Neighbor-joining trees for subspecies were constructed on the basis of phenotypic distances using MATLAB scripts (sampling either all 64 embedding axes with 1 replicate or subsamples of 8 or 32 axes with 100 replicates). Neighbor joining is a simple and fast algorithm for phylogenetic reconstruction, which reconstructs relationships based on phenetic (overall) similarity (39) e.g., Euclidean phenotypic distance, as applied here. Neighbor joining does not require an a priori mechanistic model for the evolutionary process in question (e.g., evolution of butterfly wing pattern phenotype), in contrast to maximum likelihood models of DNA substitution, for example. This method is therefore suitable for this first phylogenetic study of phenomic distances calculated using deep learning on butterfly photographs. The correlation was then statistically compared between the resultant phenotypic neighbor-joining trees and genetic phylogenies reconstructed with Bayesian methods (which incorporate DNA substitution models) (27). To test the phylogenetic informativeness of the phenotypic distances against such independent data sources, sets of neighbor-joining phenotypic trees (of either all subspecies, H. erato only, or H. melpomene only) were compared against random tree topologies and phylogenies (26) reconstructed from published gene sequences (27) from gene loci (sampled from a different, smaller set of 127 butterfly individuals), which were either associated with Heliconius wing color pattern (optix, bves, kinesin, GPCR, and VanGogh) (27) or were neutral markers (mt COI-COII, SUMO, Suz12, 2654, and CAT). Pairwise distances between trees from the different sets were calculated using the Robinson-Foulds (symmetric distance) metric in the program PAUP and statistically compared using nonparametric Mann-Whitney tests in the program PAST (after Shapiro-Wilk’s tests indicated non-normal distributions). Tree space visualizations of tree similarity were produced, based on the Robinson-Foulds distance, using the tree set visualization package in the program Mesquite. Consensus networks were constructed to visualize all splits (taxon partitions) implied among sets of trees using the program SplitsTree 4.

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