Deep learning on butterfly phenotypes tests evolution's oldest mathematical model

Abstract: Traditional anatomical analyses captured only a fraction of real phenomic information. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of $\textit{Heliconius erato}$ and $\textit{Heliconius melpomene}$. Euclidean phenotypic distances, calculated using a deep convolutional triplet network, demonstrate significant convergence between interspecies co-mimics. This quantitatively validates a key prediction of M\"ullerian mimicry theory, evolutionary biology's oldest mathematical model. Phenotypic neighbor-joining trees are significantly correlated with wing pattern gene phylogenies, demonstrating objective, phylogenetically informative phenome capture. Comparative analyses indicate frequency-dependent, mutual convergence with coevolutionary exchange of wing pattern features. Therefore, phenotypic analysis supports reciprocal coevolution, predicted by classical mimicry theory but since disputed, and reveals mutual convergence as an intrinsic generator for the surprising diversity of M\"ullerian mimicry. This demonstrates that deep learning can generate phenomic spatial embeddings which enable quantitative tests of evolutionary hypotheses previously only testable subjectively.