as well. A shortcoming that slows down the genomic selection deployment is that the accuracy of the prediction is not known a priori. We propose EthAcc (Estimated THeoretical ACCuracy) as a method for estimating the accuracy given a training set that is genotyped and phenotyped. EthAcc is based on a causal quantitative trait loci model estimated by a genome-wide association study. This estimated causal model is crucial; therefore, we compared different methods to find the one yielding the best EthAcc. The multilocus mixed model was found to perform the best. We compared EthAcc to accuracy estimators that can be derived via a mixed marker model. We showed that EthAcc is the only approach to correctly estimate the accuracy. Moreover, in case of a structured population, in accordance with the achieved accuracy, EthAcc showed that the biggest training set is not always better than a smaller and closer training set. We then performed training set optimization with EthAcc and compared it to CDmean. EthAcc outperformed CDmean on real datasets from sugar beet, maize, and wheat. Nonetheless, its performance was mainly due to the use of an optimal but inaccessible set as a start of the optimization algorithm. EthAcc's precision and algorithm issues prevent it from reaching a good training set with a random start. Despite this drawback, we demonstrated that a substantial gain in accuracy can be obtained by performing training set optimization.

On the Accuracy of Genomic Selection.

Genomic selection is focused on prediction of breeding values of selection candidates by means of high density of markers. It relies on the assumption that all quantitative trait loci (QTLs) tend to be in strong linkage disequilibrium (LD) with at least one marker. In this context, we present theoretical results regarding the accuracy of genomic selection, i.e., the correlation between predicted and true breeding values. Typically, for individuals (so-called test individuals), breeding values are predicted by means of markers, using marker effects estimated by fitting a ridge regression model to a set of training individuals. We present a theoretical expression for the accuracy; this expression is suitable for any configurations of LD between QTLs and markers. We also introduce a new accuracy proxy that is free of the QTL parameters and easily computable; it outperforms the proxies suggested in the literature, in particular, those based on an estimated effective number of independent loci (Me). The theoretical formula, the new proxy, and existing proxies were compared for simulated data, and the results point to the validity of our approach. The calculations were also illustrated on a new perennial ryegrass set (367 individuals) genotyped for 24,957 single nucleotide polymorphisms (SNPs). In this case, most of the proxies studied yielded similar results because of the lack of markers for coverage of the entire genome (2.7 Gb).

Detecting and locating whole genome duplications on a phylogeny: a probabilistic approach.

Whole genome duplications (WGDs) followed by massive gene loss occurred in the evolutionary history of many groups. WGDs are usually inferred from the age distribution of paralogs (Ks-based methods) or from gene collinearity data (synteny). However, Ks-based methods are restricted to detect the recent WGDs due to saturation effects and the difficulty to date old duplicates, and synteny is difficult to reconstruct for distantly related species. Recently, Jiao et al. (Jiao Y, Wickett N, Ayyampalayam S, Chanderbali AS, Landherr L, Ralph PE, Tomsho LP, Hu Y, Liang H, Soltis PS, et al. 2011. Ancestral polyploidy in seed plants and angiosperms. Nature 473:97-100) introduced an empirical method that aims to detect a peak in duplication ages among nodes selected from a previous phylogenetic analysis. In this context, we present here two rigorous methods based on data from multiple gene families and on a new probabilistic model. Our model assumes that all gene lineages are instantaneously duplicated at the WGD event with a possible almost-immediate loss of some extra copies. Our reconciliation method relies on aligned molecular sequences, whereas our gene count method relies only on gene count data across species. We show, using extensive simulations, that both methods have a good detection power. Surprisingly, the gene count method enjoys no loss of power compared with the reconciliation method, despite the fact that sequence information is not used. We finally illustrate the performance of our methods on a benchmark yeast data set. Both methods are able to detect the well-known WGD in the Saccharomyces cerevisiae clade and agree on a small retention rate at the WGD, as established by synteny-based methods.