The Timing and Direction of Introgression Under the Multispecies Network Coalescent

Abstract

Introgression is a pervasive biological process, and many statistical methods have been developed to infer its presence from genomic data. However, many of the consequences and genomic signatures of introgression remain unexplored from a methodological standpoint. Here, we develop a model for the timing and direction of introgression based on the multispecies network coalescent, and from it suggest new approaches for testing introgression hypotheses. We suggest two new statistics, D 1 and D 2 , which can be used in conjunction with other information to test hypotheses relating to the timing and direction of introgression, respectively. D 1 may find use in evaluating cases of homoploid hybrid speciation (HHS), while D 2 provides a four-taxon test for polarizing introgression. Although analytical expectations for our statistics require a number of assumptions to be met, we show how simulations can be used to test hypotheses about introgression when these assumptions are violated. We apply the D 1 statistic to genomic data from the wild yeast Saccharomyces paradoxus-a proposed example of HHS-demonstrating its use as a test of this model. These methods provide new and powerful ways to address questions relating to the timing and direction of introgression.

Assessing biological factors affecting postspeciation introgression

“…), although these values consistently fractionally underestimated known admixture. This underestimation was largest when the direction of introgression was P2 → P3 rather than P3 → P2—as expected because P2 → P3 introgression results in genealogies with shorter internal branches (Hibbins and Hahn ), allowing less time for ABBA substitutions to accumulate. The timing of introgression has comparatively little effect in all cases (Fig.…”

“…For all trios in which we inferred significant introgression, we also determined the primary direction of introgression using the D 2 statistic (Hibbins and Hahn ). Briefly, this statistic is based on a prediction of the multispecies network coalescent that, in a rooted three‐taxon tree, the direction of introgression between one nonsister pair can affect the degree of divergence between the nonsister pair not involved in introgression.…”

“…() as proxies for lineage‐specific variation in theta or the population mutation rate. D 2 is largely robust to variation in theta between internal branches at introgressed versus nonintrogressed loci (at least up to twofold differences), but does have some sensitivity to variation in the split times when introgression is primarily P2 → P3 (Hibbins and Hahn ). Other deviations in theta, including between the ancestral population or tip branches, should not bias the statistic, as they affect introgressed and nonintrogressed loci equally.…”

“…A similar structure can be used to test the a priori expectation that gene flow is expected to be more frequent between lineages with shared versus different mating systems. Within trios that show evidence for gene flow, the prevalent direction of gene flow between different mating systems can be further assessed with additional statistics that evaluate the direction of introgression (e.g., Hibbins and Hahn ). More generally, four‐taxon tests that involve increasing evolutionary divergence between the P1/P2 and P3 lineages can be used to evaluate evidence that introgression is on average more prevalent between more closely related taxa.…”

Genome Scans for Selection and Introgression based on k-nearest Neighbor Techniques

“…Currently, the most widely applied methods are the ABBA-BABA family of methods which are based on a four-taxon system (Durand et al, 2011;Green et al, 2010;Martin et al, 2014;Pfeifer and Kapan, 2019), where the fourth taxon acts as the outgroup. Since an outgroup is not always available, several other approaches based on fewer taxa were also introduced (Geneva et al, 2015;Hahn and Hibbins, 2019;Hibbins and Hahn, 2019).…”