Genetic Exchangeability
Following the Bond and Stockman (2008) flowchart for delimiting cohesion species, we first established a “basal lineage” starting point, resulting in five lineages. Lineage name designations were based on clade labels from Hendrixson and Bond (2005b; see Figure 2): A. microunicolor and four lineages within A. unicolor (A, B1, B2, and B3). We assessed the potential for gene flow (i.e. genetic exchangeability) between sister lineages by evaluating the distributions of these lineages (Figure 1).
To help elucidate the potential for gene flow, several clustering analyses were performed. STRUCTURE v 2.3.4 (Pritchard et al., 2000) was run with several data matrices of unlinked SNPs for 1,000,000 generations and 100,000 burn-in using the admixture model featuring K values ranging from 1-10, with five replicate runs for each K value. The package pophelper (Francis, 2017) in R v.3.5.3 (R Core Team, 2019) was used to calculate the optimal K value via the Evanno method of calculating 𝚫K (Evanno, Regnaut, and Goudet 2005) as well as view the output (Figure 3a). In addition to STRUCTURE, we also used the R package adegenet (Jombart, 2008; Jombart & Ahmed, 2011) to perform a principal components analysis (dudi.pca function) and visualize the clustering of each lineage (Figure 3b). Also, an unsupervised machine learning approach, specifically a Variational Autoencoder (VAE), was implemented to provide another clustering algorithm (Figures 3c & 3d; for details see Derkarabetian et al. 2019). This approach, which relies on the inherent structure within the data for clustering individuals, alleviates the need for a priori hypotheses of species number, level of divergence, and any population parameters. VAEs, derived from Bayesian probability theory, provide relatively clear visualization for assessing cluster uncertainty due to the standard deviation around samples/clusters (Derkarabetian et al., 2019).
In cases of allopatric lineages, we considered the lineages isolated and genetic exchangeability was rejected. However, in cases of sympatric or parapatric lineages with uncertainty of whether a barrier to gene flow is present, we tentatively accept genetic exchangeability unless the clustering analyses indicate separate clusters. Because cohesion species can be rejected by either not being genetically exchangeable orecologically interchangeable, these lineages were also tested for ecological interchangeability.