Fig 1.
Modelling quantitative trait evolution under the combined effects of ILS and introgression.
1) From a phylogenetic network with known parameters, the multispecies network coalescent model can be used to predict the expected frequency and branch lengths of each gene tree topology. 2) These gene trees contribute to trait covariances through their internal branches, and to trait variances through their total heights. The contribution of each gene tree to the overall quantities in T is weighted by its expected frequency. 3) Once the values of T are estimated, character states under Brownian motion can be simulated by drawing from a multivariate normal with a mean of 0 and variance of σ2T.
Fig 2.
Quantifying the effect of introgression on quantitative trait variation.
For ILS-only (top row) and ILS + introgression (bottom row) conditions, we show the expected variance/covariance matrix (middle-left column, variances not shown for clarity) and the average difference in quantitative trait values between each pair of species across 20,000 simulated traits (middle-right column). The expectations for the Q3 statistic are also shown (far-right column).
Fig 3.
Power analysis of the ability of Q3 to detect a signature of introgression from 15,000 simulated genes (σ2 = 1).
Each cell reports the proportion of 100 simulated datasets where Q3 was significantly different from 0 in the direction expected from the simulated history of introgression. Within each matrix, the x-axis is the time of introgression relative to speciation (larger values mean relatively more recent introgression), and the y-axis is the rate of introgression. There is one matrix for each of three times between speciation events, which determine the levels of ILS (decreasing from left to right, as the times increase). The greatest power comes in scenarios with little ILS, high rates of introgression, and recent introgression events.
Fig 4.
Ovule gene expression variation in tomatoes is consistent with inferred histories of introgression.
A) Histories of speciation and introgression for our chosen triplets in Solanum. B) Mean and standard error of Q3 across all genes in each triplet. C) Difference in the number of genes with a negative vs. positive Q3 value for both triplets. Density plots show the distribution of this difference across 10,000 bootstrapped datasets. Observed values for the two triplets relative to the bootstrap distributions are shown with arrows.
Fig 5.
Relationships between coding sequence tree topology (rows) and gene expression similarity (columns) in the low (A) and high (B) triplets. Note that for expression similarity, we did not explicitly construct trees from expression data—the tree representation is simply meant to depict observed expression distances. Only discordant trees and expression patterns are shown, but χ2 P-values (0.776 and 0.019 for panels A and B, respectively) are reported from the full 3x3 table (see S1 and S2 Tables for the full tables). The cases where both the tree topology and pattern of expression are consistent with the inferred history of introgression for that triplet are highlighted in blue. Each cell reports the observed number of genes (O) in each category, and the number expected (E) from the χ2 distribution.