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.