2.7. Phylogenetic network estimations and tests for introgression

We estimated phylogenetic networks while accounting for ILS and gene flow using two approaches to explore intraspecific relationships in Nitzschia palea. First, we estimated a phylogenetic network under maximum pseudo‐likelihood using the InferNetwork_MPL command in PhyloNet (Yu and Nakhleh ²⁰¹⁵, Wen et al. ²⁰¹⁸). We used the complete set of rooted gene trees, applied a bootstrap support threshold of 95%, ran ten independent network searches, and sequentially tested the allowance of 0 to 3 hybridization/reticulation branches. We selected the run with the highest log pseudo‐likelihood as the best estimate. We visualized PhyloNet results using Dendroscope (Huson et al. ²⁰⁰⁷). A sharp improvement in score is expected until it reaches the best value and has a slower, linear improvement after that. Second, we estimated a phylogenetic network using the NANUQ algorithm (Allman et al. ²⁰¹⁹). We used all gene trees and ran NANUQ through the MSCquartets R package (Rhodes et al. ²⁰²¹). We used a small alpha (0.01) and a large beta (0.95) for hypothesis testing following the developer's recommendations. We used the test results on the quartet counts from all gene trees to calculate a network distance matrix between taxa. We then inferred a split network from the distance matrix using the Neighbor‐Net algorithm (Huson and Bryant ²⁰⁰⁶). As a complement to the network approaches, we also performed introgression tests for the putative hybrid (TCC907) with Patterson's D‐statistic (Durand et al. ²⁰¹¹), commonly known as the ABBA‐BABA test. The ABBA‐BABA test is based on site patterns in the alignments under a null ILS model (i.e., no gene flow). Given the genome sequences of three ingroups and an outgroup population with the relationship (((P1,P2),P3),O), ABBA sites are those at which P2 and P3 share a derived allele (B), while P1 has the ancestral state (A). The BABA pattern represents sites at which P1 and P3 share the derived state. The ABBA‐BABA test approximates the proportion of the genome represented by these two discordant topologies. In the absence of any deviation from a strict bifurcating topology (i.e., no gene flow), we expect to find roughly equal proportions of ABBA and BABA site patterns in the genome. The D‐statistic test is used to quantify deviations from this proportion. We calculated D using the calcD function in the R package evobiR (Blackmon and Adams ²⁰¹⁵) and assessed the significance of D using a block jackknife approach (block‐size 1000 sites, 1000 replicates).